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KONINKLIJKE AKADEMIE

VAN WETENSCHAPPEN
-- TE AMSTERDAM -:-

peOckE DINGS OF THE
SE CRON OF SCIENCES

VOLUME XVII

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JOHANNES MULLER :—: AMSTERDAM
JUNE 1915

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KONINKLIJKE AKADEMIE
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-- TE AMSTERDAM -:-

ER@ChReOUINGS OF THE
SECBION OF SCIENCES

VOLUME XVII
(5) PART — ))

JOHANNES MULLER :—: AMSTERDAM
: DECEMBER 1914: :

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CONTENTS.

ABEL’s polynomia (On Hermrre’s and). 192.
ABSORPTION LINES D, and Ds, (On the structure of the). 720.
ATR-BLADDER (The physiology of the) of fishes. 1088.
ALBUMINOUs FLUIDS (The identification of traces of bilirubin in). 807.
ALKALIES (The coloration of some derivatives of Picrylmethylamide with). 647.
aLLorropy (The) of cadmium. IT. 54, II. 122. [V. 688. V. 1050.
— of zine. II. 59. ILL. 641.
— of copper. II. 60.
— of antimony. I. 645.
— of lead. 1. 822. Note. 1055.
— of potassium. I. 1115.
— of bismuth. Il. 1236.
— (The application of the theory of) to electromotive equilibria. IT. 37, IIT. 680.
— (The metastability of metals in consequence of) and its significance for Chemistry,
Phyics and Technics. 200. III. 926. LV. 1238.
— (The metastable continuation of the mixed crystal series of pseudo-components
in connection of the phenomenon). II. 672.
ALMOND (Gummosis in the fruit of the) and the Peachalmond as a process of normal
life. 810.
amipEs of gz-oxyacids (Action of sodium-hypochlorite on). 1163.
ammonra (On the interaction of) and methylamine on 2.3.4-trinitrodimethylaniline.
1034.
ammonta-water (The system), 182.
AMORPHOUS CARBON (The decoloration of fuchsin-solutions by). 1322.
Anatomy. P. Réraic and C. U. Arrins Kappers: “Further contributions to our
knowledge of the brain of Myxine glutinosa”. 2.
— ©. Winker: “A case of occlusion of the arteria cerebelli posterior inferior”. 914.
— J. Borke: “On the termination of the efferent nerves in plain muscle-cells,
and its bearing on the sympathetic (accessory) innervation of the striated muscle-
fibre”. 982.

— J. Borke: “On the mode of attachment of the muscular fibre to its tendonfibres
in the striated muscles of the vertebrates’. 989.

— H. A. VERMEULEN: “The vagus area in Camelidae”. 1119.
ANOMALIES (On SBELIGER’s hypothesis ubout the) in the motion of the inner planets, 23.
ANTIBODIES (On the formation of) after injection of sensitized antigens. Il. 81S,
89
Proceedings Royal Acad, Amsterdam, Vol, XVII,

ap CONTENTS.

\NTIGENS (On the formation of antibodies after injection of sensitized). II. 318.

antimony (The allotropy of). [. 645.

APOPHYLLITE (On the real symmetry of cordierite and). 480.

ARIENS KAPPERS (c. U.). v. Kappers (C. U. ARrENs).

ARSENIC TRISULPHIDE soLs (The connection between the limit value and the concen-
tration of). 1158.

ARSENIOUS OXIDE (Compounds of). I. 1111.

ARTERIA cerebelli posterior inferior (A case of occlusion of the). 914.

Astronomy. J. Wouter Jr.: “On Seeiiaer’s hypothesis about the anomalies in the
motion of the inner planets”. 23.

— W. ve Srrrer: “Remarks on Mr. WotLtyEr’s paper concerning SRELIGER’s
hypothesis”. 33.

— W. ve Sitrer: “The figure of the planet Jupiter”. 1047.

— W. vr Sirrer: “On the mean radius of the earth, the intensity of gravity and
the moon’s parallax”. 1291.

— W. ve Srrrer: “On isostasy, the moments of inertia and the compression of
the earth”. 1295.

— VW. pe Srrver: ‘The motions of the lunar perigee and node and the figure of
the moon”. 1309.

ATEN (A. H. Ww.) and A. Smivs. The application of the theory of allotropy to electro-
motive equilibria. If. 37. III. 680.

ATLANTIC OCEAN (On the relation between departures from the normal in the strength
of the trade-winds of the) and those in the waterlevel and temperature in the
Northern Kuropean seas. 1147.

atomic Forces (The caleulation of the molecular dimensions from the supposition of
the electric nature of the quasi-elastic). 877.

BAA T (W. c. DB) and F,A, H. Scurernemakers. The system : copper sulphate, copper
chlorid, potassium sulphate, potassium chlorid and water at 30° C. 533.

— On the quaternary system KCl—CuCl,—BaClo—H,O. 781.
— Compounds of the arsenious oxide. I. 1111.

BACKER (H. J.) and A. P. N. Francurmont. The coloration of some derivatives of
picrylmethylamide with alkalies. 647.

— z-Sulpho-propionie acid and its resolution into optically active isomerides. 653.

BAKHUYZEN (H.G. VAN DE SANDE). Comparison of the Dutch platinum-
iridium Metre N°. 27 with the international Metre MM as derived from the
measurements by the Duth Metre Commission in 1879 and 1880, and a prelimi-
nary determination of the length of the measaring-bar of the French base
apparatus in international metres. 311.

~- N. Witpeporr and J. W. Dteeertnk: “Comparison of the measuring bar
used in the base measurement at Stroe with the Dutch Metre N® 27. 300.

BASE MEASUREMENT (Comparison of the measuring bar used in the) at Stroe with the
Dutch Metre No. 27. 300.

BEEGER (N. G W. H.). On Hermrre’s and ABEL’s polynomia, 192.

BENZENE DERTVATIVES (The replacement of substituents in). 1027,

COP ND ky) Nat Ss. Lent

BENZENES (The nitration of the mixed dihalogen), 846.

BEIJERINCK (mM. w.). Gummosis in the fruit of the Almond and the Peachalmond
as a process of normal life. 810.

BILIRUBIN (The identification of traces of) in albuminous fluids. 807.

BINARY MIXTURES (Isothermals of monatomic substances and their). XVI. 275.
— (Isothermals of di-atomic substances and their). XV. 950. XVI. 959.
BINARY SYSTEM (On unmixing in a) for which the three-phase pressure is greater than
the sum of the vapour tensions of the two components, 834.
BismutH (The allotropy of). II. 1236.
BOEKE (J.). On the termination of the efferent nerves in plain muscle-cells and its
bearing on the sympathetic (accessory) innervation-of the striated muscle-fibre. 982.
— On the mode of attachment of the muscular fibre to its tendonfibres in the
striated muscles of the vertebrates. 939.
— presents a paper of Dr. A. B. Droocierver Forruyn: “The decoloration of
fuchsin-solutions by amorphous carbon”. 1322.
BOER (s. DE). On the heart-rhythm. 1075 IL. 1135.
BOESEKEN (J.). On catalyse. 546.
— and W. D. Coney. The reduction of aromatic ketones. II!. Contribution to the
knowledge of the photochemical phenomena. 849.
BOILING PoINTs (The influence of the hydration and of the deviations from the ideal
gas-laws in aqueous solutions of salts on the solidifying and the). 1036,
BOIs (H. DU). Modern electromagnets, especially for surgical and metalJurgic
practice. 468.
— The universality of the Zpeman-effect with respect to the Srark-ellect in canal-
rays. 873.
BOKHORST (s. c.) and A. Smits. On the vapour pressure lines in the system phos-
phorus. Il. 678. III. 962.
— Further particulars concerning the system phosphorus. 973.
BOLK (4.) presents a paper of Dr. P. Rorate and Dr. C. U. Ariens Kapprrs:
“Further contributions to our knowledge of the brain of Myxine glutinosa”. 2.
— presents a paper of Dr. H. A. Vermeunen: “The vagus area in Camelidae”. 1119,
BOSCH (J. C, VAN DEN) and Erns? Conen. The allotropy of antimony, I. 645.
Botany. Miss Lucie C. Dover: “Euergy transformations during the germination of
wheat-grains’’. 62.
— M. W. Betertnck: “Gummosis in the fruit of the Almond and the Peachal-
mond as a process of normal life”. 810,
— C. E. B. Bremexame: “The mutual iufluence of phototropic and geotropic
reactions in plants”. 1278.
BratN of Myxine glutinosa (Further contributions to our knowledge of the). 2.
uravats (The theoty of) (on errors in space) for polydimensional space with
applications to correlation (Continuation). 150.
BREMEKAMP (c. E. B.). On the mutual influence of phototropic and geotropic
reactions in plants. 1278,

89*

IV CONTENTS.

BROUWER (u. A.). On the granitie area of Rokan (Middle-Sumatra) and on contact

phenomena in the surrounding schists. 1190.

BRUTIN (G, DB). A erystallized compound of isoprene with sulphur dioxide. 585.

— and Ernst Couey. The metastability of the metals in consequence of allotropy,
and its significance for Chemistry, Physies and Technics. III. 926.

BiicHNER (x. u.) and L. K. Wotrr. On the behaviour of gels towards liquids and
the vapours thereof. Il. 92.

capmtum (The allotropy of). IL, 54. ILL. 122. IV. 638. V. 1050.

CAMELIDAR (The vagus area in). 1119.

cANAL-RAYS (The universality of the ZeeMAN-ellect with respect to the Srark-effect
in). 873.

CAPILLARY PREssURE (On the measurement of the) in a soap-bubble. 946,

CAPILLARITY (Measurements on the) of liquid hydrogen. 528.

caTALYSE (On). 546.

CHEMICAL constanr (The) and the application of the quantumtheory by the method
of the natural vibrations to the equation of state of an ideal monatomic gas. 20.

Chemistry. A. Smivs and A. H. W. Aven: “The application of the theory of allotropy
to electromotive equilibria”. IL. 37. ILI. 680.

— E. Coney and W. D. Hetperman: “The allotropy of cadmium, IL. 54, IIT. 122.
IV. 638. V. 1050.

— FE. Commn and W. D. Hetprerman: “The allotropy of zine.” IT. 59. IIL. 641.

— E. Conen and W. D. Herperman: “The allotropy of copper”. II. 60.

— F. A. H. Scureremakers: “Equilibria in ternary systems’, XV, 70. XV1. 169.
XVIT. 767. XVIII. 1260.

— L. k. Worrr and EK. H. Biicuner: “On the behaviour of gels towards liquids,
and the vapours thereof”. IL. 92.

— A. Smrrs and 8. Postma: “The system ammonia-water’’. 182.

— Ernst Conen: “The metastability of the metals in consequence of allotropy and
its significance for Chemistry, Physics and Technics’. 200.

— F. M. Janepr and Ant. Sirmex: “Studies in the field of Silicate-chemistry”.
I}. 239. TIT. 251.

— I. M. Jarcrr: “The temperature-coefticients of the free surface-energy of liquids
at temperatures from —80° to 1650° C. I. 329. F. M. Jazerer and M. Surv,
IT. 365. ILL. 386. F. M. Jananr and J. Kany, IV, 395. F. M. Janorr. V. 405.
VI. 416. VII. 555. VIII. 571.

— I. A. H. Scaremyemakers and Miss W. C. pg Baar: “The system: copper
sulphate, copper chlorid, potassium sulphate, potassium chlorid and water at
30° C.” 533.

— J. Borsrxen: “On catalyse”. 546.

— G. pe Bruin: “A erystallized compound of isoprene with sulphur dioxide”, 585,

— H. R, Kruyt: “Current potentials of electrolyte solutions”. 615.

— H. R. Kruyt: “Electric charge and limit value of colloids”. 623.

— Erxst Coney and J, C van pen Boscu: “The allotropy of antimony”. I, 645,

CONTENTS. v

Chemistry. A. P. N. Francurmontr and H. J. Backer: “The coloration of some deri-
vatives of Picrylmethylamide with alkalies”. 647.

— A. P.N. Francurmontr and H. J. Backrr: “2 Sulpho-propionic acid and its
resolution into optically active isomerides”. 653.

— A. Smits: “The metastable continuation of the mixed crystal series of pseudo-
components in connection with the phenomenon allotropy”. [L. 672.

— A. Smrrs and 8. C. Bokuorsr: “On the vapour pressure lines of the system
phosphorus”. If. 678.

— F, EH. C. Scugrrer;: “On gas equilibria and a test of Prof. v. p. Waats Jr.s
formula”, I, 695, Lf. 1011.

— W. Rernpers: “Equilibria in the system Pb-S-O, the roasting reaction
process”. 703.

— F. A. H. Sctretnemakers and Miss W. C. pe Baar: “On the quaternary
system KCl-CuClo-BaCl2-H.0”. 781

— Ernst Conen and W, D, Heiperman: “The allotropy of lead’, 822. Note. 1055.

— A. F. Houtemaw: “The nitration of the mixed dihalogenbenzenes”. $46.

— J. Borsexen and W. D, Conen: “The reduction of aromatic ketones. III, Contri-
bution to the knowledge of the photo-chemical phenomena”. 849.

— Ernst Couen and G. ve Bruin; “The metastability of the metals in conse-
quence of allotropy and its significance for Chemistry, Physics and Technics”.
Ill. 926.

— A Smits and 8S. ©. Bokuorst: “On the vapour pressure lines of the system
phosphorus”. If. 678. I[f. 962.

— A. Smits and 8, C, Bokuorst: “Further particulars concerning the system
phosphorus”. 973.

— A. F. Hotieman: “The replacement of substituents in benzene derivatives’. 1027.

— P. van Romburcu and Miss D. W. Wensink: ‘On the interaction of ammonia
and methylamine on 2.3,4.-trinitrodimethylaniline”. 1034.

— C. H. Sturrer: “The influence of the hydration and of the deviations from the
ideal gas-laws in aqueous solutions of salts on the solidifying and the boiling
points”. 1036.

— Miss Apa Prins: ‘On critical end-points and the system ethanenaphtalene”’. 1095.

— F. A. H. Scursinemakers and Miss W. C. pt Baat: “Compounds of the
arsenious oxyde”. L111.

— Ernst Conen and 8. Wourr: “The allotropy of potassium”. I. 1115.

— H. R. Kruyr and Jac. van per Spex: ‘The connection between the limit
value and the concentration of arsenic trisulphide sols”, 1158.

— R. A. Weerman: “Action of sodium hypochlorite on amides of z-oxyacids”’. 1163.

— FE. M. Jarcer: “Researches on Pasteur’s principle of the connection between
molecular and physical dissymmetry”. I. 1217.

— Ernst Conen: “The allotropy of bismuth”. [I. 1236.

— Ernsr Couen and W. D. HELpermMan: “The metastability of the metals in
consequence of allotropy and its significance for Chemistry, Physics and Tech-
nics”, IV, 1238.

VI CONTENTS.

Chemistry. A. W. k. pp Jone: “Action of sunlight on the cinnamie acids”. 1274.
CINNAMIC aciDs (Action of sunlight on the). 1274.
crncLes (Systems of) determined by a pencil of conics. 1107,
COUEN (ERNST). The metastability of the metals in consequence of allotropy, and
its significance for Chemistry, Physics and Technics, II. 200.
— presents a paper of Dr. H. R. Kruyr: “Current potentials of electrolyte
solutions”. 615.
— presents a paper of Dr. H. R. Kruyt: “Electric charge and limit value of
colloids”. 623,
— presents a paper of Dr. H. R, Kruyr and Jac. vAN per Spek: “The connection
between the limit value and the concentration of arsenic trisulphide sols”. 1158.
— The allotropy of bismuth. IL. 1236.
— and J. C. van pen Boscu. The allotropy of antimony. I. 645.
— and G. pe Bruin. The metastability of the metals in consequence of allotropy
and its significance for Chemistry, Physics and Technics. III. 926.
— and W. D. Hexperman. The allotropy of Cadmium. IL. 54, ILL. 122. LV. 638.
V. 1050.
— The allotropy of zine. If. 59. ILI. 641.
— ‘The allotropy of copper. IL. 60.
— The allotropy of lead. I. 822. Note 1055.
— The metastability of the metals in consequence of allotropy and its significance
for Chemistry, Physics and Technics, IV. 1238.
— and S. Wotrr. The allotropy of potassium. L. 1115.
COMUEN (w. D.) and J. Borsnxen. The reduction of aromatic ketones. [II. Contri-
bution to the knowledge of the photochemical phenomena. 849,
coLLorps (Electrie charge and limit value of). 623.
coLORATION (The) of some derivatives of Picrylmethylamide with alkalies. 647.
coLtoyurs (On IresNeL’s coefficient for light of different). Ist part. 445.
compound (A crystallized) of isoprene with sulphur dioxide. 585.
COMPOUNDS of arsenious oxide. I. L111.
CONCENTRATION (The connection between the limit value and the) of arsenic trisulphide
sols. 1158. :
CONGRUENCE (A bilinear) of rational twisted quinties. 1250.
CONGRUENCES (Some particular bilinear) of twisted cubics. 1256.
conics (Systems of circles determined by a pencil of). 1107.
CONTACT=PHENOMENA (On the granitic area of Rokan (Middle Sumatra) and on) in
the surrounding schists. 1190.
coprer (The allotropy of). II. 60.
— (Measurements on the specific heat of lead between 14° and 80° K. and of)
between 15° and 22° K. 894.
COPPER SULPHATE, Copper chlorid (The system :), potassium sulphate, potassium chlorid
and water at 30°. 533.

CORDIERTTE and Apophyllite (On the real symmetry of). 430,

Gon Tren Ts. VIl

CORRELATION (The theory of Bravats (on errors in space) for polydimensional space,
with applications to) (Continuation). 150.

CORRESPONDING sTATEs (Contribution to the theory of), 840.

CRITICAL POINT (Vapour pressures of oxygen and) of oxygen and nitrogen. 950.

CRITICAL QUANTITIES (A new relation between the) and on the unity of all substances
in their thermic behaviour. 451.

— (Some remarks on the values of the) in case of association. 598.

CROMMELIN (ec. 4.) Isothermals of monatomic substances and their binary mix-
tures. XVI. 275.

— Isothermals of di-atomic substances and their binary mixtures. XVI, Vapour
pressures of nitrogen between the critical point and the boiling point. 959.
— E. Marutas and H. Kameruineu Oxnes. The rectilinear diameter of nitrogen, 953.

CRYSTAL sERIFS (The metastable continuation of the mixed) of pseudo-components in
connection with the phenomenon allotropy. LI. 672.

crysTaLs (On a new phenomenon accompanying the diffraction of RONTGEN rays in
birefringent). 1204.

cue (The different ways of floating of an homogeneous). 224.

cusres (Some particular bilinear congruences of twisted). 1256.

curves (Characteristic numbers for nets of algebraic). 935.

— (Characteristic numbers for a triply infinite system of algebraic plane). 1055,

DECOLORATION (The) of fuchsin-solutions by amorphous carbon. 1322.

DEEP reflexes (Exaggeration of). 885.

pensity (On the manner in which the susceptibility of paramagnetic substances depends
on the). 110.

— (Accidental deviations of) and opalescence at the critical point of a single
substance. 793.

DIAMETER (The rectilinear) of nitrogen. 953.

DIEPERINK (J. G.), N. Winpesorr and H. G. vaN DE SanpE Bakuuyzen. Com-
parison of the measuring bar used in the base measurement at Stroe with the
Dutch Metre N°. 27. 300.

DIFFRACTION (On a new phenomenon accompanying the) of Rontgen rays in bire-
fringent crystals. 1204.

DIFFUSYON COEFFICIENT (The) of gases and the viscosity of gas-mixtures. 1068.

DISCONTINUITIES (On apparent thermodynamic) in connection with the value of the
quantity 2 for infinitely large volume. 605.

DISSYMMETRY (Researches on PastTEUR’s principle of the connection between molecular
and physical). I, 1217.

DORSMAN (c.), H. KameruincH Onnes and G. Hoxsr. Isothermals of di-atomie
substances and their binary mixtures. XV. Vapour pressures of oxygen and critica!
point of oxygen and nitrogen, 950.

DOYER (LUCIE c.). Energy transformations during the germination of wheat-grains. 62.

DROOGLEEVER FORTUYN (a. B.). v. Fortuyn (A, B. DrooGieever).

DROSTE (J.). On the field of a single centre in Ernsrein’s theory of gravi-
tation. 998,

VIII CONTENTS.

varru (The mean radius of the), the intensity of gravity and the moon’s parallax. 1291.
— (On isostasy, the moments of inertia and the compression of the). 1295.

PHRENFeEST (P.) and H. KameRLINGH OnNes. Simplified deduction of the formula
from the theory of combinations which PLaNck uses as the basis of his radiation-
theory. 870.

— On interference phenomena to be expected when RONTGEN rays pass through a
di-atomie gas. 1184.
— On the kinetic interpretation of the osmotic pressure. 1241.

EWRENPEST (t.)—AvaNaSsJEWA, Contribution to the theory of corresponding
states. 840.

EINSTEIN’s theory of gravitation (On the field of a single centre in). 998.

EINTHOVEN (On the theory of the string-galvanometer of). 784.

ELASTIC DEFORMATION (On the lowering of the freezing point in consequence
of an). 732.

ELECTRIC CHARGE and limit value of colloids, 623,

ELECTRODES (The effect of magnetisation of the) on the electromotive force. 745.

ELECTROLYTE SOLUTIONS (Current potentials of) 615.

ELECTROMAGNETS (Modern), especially for surgical and metallurgic practice. 468.

ELECTROMETER (A new) specially arranged for radio-active investigations. 659.

ELECTROMOTIVE FORCE (‘Lhe etlect of magnetisation of the electrodes on the). 745.

ELIAS (G, J.). On the structure of the absorption lines D,; and Dy. 720.

— On the lowering of the freezing point in consequence of an elastic deforma-
tion, 732.
— The etlect of magnetisation of the electrodes on the electromotive force. 745.

END-POINTS (On critical) and the system ethane-naphtalene. 1095,

ENERGY- SURFACE (Lhe temperature-coeflicients of the free) of liquids at temperatures
from —80° C, to 1650° C. 1. 329. If. 365. IIL. 386. LV. 395. V. 405. VI. 416.
WUE Gibias MANE. by7pl-

ENERGY-TRANSFORMATIONS during the germination of wheat-grains. 62.

ENTROPY CONSTANY (Theoretical determination of the) of gases and liquids. 1167,

EQUATION OF sTaTE (The chemical constant and the application of the quantum theory
by the method of the natural vibrations to the) of an ideal monatomic gas. 20.

EQUILIBRIA (The application of the theory of allotropy to electromotive). Il. 37. III. 680.

— in the system Pb—SO, the roasting reaction process. 703.
-- in ternary systems. XV. 70. XVI. 169. XVII. 767. XVIII. 1260.

ERRATUM. 944. L073. 1202.

ERRORS IN sPACcE (The theory of Bravats, on) for polydimensional space with appli-
cations to correlation. (Continuation). 150.

FTHANE-naphtalene (On critical end-points and the system). 1095.

EUROPEAN SEAS (On the relation between departures from the normal in the strength
of the trade-winds in the Atlantic Ocean and those in the waterlevel and tem-
perature in the Northern), 1147.

BYKMAN (c,) presents a paper of Dr. L. K, Wourr: “On the formation of antibodies
after injection of sensitized antigens”. IL, 318,

CRO MN es ONT 8, IX

FISHES (The physiology of the air-bladder of). 1088.

FLOSTING (The different ways of) of an homogeneous cube. 224.

FLoreEs (On the tin of the island of). 474.

FOLMER (MISS H.). A new electrometer, specially arranged for radio-active
investigations. 659.

FONTAINE SCHLUITER (J. J. DE LA). v. ScHLuiter (J. J. pe LA Fonratne).

FORTUYN (A. B. DROOGLEEVER). The decoloration of fuchsin-solutions by
amorphous carbon, 1322.

FRANCHIMONT (4. P. N.) presents a paper of Dr. R. A. WeerMAN: “Action
of sodium hypochlorite on amides of g-oxyacids”. 1163.

— and H. J. Backer. The coloration of some derivatives of Picrylmethylamide with
alkalies, 647.

— a-sulpho-propionie acid and its resolution into optically active isomerides. 653.
FREEZING POINT (On the lowering of the) in connection of an elastic deformation. 732.
FREQUENCIES (The treatment of) of directed quantities. 586,

FRESNEL’s coefficient (On) for light of different colours. 445.

FUCHSIN-SOLUTIONS (The decoloration of) by amorphous carbon. 1322.

FuNcTIONS of HERMITE (On the). 1st part. 139.

GALLE (ve. H.). On the relation between departures from the normai in the strength
of the trade-winds of the Atlantic Ocean and those in the waterlevel and tem-
perature in the Northern European seas. 1147.

Gas (The chemical constant and the application of the quantum theory by the method
of the natural vibrations to the equation of state of an ideal monatomic). 20.

— (On interference phenomena to be expected when Rontgen rays pass through a
di-atomic). 1184.

Gass (The diffusion-coefficient of) and the viscosity of gas-mixtures. 1068.

— (Tueoretical determination of the entropy constant of) and liquids. 1167.

Gas EQuiLiBriaA (On) and a test of Prof. v. p. Waaus Jr.’s theorema.]. 695. IL. 1011.

Gas-Laws (The influence of the hydration and of the deviations from the ideal) in
aqueous solutions of salts on the solidifying and the boiling points. 1036.

GaS-MINTURES (The diffusion-coefficient of gases and the viscosity of). 1068.

GeELs (On the behaviour of) towards liquids and the vapours thereof. IT. 92.

Geodesy. H. G. van De Sande Baknuyzen, N. WiLpEsorR and J. W. Dreperin«k :
“Comparison of the measuring bar used in the base-measurement at Stroe, with
the Dutch Metre N® 27”. 300.

— H. G. van bE Sanpe Baxkauyzen: “Comparison of the platinum-iridium Metre
No. 27 with the international Metre M as derived from the measurements by
the Metre-Commission in 1879 and 1880, and a preliminary determination of
the length of the measuring-bar of the French base-apparatus in international
metres”. 311.

Geology. H. A. Brouwer: “On the granitic area of Rokan (Middle-Sumatra) and on
contact-phenomena in the surrounding schists’. 1190.

Geophysics. J. P. van pDER Stok: “The treatment of frequencies of directed quanti-
ties”. 586, 5

x CONTENTS.

Geophysics. P. H. Ganié: “On the relation between departures from the normal in the
strength of the trade-winds of the Atlantic Ocean and those in the waterlevel
and temperature in the Northern European seas”. 1147.

GroTROPIC REACTIONS (On the mutual influence of phototropic and) in plants. 1278.
GERMINATION (Energy transformations during the) of wheat-grains. 62.

GRANITIC AREA (On the) of Rokan (Middle-Sumatra) and on contact-phenomena in

the surrounding schists. 1190.
GRAVITATION (On the field of a single centre in Ernstetn’s theory of). 998.
Gravity (The mean radius of the earth, the intensity of) and the moon’s parallax. 1291.

GuMMosis in the fruit (of the Almond and the Peachalmond as a process of normal
life. 810.

I1AGA (H.) presents a paper of Miss H. J. Foumer: “A new electrometer, especi-
ally arranged for radio-active investigations”. 659.

— presents a paper of Prof. I. M. Jancer: “On a new phenomenon accompanying
the diffraction of Réntgenrays in birefringent crystals”. 1204.

— and F. M, Jarcer. On the real symmetry of cordierite and apophyllite. 430.

HAMBURGER (H. J.) presents a paper of Dr. E, Laqueur: ‘On the survival of
isolated mammalian organs with automatic function”. 270,

— presents a paper of Prof. A. A. Hymans van pDeN Bercu and J. J. pe La
FontaIne Scutuirer: “The identification of traces of bilirubin in albuminons
fluids”. 807.

— Phagocytes and respiratory centre, 1325.

HEART-RHYTHM (On the). 1075. IT, 1135.
WELDERMAN (Ww. D.) and Ernsr Conen. The allotropy of cadmium, IL. 54, ILL.
122. IV, 638. V. 1050.

— The allotropy of zine. IL. 59.

— The allotropy of copper. II. 60.

— The allotropy of lead. 1. 822. Note. 1055.

— The metastability of the metals in consequence of allotropy and its significance
for Chemistry, Physics and Technics. LV. 1288.

neLiuM (Further experiments with liquid), [. 12. 278. K. 283. L. 514. N.520. M. 760,
HERMITE (On the functions of). 1st part. 139.
— and ABEL’s polynomia (On). 192.
oF (K) and H. Kamerurnen ONNEs, Further experiments with liquid helium. N. 520,
HOLLEMAN (A. F.) presents a paper of Dr. L. K. Wourr and Dr. EK. H, Bicaner:
“On the behaviour of gels towards liquids and the vapours thereof. IL. 92.

— presents a paper of Prof. J. BoEsEKEN: “On catalyse”. 546.

— The nitration of the mixed dihalogen benzenes. 846.

— presents a paper of Prof. J. Borseken and W. D. Couen: “The reduction of
aromatic ketones, II. Contribution to the kuowledge of the photochemical
phenomena”. 849,

— The replacement of substituents in benzene derivatives. 1027. a

— presents a paper of Dr. C, H. Suurrer: “The influence of the hydration and

CUGeN DORN T's; xl

of the deviations from the ideal gaslaws in aqueous solutions of salis on the
solidifying and the boiling points’. 1036.
HOLLEMAN (A. F.) presents a paper of Miss ADA Prins: ,,On critical end-points
and the system ethane-naphtalene’. 1095,
noustT (G.) and H. KaMertinen Onnes. The measurement of very low temperatures.
XXIV. The hydrogen and helium thermometers of constant volume down to the
freezing point of hydrogen compared with each other and with the platinum-
resistance thermometer, 501.
— On the electrical resistance of pure metals. IX. 508.
— Further experiments with liquid helium. M. 760.
— H. Kameruncu OnnEs and C. Dorsman. Isothermals of di-atomie substances
and their binary mixtures. XV. Vapour pressures of oxygen and critical point
of oxygen and nitrogen. 950,
HOOGEWERFF (s.) presents a paper of Prof, W. Remnpers: “Equilibria in the system
Pb-S-O, the roasting reactionprocess. 703.

HULSHOF (H.). On the thermodynamic potential as a kinetic quantity. Ist part. 85,

HYDRATION (The influence of the) and of the deviations from the ideal gas-laws in
aqueous Solutions of salts on the solidifying and the boiling points. 1036,

HYDROGEN (Measurements of isotherms of) at 20° C. and 13.°5 C. 203.

— (Measurements on the capillarity of liquid). 528.

HYDROGEN ISOTHERMS (The) of 20° C. and of 15°.5 C, between 1 and 2200 atms. 217.

Hydrostatics. D. J. Korrewec: “The different ways of floating of an homogeneous
cube”. 224.

HYMANS VAN DEN BERGH (a. a.) and J. J. DE wa Fonraine Scuuurrer. The
identification of traces of bilirubin in albuminous fluids. 807.

INERTIA (On isostasy, the moments of) and the compression of the earth, 1295.
INNERVATION (On the termination of the eiferent nerves in plain muscle-cells and
its bearing on the sympathetic (accessory) ) of the striated muscle-tibre, 982.

INTEGRAL EQUATIONS (On some). 286,
INTEGRAL-FORMULA (On an) of STIELTJEs. 829.
INTERFERENCE-PHENOMENA (On) to be expected when Roéuntgen-rays pass through a
di-atomic gas. 1184.
INVOLUTION (A cubic) of the second class, 105.
— (A triple) of the third class, 134.
ISOMERIDES (g-Sulpho-propionic acid and its resolution into optically active). 653.
1soOPRENE (A crystallized compound of) with sulphur dioxide. 585.
isostasy (On), the moments of inertia and the compression of the earth, 1295,
ISOPHERMALS of di-atomic substances and their binary mixtures. XV. Vapour pressures
of oxygen and critical point of oxygen and nitrogen. 950. XVI. Vapour-pressures
of nitrogen between the critical point and the boiling point. 959.
— of monatomic substances and their binary mixtures. XVI. 275.
IsOTHERMS (The hydrogen) of 20° C. and of 15°95 C. between 1 and 2200 atms. 217.
— of hydrogen (Measurements of) at 20° C. und 1595 ©, 208,

XII CRONE DL EN DiS:

JABGER (er. M.). The temperature-coeflicients of the free surface-energy of liquids at
temperatures from —80° C. to 1650° C, I. 329. V. 405. VI. 416. VIT. 555.
VHI. 571.

— On a new phenomenon accompanying the diffraction of Rontgenrays in birefrin-
gent crystals. 1204.
— Researches on Pasreur’s principle of the connection between molecular and
physical dissymmetry. I. 1217.
— and H Haga. On the real symmetry of cordierite and apophyllite. 430.
— and Juz. Kaun. The temperature coefficients of the free surface-energy of
liquids at temperatures from —80° C. to 1650° C, LV. 395.
— and Ant. Srmex. Studies in the field of silicate-chemistry, If. 239. IIL. 251.
— and M. J, Suir. The temperature-coefficients of the free surface energy of liquids
at temperatures from —80° C. to 1650° C. IT. 365. IIL. 386,
JONG (A. W. kK. DE). Action of sunlight on the cinnamic acids. 1274.
Jupiter (The figure of the planet), 1047.

KAUN (JUL) and F. M. Jatcer, The temperature-coefficients of the free surface-
energy of liquids at temperatures from —80° C. to 1650° C. LV. 395.

KAMERLINGH ONNES (H.). vy. Onnes (H. KAaMERLINGH).

KAPPERS (Cc. U. ARIENS) and P. Roratc. Further contributions to our know-
ledge of the brain of Myxine glutinosa, 2.

KAPTEYN (J. Cc.) presents a paper of Prof. M. J. van Uven: “The theory of
Bravais (on errors in space) for polydimensional space, with applications to
correlation”. Continuation. 150.

KAPTEYN (w.). On the functions of Hermite. Lst part. 139.

— presents a paper of Dr. N, G. W. H. Bescer: “On Hermire’s and ABEL’s
polynomia”, 192.

— On some integral equations. 286.

— presents a paper of Prof. M. J. van Uven: “The theory of the combination
of observations and the determination of the precision, illustrated by means of
vectors’, 490.

KEESOM (w. H.). The chemical constant and the application of the quantum theory
by the method of the natural vibrations to the equation of state of an ideal
monatomic gas. 20.

— On the matter in which the susceptibility of paramagnetic substances depends
on the density. 110.

— and H. Kamerttncu Onves. The specific heat at low temperatures. I. Measure-
ments on the specific heat of lead between 14° and 80° K. and of copper
between 15° and 22° K, 894.

KetToNES (The reduction of aromatic). III. Contribution to the knowledge of the photo-
chemical phenomena. $49.

KINETIC INTERPRETATION (On the) of the osmotic pressure. 1241.

KINETIC QUANTITY (On the thermodynamic potential as a). 1st part. 85.

KLUYVER (J. c.). On an integral formula of STIELTJES. 829.

CONTENTS XI

KOHNSTAMM (eH.) and kK, W. Watsrra. Measurements of isotherms of hydrogen
at 20° C. and 159.5 C. 203.
KORTEWEG (pb. J.). The different ways of floating of an homogeneous cube. 224,
KRUYT (H. R.). Current potentials of electrolyte solutions. 615.
— Electric charge and limit value of colloids. 623.
— and Jac. van DER Spex. The connection between the limit value and the
concentration of arsenic trisulphide sols, 1158.

KUENEN (J. e.). On the measurement of the capillary pressure in a soap-bubble. 946.
— The diffusion-coefficient of gases and the viscosity of gas-mixtures, 1068.

KUIPER JR, (K.). Lhe physiology of the air-bladder of fishes. 1088.

KUYPERS (H. A.) and H. KaweruincH OnNeEs. Measurements on the capillarity of
liquid hydrogen. 528.

LAAR (J. J. VAN). A new relation between the critical quantities and on the unity
of all substances in their thermic behaviour. 451.

— Some remarks on the values of the critical quantities in case of association. 598.

— On apparent thermodynamic discontinuities in connection with the value of the
quantity 4 for infinitely large volume. 606,

— The calculation of the molecular dimensions from the supposition of the electric
nature of the quasi-elastic atomic forces. 877.

LAQUEUR (&). On the survival of isolated mammalian organs with automatic
function. 270.

LEAD (The allotropy of). I. 822. Note. 1055.

— (Measurements on the specific heat of) between 14° and 80° k. and of copper
between 15° and 22° K, 894.

LIGHT (On FResNEL’s coefficient for) of different colours. 445.

LIMIT VALUE (Electric charge and) of colloids. 623.

— (The connection between the) and the concentration of arsenic trisulphide
sols. 1158.

11auIps (On the behaviour of gels towards) and the vapours thereof. II, 92.

— (Theoretical determination of the entropy constant of gases and). 1167.

— (The temperature-coefficients of the free energy-surface of) at temperatures from
—80° C. to 1650° C. I. 329. IL 365. ILL. 389. LV. 395. V. 405. VI. 416. VII.
556. VILL. 571.

LORENTZ (H. A.) presents a paper of Dr. J. J. van Laar: “A new relation between
the critical quantities and on the unity of all substances in their thermic
behavtour’. 451.

—- presents a paper of Dr. J. J. van Laan: “Some remarks on the values of the
critical quantities in case of association’’. 598.

— presents a paper of Dr. J. J. van Laan: “On apparent thermodynamic discon-
tinuities in connection with the value of the quantity 4 for infinitely large
volume”. 606,

— presents a paper of Dr. G, J. Evras; “On the structure of the absorption lines
D, and Ds”, 720.

XIV CONTENTS.

LORENZ (H. A.) presents a paper of Dr. G. J. Enias: “On the lowering of the
freezing point in consequence of an elastic deformation”. 732.

— presents a paper of Dr. G, J. Extras: “The effect of magnetisation of the elec-
trodes on the electromotive force”. 745.

— presents a paper of Dr. L. S. Ornstetn: “On the theory of the string galvano -
meter of Er1ntHOVEN”. 784.

— presents a paper of Dr. L. S. Ornstein and Dr. F. Zeentke: “Accidental
deviations of density and opalescence at the critical point of a single sub-
stance’. 793.

— presents a paper of Mrs. T. Eurenrest —AranassJewa : “Contribution to the
theory of corresponding states’. 840.

— presents a paper of Dr. J. J. van Laan: “The caleulation jof the molecular
dimensions from the supposition of the electric nature of the quasi-elastic atomic
forces”. 877.

— presents a paper of Mr, J. Droste: “On the field of a single centre in
ErNsTern’s theory of gravitation”. 998.

— presents of paper of Mr. H. Terrope: ‘Theoretical determination of the entropy
constant of gases and liquids”. 1167.

— presents a paper of Prof, P. Kurmnrest: “On interference-phenomena to be
expected when R6NTGEN rays pass through a di-atomic gas”. 1184.

— presents a paper of Prof. P. Eurenrest: “On the kinetic interpretation of the
osmotic pressure”. 1241.
LUNAR PERIGEE (The motions of the) and node and the figure of the moon. 1309.
MAGNETISATION (‘The effect of) of the electrodes on the electromotive force. 745.
MAMMALIAN ORGANS (On the survival of isolated) with automatic function. 270.
Mathematics. Jan pe Vries: “A cubic involution of the second class”. 105.

— Jan pve Vrigs: “A triple involution of the third class”. 134.

— W. Kapreyn: “On the functions of Hermite”. 3th part. 139.

— M. J. van Uven: “The theory of Bravats (on errors in space) for polydi-
mensional space with applications to correlation”. (Continuation). 150.

— M. J. van Uven: “Combination of observations with and without conditions
and determination of the weights of the unknown quantities, derived from me-
chanical principles”. 157.

— N. G. W. H. Beraer: “On Hermrre’s and AsBet’s polymonia”. 192.

— W. Kapreyrn: “On some integral equations”. 286.

— M. J. van Uven: “The theory of the combination of observations and the
determination of the precision, illustrated by means of vectors”. 490.

— J. ©. Kivyver: “On an integral formula of Srievtses”. 829.

—- JAN DE Vrizs: “Characteristic numbers for nets of algebraic curves”. 935,

— Jan pe Vries: “Characteristic numbers for a triple infinite system of algebraic
plane curves”. 1055.

— Jan pr Varies: “Systems of circles determined by a pencil of conics”. 1107.

— W. van per Woupe: “On Norner’s theorem”, 1245.
— Jan pe Vries: “A bilinear congruence of rational twisted quintics”. 1250,

CON TEN T §&. >A

Mathematics. JAN pe Vries: “Some particular bilinear congruences of twisted cubics”.
1256.

MATHIAS (£.), H. Kamertincu Onnes and C. A, Crommenin. The rectilinear
diameter of nitrogen. 953.

MEASUREMENT (The) of very low temperatures. XXIV. The hydrogen and helium.
thermometers of constant volume, down to the freezing point of hydrogen compared
with each other and with the platinum-resistance thermometer. 501.

MEASUREMENTS On the capillarity of liquid hydrogen, 528.

— of isotherms of hydrogen at 20° C. and 1595 C. 203.

— on the specific heat of lead between 14° and 80° k. and of copper between
15° and 22° K. 894.

MEASURING Bar (Comparison of the) used in the base measurement at Stroe with the
Dutch Metre N® 27. 300.

— (Comparison of the Dutch platinum-iridium Metre N®%, 27 with the international
Metre M as derived from the measurements by the Dutch Metre-Commission in
1879 and 1880, and a preliminary determination of the length of the) of the
French base-apparatus in international metres. 311.

MECHANICAL PRINCIPLES (Combination of observations with and without conditions and
determination of the weights of the unknown quantities derived from). 157.
METALS (The metastability of) in consequence of allotropy, and its significance for

Chemistry, Physies and Technics. 200. III. 926. 1V. 1238.

— (On the electrical resistance of pure). IX. 508.

METASTABILITY (The) of metals in consequence of allotropy and its significance for
Chemistry, Physics and Technics. 200. III. 926. IV. 1238.

METHYLAMINE (On the interaction of ammonia and) on 2. 3. 4.-trinitrodimethylaniline.
1034,

METRE No. 27 (Comparison of the Dutch platinum-iridium) with the international
metre M/ as derived from the measurements by the Dutch Metre-Commission in
1879 and 1880, and a preliminary determination of the length of the measu-
ring bar of the French baseapparatus in international metres. 311.

Mineralogy. H. Haca and I’. M, Jararer: “On the real symmetry of cordierite and
apophyllite”. 430.

— C. E, A. Wichmann: “On the tin of the island of Flores”, 474.

MOLECULAR DIMENSIONS (The calculation of the) from the supposition of the electric
nature of the quasi-elastic atomic forces, 877.

MOLENGRAAFF (G. 4. F.) presents a paper of Dr. H. A. Brouwer: “On the
granitic area of Rokan (Middle-Sumatra) and on contact-phenomena in the sur-
rounding schists”. 1190.

moon (The motions of the lunar perigee and node and the figure of the). 1309.

MOON’S PARALLAX (The mean radius of the earth, the intensity of gravity and the), 1291.

MUSCLE-CELLS (On the termination of the efferent nerves in plain) and its bearing
- on the sympathetic (accessory) innervation of the striated muscle-fibre. 982.

MUSCULAR FIBRE (On the mode of attachment of the) to its tendontibres in the
striated muscles of the vertebrates, 989,

XVI CONTENTS.

MYXINE GLUTINOsA (Further contributions to our knowledge of the brain of). 2.
NERVE-DISTRIBUTION (On the) in the trunk-dermatoma. 632.
Nerves (On the termination of the efferent) in plain muscle cells and its bearing on
the sympathetic (accessory) innervation of the striated muscle-fibre. 982.
Nets (Characteristic numbers for) of algebraic curves. 935,
NITRATION (The) of the mixed dihalogen benzenes. 846.
NITROGEN (Vapour pressures of oxygen and critical point of oxygen and). 950.
— (The rectilinear diameter of). 953.
-—— (Vapour pressures of) between the critical point and the boiling point. 959.
NOTHER’s theorem (On). 1245.
occLusion (A case of) of the arteria cerebelli posterior inferior. 914.
ONNES (HW. KAMERLINGH). Further experiments with liquid helium. J. 12.
278. K. 283. L. 514.

— presents a paper of Dr. W. H, Kegsom: “The chemical constant and the appli-
cation of the quantum-theory by the method of the natural vibrations to the
equation of state of an ideal monatomic gas’. 20.

— presents a paper of Dr, W. H. Kersom: “On the matter in which the suscep-
tibility of paramagnetic substances depends on the density”. 110,

— presents a paper of Dr. C. A. Crommezin: “Tsothermals of monatomic sub-
stances and their binary mixtures”. XVI. 275.

— presents a paper of Dr. C. A. Cromme in: “Isothermals of di-atomic substances
and their binary mixtures”, XVI. 959.

— C. Dorsman and G. Hotsr. Isothermals of di-atomic substances and their binary
mixtures. XV. Vapour pressures of oxygen and critical point of oxygen and
nitrogen. 950.

— and P. Enerenrest. Simplified deduction of the formula from the theory of
combinations which PLANoK uses as the basis of his radiation theory. 870.

— and K. Hor. Further experiments with liquid helium, N. 520,

— and G. Hotst. The measurement of very low temperatures. XXIV. The hydrogen
and helium thermometers of constant volume down to the freezing point of
hydrogen compared with each other and with the platinum-resistance thermo-
meter. 501.

— On the electrical resistance of pure metals. 1X. 508.

— Further experiments with liquid helium, M. 760.

—and W. H. Keresom. The specific heat at low temperatures. I. Measurements
on the specific heat of lead between 14° and 80° Kk. and of copper between
15° and 22° K, 894.

— and H. A. Kuypers. Measurements on the capillarity of liquid hydrogen. 528.

— BE. Marutas and C. A. Crommenin. The rectilinear diameter of nitrogen. 953.

OPALESCENCE (Accidental deviations of density and) at the critical point of a single
substance. 793.
ORNSTEIN (4. 8.). On the theory of the stringgalvanometer of ErNTHOVEN. 784.

— and F. Zerntxe. Accidental deviations of density and opalescence at the critical
point of a single substance. 793.

CONTENTS Xvit

OSMOTIC PRESSURE (On the kinetic interpretation of the). 1241.
OXYGEN (Vapour pressures of) and critical point of oxygen and nitrogen. 950.

PARAMAGNETIC SUBSTANCES (On the matter in which the susceptibility of) depends on
the density. 110.

PASTEUR’s principle (Researches on) of the connection between molecular and
physical dissymmetry. I. 1217.

PEACHALMOND (Gummosis in the fruit of the Almond and the) as a process of normal
life. 810.

'Petrography. A. Wicumann: “On some rocks of the island of Taliabu (Sula islands). 226.

PHAGOCYTES and respiratory centre. 1325.

PHosPHORUs (On the vapour pressure lines of the system). Il. 678. IIL. 962.

— (Further particulars concerning the system). 973.

PHOTOCHEMICAL phenomena (Contribution to the knowledge of the). $49.

PHOTOTROPIC and geotropic reactions (On the mutual inftuence of) in plants, 1278.

Physics. H. Kamprimcu Onnes: “Further experiments with liquid helium”. J. 12.
278. K. 283. L. 514, N. 520. M. 760.

— W. H. Kersom: “The chemical constant and the application of the quantum-
theory by the method of the natural vibrations to the equation of state of an
ideal monatomic gas”, 20.

— H. Huusuor: “On the thermodynamic potential as a kinetic quantity”. 1st part. 85.

-- W. H. Kexrsom: “On the manner in which the susceptibility of paramagnetic
substances depends on the clensity”. 110.

— Pu. Konnstamm and k. W. Watsrra: “Measurement of isotherms of hydrogen
at 20° C. and 15° C.” 203.

— K. W. Watstra: “The hydrogen isotherms of 20° C. and of 15°95 C. between
1 and 2200 atm.” 217.

— C, A. Cromme.in: “‘Isothermals of monatomic substances and their binary
mixtures”, XVI, 275.

= P. Zeeman: ‘'FResNoL’s coefficient for light for different colours”. 1stpart. 445,

= J. J. van Laar: “A new relation between the critical quantities and on the
unity of all substances in their thermic behaviour’. 451.

= H. vu Bois: “Modern electromagnets, especially for surgical and metallurgic
practice”. 468,

= H. Kamerninc Onnes and G, Horsr: “On the measurement of very low
temperatures. XXIV. The hydrogen and helium thermometers of constant volume,
down to the freezing-point of hydrogen compared with each other and with the
platinum resistance thermometer’. 501.

=— H. Kamerninau Onnus and G. Housr: “On the electrical resistance of pure
metals ete.”. [X. 508.

— H. Kamernrnen Onnus and H, A. Kuyerrs: ‘Measurements on the capillarity
of liquid hydrogen”. 528)

= J. J. van Laan: “Some remarks on the values of the critical quantities in case

of association’’. 598.
90)
Procéedings Royal Acad. Amsterdam. Vol. XVII,

XVIII CONTENTS.

Physics. J. J. van Laar: “On apparent thermodynamic discontinuities in connection
with the value of the quantity 4 for infinitely large volume’’. 606.
— Miss H. J. Foumpr: “A new electrometer, especially arranged for radio-active
investigations”. 659.
— G. J. Brras: “On the structure of the absorptionlines D,; and ),”. 720.
— G. J. Evras: “The lowering of the freezing point in consequence of an elastic

deformation”. 732.
— G. ap Enras: “The effect of magnetisation of the electrodes on the electromotive
force”. 745.
— L. 8. Ornstern: “On the theory of the string-galvanometer of ErytHoven’’. 784.
— L. 8. Ornsrern and F. Zernike: “Accidental deviations of density and opales-

cense at the critical point of a single substance”. 793.

— F. E. C. Scnerrer; “On unmixing in a binary system for which the three
phase pressure is greater than the sum of the vapour tensions of the two compo-
nents’. 834.

— Mrs. T. Exrenrest—Aranasssewa: “Contribution to the theory of corresponding
states”. 840.

— P. Burenrest and H, KameruincuH Onnes: “Simplified deduction of the
formula from the theory of combinations which PLANcK uses as the basis of his
radiationtheory”. 870.

— H. pu Bors: “The universality of the Zeeman-elfect with respect to the SrarK-
effect in canal-rays”. 873.

— J. J. van Laar: “The calculation of the molecular dimensions from the suppo-
sition of the electric nature of the quasi-elastic atomic forces”, 877.

— W. H. Kersom and H. Kameruineu Onnes: “The specific heat at low tempe-
ratures. I. Measurements on the specific heat of lead between 14° and 80° K,
and of copper between 15° and 22° K.” 894.

— J. P. Kunnen: “On the measurement of the capillary pressure in a soap-bubble”.
946.

— H. Kamertincu Onnes, C. Dorsman and G. Horst: “Isothermals of di-atomic
substances and their binary mixtures. XV. Vapour pressures of oxygen and critical
point of oxygen and nitrogen”. 950.

— E. Mararas, H. Kameruincn Onneis and C, A. CromMEtiIn: “The rectilinear
diameter of nitrogen”. 953.

— ©, A. Crommeniy: “Isothermals of di-atomic substances and their binary mixs
tures. XVI. Vapour pressures of nitrogen between the critical point and the
boiling point”, 959,

«- J, Droste: “On the field of a single centre in ErnsTEty’s theory of gravitation”,
998.

«- J, P, Kusnex: “The diffusion coefficient of gases and the viscosity of gasa
mixtures”. 1068,

s H: Terropk: “Theoretical determination of the entropy constant of gases and
liquids”. 1167.

CROPNELS ENG TCS XIX

Physics. P. Enrenrest: “On interference phenomena to be expected when Réntgen
rays pass through a di-atomic gas’. 1184.
_— F. M. Jazcer: “On a new phenomenon accompanying the diffraction of

R6ntgen rays in birefringent crystals’. 1204.
— P. Enrenrest: “On the kinetic interpretation of the osmotic pressure”. 1241.
Physiology. ££. Laaueur: “On the survival of isolated mammalian organs with auto-
matic function”. 270.
—L. K. Wotrr: “On the formation of antibodies after injection of sentizised
antigens”. II. 318.
— G. van Risnperk: “On the nerve-distribution in the trunk-dermatoma’’. 632.
— A. A. Hymans vAN DEN Bereu and J. J. pe ta Fontatne Scauurrur: “The
identification of traces of bilirubin in albuminous fluids”. 807.

— I. K. A. Werraetm Satomonson: “Exaggeration of deep reflexes”. 885.

— S. pe Borer: “On the heart-rhythm”. 1075. If. 1135.

— A. B. Droocierver Fortuyn: “The decoloration of fuchsin-solutions by amor-

phous carbon”, 1322.
— H. J. Hameurcer: “Phagocytes and respiratory centre”. 1525.
PICRYLMETHYLAMIDE (The coloration of some derivatives of) with alkalies. 647.
PLANCK (Simplified deduction of the formula from the theory of combinations which)
uses as the basis for his radiation theory. 870.

PLANET Jupiter (The figure of the). 1047.

PLANETS (On SEELIGER’s hypothesis about the anomalies in the motion of the
inner). 23.

PLANTs (On the mutual influence of the phototropic and geotropic reactions in). 1278

poLyNoMIA (On Hermitre’s and ABEL’s). 192.

PostTMA (s.) and A. Smits. The system Ammonia-water. 182.

porass1uM (The allotropy of). I. 1115.

POTASSIUM SULPHATE, potassium chlorid (The system: copper sulphate, copper chlorid)
and water at 30°. 532.

POTENTIAL (On the thermodynamic) as a kinetic quantity. Ist part, 85.

POTENTIALS (Current) of electrolyte solutions. 615.

PRECISION (The theory of the combination of observations and the determination of
the), illustrated by means of vectors. 490.

PRINS (Miss ADA). On critical end-points and the system ethane-naphtalene. 1095.

PSEUDO-COMPONENTS (The metastable continuation of the mixed crystal series of) in
connection with the phenomenon allotropy. I. 672.

quantity 4 (On apparent thermodynamic discontinuities in connection with the value
of the) for infinitely large volume. 606.

QuaNnTUM-rtHEORY (The chemical constant and the application of the) by the method
of the natural vibrations to the equation of state of an ideal monatomic gas). 20

QUATERNARY sysTEM KCl—CuClz2—BaCl,—H20 (On the). 781.

auinrics (A bilinear congruence of rational twisted). 1250.

RADIATION THEORY (Simplified deduction of the formula from the theory of combina-
tions which PLancK uses as the basis for his). 870.

XX CONTENTS

RADIO-ACTIVE investigations (A new electrometer, specially arranged for). 659.
REPLEXES (Exaggeration of deep). 885.
REINDERS (w.). Equilibria in the system Pb-S-O, the roasting reaction process. 703.
RESISTANCE (On the electrical) of pure metals. 1X. 508.
RESPIRATORY CENTRE (Phagocytes and), 1325.
ROASTING REACTION PROCESS (f{quilibria in the system Pb-S-O, the). 703.
rocks (On some) of the island of Taliabu (Sula islands). 226.
ROKAN (Middle-Sumatra) (On the granitic area of) and on contact phenomena in the
surrounding schists, 1190.
ROMBURGH (e. VAN) presents a paper of Prof. F. M. Jareer and Dr. Ant. SimEk:
“Studies in the field of silicate-chemistry”. Il. 239. ILI. 251.
— presents a paper of Prof. F. M. Jarcer: “The temperature-coefticients of the
free surface-energy of liquids at temperatures from —S8U° to 1650° C.” I. 329.
II. 365. ILI. 886. IV. 395. V. 405. VI. 416. VII. 555. VILL. 571.
— presents a paper of Mr. G. pr Bruin: “A crystallized component of isoprene
with sulphur dioxide”. 585.
— presents a paper of Prof. F, M. Jazcrr: “Researches on Pasteur’s principle of
the connection between molecular and physical dissymmetry”. I. 1217.
— presents a paper of Dr. A. W. K. pg Jona: ‘Action of sunlight on the cin-
namic acids’. 1274.
— and Miss D, W. Weysinx. On the interaction of ammonia and methylamine
on 2.3.4,-trinitrodimethylaniline. 1034.
RONTGEN Rays (On interference phenomena to be expected when) pass through a
di-atomic gas. 1184.
— (On a new phenomenon accompanying the diffraction of) in birefringent
crystals. 1204.
ROTHIG (p.) and C. U. ArtENs Kappers. Further contributions to our knowledge
of the brain of Myxine glutinosa. 2.
RIJNBERK (G. VAN) On the nerve-distribution of the trunk-dermatoma. 6382.
SALOMONSON (J. K. A. WERVHEIM). Hxaggeration of deep reflexes. 885.
— presents a paper of Dr. S. p—E Boer: ‘On the heart-rhythm’. 1075. LI. 1135.
saLts (The influence of the hydration and of the deviations from the ideal gas-laws
in aqueous solutions of) on the solidifying and the boiling point. 1036.
SANDE BAKHUYZEN (H. G VAN DE). vy. Bakauyzen (H. G. vaAN DE Sanpg),
SCHEFFER (Ff. E. c.). On gas equilibria and a test of Prof. v. p. Waats-JR.’s
theorema. I. 695. Il. 1011.
— On unmixing in a binary system for which the three-phase pressure is greater
than the sum of the vapour tensions of the two components. 834,
SCHLUITER (J. J. DE LA FONTAINE) and A. A. HyMans VAN DEN BERGH.
The identification of traces of bilirubin in albuminous fluids. 807.
SCHREINEMAKERS (fF. A. H.). Equilibria in ternary systems. XV. 70. XVI.
169. XVII. 767. XVIII. 1260.
— and Miss W. C. pe Baat. The system: copper sulphate, copper chlorid, potas-
sium sulphate, potassium chlorid and water at 30° C. 533,

CONTENTS. XXI

SCHREINEMAKERS (Ff. A. H.) and Miss W. C. pe Baar. On the quaternary
system KCl-CuClg-BaClo-H,C. 781.
— Compounds of the arsenious oxide, I. 1111.
8EEL1GER’s hypothesis (On) about the anomalies in the motion of the inner planets. 23.
— (Remarks on Mr. WoLtsEr’s paper concerning). 33.
SILICATE-CHEMISTRY (Studies in the field of). If. 239. III. 251.

SIMEK (anv) and F, M. Jazcpr. Studies in the field of silicate-chemistry. IT.
239, IIL. 251.
SITTER (Ww. DE) presents a paper of Mr. J. Wouter oro: “On SEELIGER’s hypo-

thesis about the anomalies in the motion of the inner planets”. 23.
— Remarks on Mr. Woutyer’s paper concerning SrenicEr’s hypothesis. 33.
— The figure of the planet Jupiter. 1047.
— On the mean radius of the earth, the intensity of gravity and the moon’s parallax. 1291.
— On isostasy, the moment of inertia and the compression of the earth. 1295.
— The motions of the lunar perigee and node and the figure of the moon. 1309
sLUITER (c. H.). The influence of the hydration and of the deviations from the idenl
gas-laws in aqueous solutions of salts on the solidifying and the boiling-point. 1036.
smivt (m.) and F, M. Jancrer. The temperature-coefficients of the free-surface-energy
of liquids at temperatures from —S0° C. to 1650° C. Il. 365. IIT, 381. i.
sMits (a). The metastable continuation of the mixed crystal series of pseudo-
components in connection with the phenomenon allotropy. II, 672.
— and Aten (A. H. W.). The applicaticn cf tle theory of al’otropy to electro-
motive equilibria. 11. 37. ILI. 680.
— and 8S. C. Boxknorst. On the vapour pressure lines in the system phosphorus. {1
678. III, 962.
— Further particulars concerning the system phosphorus, 973.
— and 8, Postma. The system ammoniawater. 182.
SOAP-BUBBLE (On the measurement of the capillary pressure in a). 946,
SODIUM-HYPOCHLORITE (Action of) on amides of z-oxyacids. 1163.
SPECIFIC HEAT (The) at low temperatures. [. Measurements on the specific heat of lead
between 14° and 80° K. and of copper between 15° and 22° k, 894.
SPEK (sac. VAN DER) and H. R. Kruyt. The connection between the limit
value and the concentration of arsenic trisulphide sols. 1158,
stakK-effect (The universality of the Zeeman-eflect with respect to the) in canal-rays. 873
sT1ELTJES (On an integral-formula of). 829.
STOK (J. P. VAN DER). The treatment of frequencies of directed quantities. 586.
— presents a paper of Mr. P. H. Ga11é: “On the relation between departures
from the normal in the strength of the trade-winds in the Atlantic Ocean and
those in the waterlevel and temperature in the Northern European seas.’ 1147.
STRING-GALVANOMETER (On the the theory of the) of EintnHoven. 784.
stRoE (Comparison of the measuring bar used in the base measurement at) with the
Dutch Metre n° 27. 300.
suBsTANCES (Isothermals of monatomic) and their binary mixtures. XVI.

275.
— (Isothermals of di-atomic) and their binary mixtures, XV. 950, XVI, 959.

NXIT CONTENTS.

substances (A new relation between the critical quantities and on the unity of all)
in their thermic behaviour. 451.

suBsTItuENTS (The replacement of) in benzene derivatives. 1027.

4-SULPILO-PROPIONIC acrb and its resolution into optically active isomerides. 653.

SULPHUR DIOXIDE (A erystallized compound of isoprene with). 585.

SUNLIGHT (Action of) on the cinnamie acids. 1274.

system PJ-S-O (Equilibria in the), the roasting reaction process. 703.

— (The) copper sulphate, copper chlorid, potassium sulphate, potassium chlorid and
water at 30° C. 533.

— (Characteristic numbers for a triply infinite) of algebraic plane curves. 1055.

— ammonia—water (The). 182.

— ethane—naphthalene (On critical endpoints and the). 1095.

— phosphorus (On the vapour pressure lines in the). IH. 678. [[L 962.

— phosphorus (Further particulars concerning the). 973.

vALIABU (Sula islands) (On some rocks of the island of). 226.

TEMPERATURE (On the relation between departures from the normal in the strength
of the trade-winds of the Atlantic Ocean and those in the waterlevel and) in
the Northern European seas. 1147.

TEMPERATURE-COEFFICIENTS (The) of the free energy surface of liquids at tempera-
tures from —80° C. to 1650° C. I. 329. IL. 365. ILL 386. LV. 395. V. 405.
VI. 416. VIL. 555. VIII. 571:

TEMPERATURES (The measurement of very low). XXLV. The hydrogen and helium
thermometers of constant volume down to the freezing point of hydrogen com.
pared with each other and with the platinum-resistance thermometer. 501.

— (The specific heat at low). [. Measurements on the specific heat of lead between
14° and 80° K. and of copper between 15° and 22° K. 894.

TENDONFIBRES (On the mode of attachment of the muscular fibre to its) in the striated
muscles of the vertebrates. 989.

TERNARY sYSteMS ([quilibria in). XV. 70. XVL. 169. XVIL. 767. XVIII. 1260.

TETRODE (u.). Theoretical determination of the entropy constant of gases and liquids. 1167.

TuEORY of allotropy (The application of the) to electromotive equilibria. I. 37. UL 680.

— of Bravats (The) (on errors in space) for polydimensional space with applica-
tions to correlation. (Continuation). 150.

— (The) of the combination of observations and the determination of the precision,
illustrated by means of vectors. 490. i

— of combinations (Simplified deduction of the formula from the) which Pranck
uses as the basis of his radiation theory. 870.

— of corresponding states (Contribution to the). 840.

— of gravitation (On the field of a single centre in Etnsrety’s). 993.

THERMOMETERS (The hydrogen and helium) of constant volume, down to the freezing
point of hydrogen compared with each other, and with the platinum-resistan ce
thermometer, 501.

TUREE-PHASE PRESSURE (On unmixing in a binary system for which the) is greater

than the sum of the vapour tensions of the two components. 834.

CONTENTS. XXIII

Tin (On the) of the island of Flores. 474.

TRADE-WINDs (On the relation between departures from the normal in the strength
of the) in the Atlantic Ocean and those in the waterlevel and temperature in
the Northern European seas. 1147.

TRINITRODIMETHYLANILINE (On the interaction of ammonia and methylamine on
2.3.4.-). 1034.

TRUNK-DERMATOMA (On the nerve-distribution in the). 632.

UNMIXING (On) in a binary system for which the three-phase pressure is greater than
the sum of the vapour tensions of the two components. 83+.

UVEN (M. J. VAN). The theory of Bravats (on errors in space) for polydimensional
space with applications to correlation. (Continuation). 150.

— Combination of observations with and without conditions and determination of
the weights of the unknown quantities, derived from mechanical principles. 157.

— The theory of the combination of observations ani the determination of the
precision, illustrated by means of vectors. 490.

VAGUS AREA (The) in Camelidae. 1119.
VAPOUR PRESSURE LtNeés (On thie) in the system puosphorus. IL. 678. ILL. 962.
VAPOUR PRESSURES of oxygen and critical point of oxygen and nitrogen. 950.

— of nitrogen between the critical point and the boiling point. 959.

VAPOUR TENSIONS (On unmixing in a binary system for which the three-phase pressure
is greater than the sum of the) of the two components. 834.

vectors (The theory of the combination of observations and the determination of the
precision, illustrated by means of). 490.

VERMEULEN (H. A.). The vagus area in Camelidae. 1119.

VerTEBRATES (On the mode of attachment of the muscular fibre to its tendontibres
in the striated muscles of the). 989.

viscosity of gas-mixtures (The diffusion-coefticient of gases and the). 1068.

VRIES (JAN DE). A cubic involution of the second class. 105.

— A triple involution of the third class. 13+.

— presents a paper of Prof. M. J. van Uven: “Combination of observations with
and without conditions and determination of the weights of the unknown quantities,
derived from mechanical principles’. 157.

— Characteristic numbers for nets of algebraic curves. 935.

— Characteristic numbers for a triple infinite system of algebraic plane curves. 1055.

— Systems of circles determined hy a pencil of conics, 1107.

— presents a paper of Dr. W. van per Wouve: “On Noraer’s theorem”. 1245.

— A bilinear congruence of rational twisted quinties. 1250.

— Some particular bilinear congruences of twisted cubics. 1256.

WAALS (J. D. VAN DER) presents a paper of Prof. A. Smits and Dr. A. H. W,
ATEN: “The application of the theory of allotropy to electromotive equilibria”
I]. 37. ILI. 680,
— presents a paper of Dr. H. Hunsuor: “On the thermodynamic potential as a
kinetic quantity”, Ist. part. 85.

— presents a paper of Prof. A. Smits and S. Posraa: ‘The system ammonia-water.”” 182,

XALV CONTENTS.

WAALS (J. D. VAN DER) presents a paper of Prof. Pu. Kounstamm and kK. W.
Waustra: “Measurements of isotherms of hydrogen at 20° C. and 1525 C.” 203.

— presents a paper of Mr. K. W. Waustra: “The hydrogen isotherms of 20° C.
and of 15°.5 C. between 1 and 2200 atm.”, 217.

— presents a paper of Prof. A. Smits: “The metastable continuation of the
mixed erystal series of pseudo-components in connection with the phenomenon
allotropy”. II. 672.

— presents a paper of Prof. A. Sirs and S. C. Bokuorst: “The vapour pressure
lines of the system phosphorus”. II. 678. IIT. 962.

— presents a paper of Dr. F. E. ©. Scuerrer: ‘On gas equilibria and a test of
Prof. vaN per Waats Jr.’s formula”. I. 695. IL. 1011.

—— presents a paper of Dr. FB. E. C. Scnrrrer: “On unmixing in a binary system
for which the three-phase pressure is greater than the sum of the vapour tensions
of the components”. 834.

— presents a paper of Prof. A. Smrvs and 8. ©. Boknorstr: “Further particulars

concerning the system phosphorus”. 973.

WAALS JR's theorema (On gas equilibria and a test of Prof.). L695. If, 1011.

WALs@tRA (xk. w.). The hydrogen isotherms of 20° C. and of 15°5 C. between 1

and 2200 atm. 217.

— and Pu. Kounstamm. Measurements of isotherms of hydrogen at 20° C, and
159.5 C, 2038.

water (The system ammonia—), 182.

— (The system: copper sulphate, copper chlorid, potassium sulphate, potassium
chlorid and) at 30°, 533.

WATERLEVEL (On the relation between departures from the normal in the strength of
the trade-winds in the Atlantic ocean and those in the) and temperature in the
Northern European seas. 1147.

WEBER (MAX) presents a paper of Dr. K. Kuiper Jr.: “The physiology of the
air-bladder of fishes’. 1088.

WEERMAN (k. A.). Action of sodium hypochlorite on amides of ¢-oxyacids. 1163,
weicuts (Combination of observations with and without conditions and determination
of the) of the unknown quantities, derived from mechanical principles. 157.
WENsINK (Miss pv. w.) and P. van RomBurcu. On the interaction of ammonia

and methylamine on 2.3.4,-trinitrodimethylaniline. 1034.

WENT (F. A. FP. C.) presents a paper of Miss Lucin C. Dover: “Energy transfor-
mations during the germination of wheat-grains”. 62.

— presents a paper of Dr, C. E. B. Bremexame: “On the mutual influence of
phototropic and geotropic reactions in plants”. 1278.

WERTHEIM SALOMONSON (I. K. A.) v. Sanomonson (I. K. A. WERTHEIM).
WHBEAT-GRAINS (Energy transformations during the germination of). 62.
WICHMANN (a.). On some rocks of the island of Taliabu (Sula islands). 226.

— On the tin of the island of Flores. 474.

WILDEBOER (N.), J. G. Drepertnx and H. G. vAN DE SanpE BaknuyzEN. Com-
parison of the measuring bar used in the base measurement at Stroe with the
Dutch Metre No. 27. 300.

CONTENTS. XXV

WINKLER (c.) presents a paper of Prof. G. van RignBerk : “On the nerve-distri-
bution of the trunkdermatoma.” 632.
— A ease of occlusion of the arteria cerebelli posterior inferior. 914.
WoLFF (L, K.). On the formation of antibodies after injection of sensitized antigens.
II. 318.
— and E, H. Bicnner. On the behaviour of gels towards liquids and the vapours
thereof. II. 92.
WOLFF (s.) and Ernst Conen. The allotropy of potassium. I. 1115.
WOLTJER JR. (J.). On Srevicer’s hypothesis about the anomalies in the motion
of the inner planets. 23.
WOUDE (Ww. VAN DER). On Noruer’s theorem. 1245.
ZEEMAN (P.). On FRESNEL’s coefficient for light of different colours, 445.
ZEEMAN-effect (The universality of the) with respect to the Srark-ellect in canal-
rays. 873.
ZERNIKE (f.) and L, S. Ornstein. Accidental deviations of density and opalescence
at the critical point of a single substance. 793.
zinc (The allotropy of). Il, 59. III. 641.
Zoology. K. Kuiper Jr.; “The physiology of the air-bladder of fishes.” 1088.

de | ie 9

KONINKLIKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.

PROCEEDINGS OF THE MEETING
of Saturday May 30, 1914.
Von XVII.

President: Prof. H. A. Lorentz.
Secretary: Prof. P. Zueman.

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Zaterdag 30 Mei 1914, DI. XXII1).

OOyaNy PROD INES

P. Rérmie and C. U. Armys Karrrrs: “Further contributions to our knowledge of the
brain of Myxine glutinosa’”. (Communieaied by Prof. L. Bork), p. 2. (With 2 pl.).

H. Kamervincu Onnes: “Further experiments with liquid helium, J. The imitation of an
AMPERE molecular current or of a permanent magnet by means of a supra-conductor”, p. 12.

W. H. Kersom: “The chemical constant and the application of the quantum-theory by the
method of the natural vibrations to the equation of state of an ideal monatomic gas’,
(Communicated by Prof. H. Kamerrinon Onnes), p. 20.

J. Wortses Jr.: “On Srericer’s hypothesis about the anomalies in the motion of the inner
planets’. (Communicated by Prof. W. DE Sirrer), p, 23.

W. be Sirrer: “Remarks on Mr. Wortser’s paper concerning SEELIGER’s hypothesis’, p. 33.

A. Smits and A. H. W. Aten: “The application of the theory of allotropy to electromotive
equilibria”. If. (Communicated by Prof. J. D. van per WaAats), p. 37.

Ernst Conrn and W. D. Herperman: “The allotropy of Cadmium”. IT, p. 54.

Ernst Conen and W. D. Herprerman: “The allotropy of Zine”. II, p. 59.

Ernst Conen und W. D. Heriperman: “The allotropy of Copper. II, p. 60.

Lucir C. Dover: “Energy transformations during the germination of wheat grains”. (Com-
municated by Prof. F. A. F. C. Wenn), p. 62.

F. A. H. Scuremvemakers: “Equilibria in ternary systems.” XV, p. 70.

H. Hursnor: “On the thermodynamic potential as a kinetic quantity”. (First part). (Commu-
nicated by Prof. J. D. van DER WAALS), p. 85.

L. K. Worr and E. H. Biicuner: “On the behaviour of gels towards liquids and the vapours
thereof”. (Communicated by Prof. A. F. Horiieman), p. 92.

Jan DE Vries: “The quadruple involution of the cotangential points of a eubie pencil”, p. 102.

Jan dE Vries: “A cubic involution of the second class”, p. 105.

W. H. Kersom: “On the manner in which the susceptibility of paramagnetic substances
depends on the density.” (Communicated by Prof. H. Kamertincu Onnes), p. 110

Ernst Conen and W. D, Herperman: “The allotropy of Cadmium IIL’, p. 122.

Proceedings Royal Acad. Amsterdam. Vol. XVII.

»)
Anatomy. — ‘Further contributions to our knowledge of the brain
of Myaine gluitinosa.” By P. Rorsic (Berlin) and C. U. Artins
Kapprrs (Amsterdam). (Communicated by Prof. L. Bork).

(Communicated in the meeting of March 28, 1914).

The former of us has given a description of the motor roots and
nucler in’ Myxine glutinosa and in some Amphibia in Vol. XVI of
these Proceedings (p. 296).

For Myxine the topography of the V—VIL nucleus and the spino-
occipital column has been discussed, and mention was made of the
absence of the eyemuscle-nuclei and the motor glossopharyngeus.

For the discussion of the vagus roots reference was made to
further researches not yet completed at that time, which we should
accomplish in conjunction.

It is known that the vagus of Myxine glutinosa has caused
many difficulties, and before givine our own results we wish
to review the opinions of former authors, because such a review
clearly shows the points which give rise to different interpretations.

It is obvious that in doing so we shall be obliged to deal again
with other roots of the cranial nerves in Myxine.

The first deseription of the central nervous system of Myxine
elutinosa was given by Anpurs Rerzivs ?), who mentions three
nerves of the Oblongata, the Vagus, a nerve of the labyrinth (Table
VI le. Fig. 7), a cutaneous branch of this labyrinth nerve (Table
VI, Fig. 8) and several branches of the V (p. 397, 400 and 401.)

After A. Rerzivs, Jonannns MUier’*) gave an elaborate description
of the origin and periferal course of the cranial nerves in Petromyzon,
Bdellostoma and Myxine. For Myxine he gave a description of the
Trigeminus, Facialis, Acusticus and Vagus (comp. Fig. 4, 4 and 6
on Table III |. ¢. 1888).

It is interesting that he mentions a cutaneous branch of the VII
(p. 195 Le. 1838), which still wants affirmation, specially since
Miss Worrnineton *) could not find any but visceral sensory and
Deere Rerztus, Beitrag zur Anatomie des Ader- und Nervensystems der Myxine
Glutinosa (Lin.) (Aus d. Abhandlg. d. KGénigl. Sehwedischen Akademie der Wissen
schaften Jahrgang 1822 H. 2) Meikel’s Archiv fiir Anatomie u. Physiologie 1826
S. 386—404.

2) J. Miitter, Ueb. d. eigentiimlichen Bau des Gehdérorgans bei den Cyclostomen,
mit Bemerkungen itiber die ungleiche Ausbildung der Sinnesorgane bei den
Myxinoiden Abhandlg. d. Kgl. Akad. d. Wissensch. Berlin 1837 (25. LV. 1836),
und: Vergleichende Neurologie d. Myxinoiden, ibidem, 1888 (15. IL. 1838).

3) J. WortHiInaTon: Descriplve Anatomy of tbe Brain and cranial nerves of
Buellostoma dombeyi (p. 169) Quart. Journ. Miser. Science Vol. 49, 1906.

motor fibres in the facial nerve of the American Myxinoid Bdello-
stoma dombeyi.

After Jou. Minter, Gusrar Rerzius') gave very valuable contri-
butions which appeared abundantly illustrated in 1881 and 1893.
It is just the excellent descriptions given by G. Rerzits that show
how difficult the interpretation of this brain is, for G. Rerzius himself
emphasizes at the end of his elaborate description of 1893 (p. 63)
that — though he had been gathering the data concerning the
brain of this animal for several years, he had not yet succeeded in
obtaining a complete idea of its exact relations.

G. Rerzius mentions, as did P. Rérmie in his contribution (1. ¢.),
the absence of the trochlearis, oculomotorius and abducens. The
most frontal nerve roots, according to him, are two trigeminal
branches (p. 60 and Table 24, Fig. 1—3) each provided with a
spindleshaped ganglion.

Following on this he finds a small nerve without ganglion (a
motor nerve consequently) which he considers to be — like Jon.
Miitiwr — the facial nerve. Close to this nerve he finds a third
ganglionated root, which he supposes to be a third trigeminus root
and behind these the two roots of the oetavus occur whieh he had
already described before (1881): the Ramus anterior and ramus
posterior acustici. Mueh more backward the vagus roots appear
without ganglion. Dorsally from these le, however, finds a small
sensory root with an oval ganglion, which he considers to be a
sensory vagus root (p. 99).

After G. Rerzius Sanpers*) took up this subject. Since this work
was not available for us, we can only quote from it what Hon
has cited (Il. ¢. infra).

According to this author Sanpprs found the V, VI, VIII and X
nerves, but differs in so far from G. Rerztus that he considers some
roots entering the brain behind the vagus of Rurzius still as vagus
roots, whilst the latter mentions them as spino-occipital nerves.

It is Sanprrs’ merit to have first given a detailed«deseription of
the oblongata-nuclei, which he divides into two cellgroups of which
one has an entirely central position near the dorsal raphe: “ganglia
centralia’, and another near the perifery of the bulb: “ganglia latero-

1) G. Rerzius. Das Gehérorgan d. Wirheltiere Bd. I, Stockholm, 1881; Ueb. d.
Hypophyse von Myxine Biolog. Untersuchg. Bd. Vi; Das Riickenmark yon Myxine
Biolog. Untersuchg. N. F. Bd. W. 1891; Das Gehirn und das Auge von Myxine
Biolog. Untersuchg. N. F. Bd. V 1893

2) Sanpers. Researches on the nervous system of Myxine glutinosa, 1894,
Williams and Norgate, London.

ventralia”’, the latter of which extending ‘varying in size) from the
entrance of the V to the X.

In Geeenpaur’s Festschrift Fiirprincer') describes the spinal, oeci-
pito-spinal and vagal roots (p. 616 et seq.) and gives a drawing of the
roots of the American Myxinoid : Bdellostoma (Text figure 1). Acecord-
ing to him the vagus leaves the brain with 1—4 rootlets (he
draws 2) and possesses a prevailing motor character (p. 619).

Fiirprincrr states that this also holds good for Myxine. He con-
siders the glossopharyngeus — not mentioned by preceding authors —
1s represented by elements of the nervus pharyngeus X, although
he states that a branchial sack innervated by the LX is failing im
Myxinoids. In other words he grants the absence of an independent
IX, but supposes that elements of it are included in the pharyngeus
branch of the X. *)

FirBRINGuR emphasizes that the spino-occipital roots are shifted in
a frontal direction in Myxine. This holds good as well for his
first sensory spino-occipital root as for his second spino-oceipital
root. The first in his opinion enters the brain on the level of
the ramus acusticus posterior, the second near the level of the vagus
roots. FURBRINGER points cut that, in contrast to Myxine, in: Petromyzon
the spino-oceipital roots are located on a fairly large distance behind
the vagus roots.

This difference between Myxine and Petromyzon, according to
him, can be explained in two ways, either the first spino-occipital
root of Myxine is lacking in Petromyzon, or the spino-oceipital
roots are shifted forward in Myxine. Firprincer believes that the

') FiirBprineer, Ueber die spino-occipitalen Nerven der Selachier und Holoce-
phalen und ihre vergleichende Morphologie. lestschrift fiir Gge@znBAuR Teil IIL 1897
p. 249-766.

We do not deal here with the paper of Ransom and p’Arcy THompson (quoted
by Fiirsrincer) because it contains very little on our subject. Compare: On the
spinal and visceral nerves ef Cyclostomata. Zodlogischer Anzeiger No. IX, 1886
p. 421.

*) We may add here that Miss WortHinGTon, to whom we owe such an excellent
series of papers on the American Myxinoid Bdellostoma, considers this branch as
a real IX (I. ¢ p. 172), “lying so close to the X that it is difficult to distinguish
one from the other’. She also mentions that they have a common foramen and
that (p. 173) “the glossopharyngeus runs in the same sheath with the vagus as
far as the second branchial arch”. Consequently — as far as these points are
concerning — the presence of a real glossopharyngeus is not very conspicuous either
in Bdellostoma nor in Myxine — Since its periferal territory also is fairly well
alrophied — (see the following pages) these arguments for the presence of a IX
seem to be open to criticism, though in a very rudimentary way it may be
present.

o
first is true, and that consequently the first sensory spino-occipital
root of Myxine is lacking in the Lamprey.

We may remark here that, in our opinion, FirBriNcer is mistaken
when he considers the first root here mentioned as being a spino-
occipital one. We are more inclined to believe that in Myxine the
same relation is found asin Bdellostoma, for which Miss Worrninaron
has pointed out that Firericer’s first spino-oce. root is the Acusticus
b, i.e. a lateralis root. *)

The topographical difference in the spino-occipital roots between
Myxine and Petromyzon consequently is not so considerable as Fiir-
BRINGER thought, since the spino-oecipital roots of Myxine do not
reach as far frontally as the acusticus.

Still there is a conspicuous frontai displacement of spino-occipital
elements in Myxine, as appears from a comparison of Fig. 2 with
Fig. 1. In our opinion the transitory region between oblongata
and cervical cord is shifted in a frontal direction.

The vago-spino-occipital region of the oblongata has approached
the trigemino-facial region, the otic and postotie part of the bulb
being reduced. This frontal shifting of the vago-spino-occipital region
of the brain is acecompaniéd by a frontal displacement of the spino-
occipital nucleus and roots, but the vagusroots (see fig. 2) are not
so much displaced as their nucleus and remain behind, perhaps
on account of their lying on the ear capsula.

In consequence the spino-occipital and vagus roots have consider-
ably approached and the vagusroots appear crowded together on the
level of the caudal extremity of the nucleus, instead of being divided
fairly regularly over the level of the whole nucleus as is the ease
in Petromyzon.

That the whole vago-spino-occipital region of the bulb has shifted
frontally and not only the spino-occipital region, appears from the fact
that the spino-oceipital column does not overlap the vagal column
in Myxine more than in Petromyzon. ‘

As already said, this process is accompanied, if not partly caused,
by a reduction of the acoustic region of the brain. That the acoustico-
lateral system in Myxinoids is not very much developed results also
from the researches of Ayrrs and WorTHINGTON *) (see further below).
We shall now proceed to the description of the nuclear topography
of the bulb and discuss at the same time the paper published by

1) Compare: Quarterly Journal of Microscopical Science Vo!. 49, 1906 p. 171
and 175.

2) Ayers and Worruinaron: The finer anatomy of the brain of Bdellostoma
dombeyi I. The acustico-lateral system. American Journal of Anatomy vol. VIII, 1908.

SS -Tl MM-lV &:8-V © VW &e-V BE-K ZZ -X- Bh Spor.

P. ROTHIG (Berlin) and C. U. ARIENS KAPPERS (Amsterdam). Further
contributions to our knowledge of the brain of Myxine glutinosa.

frontal

Nucl. X mot.

Nucl. VII—V mot. Nucl. V mot.
Fig 3.

Myxine glutinosa Sagittal Section. Magn. 30 : 1.

Nucl. V mof.

Fig. 4.
Myxine glutinosa Magn. 20 : 1.

Frontal Section through the frontal part of the motor V nucleus.

Nucl, V mot.
Fig. 5.

Myxine glutinosa. Magn. 20 : 1.
Frontal Section through the middle part of the mot. V-nucl. (caudally from Fig. 4).

Proceedings Royal Acad. Amsterdam. Vol. XVIL.

P. ROTHIG (Berlin) and C. U. ARIENS KAPPERS (Amsterdam). Further
contributions to our knowledge of the brain of Myxine glutinosa.

Nucl. V-VIl mot. Nucl. V-VIl mot.
Fig. 6.
Myxine glutinosa. Magn. 20 : 1.
Frontal Section through the mot. V—VIl-nucleus.

Dorsal Spino-occipital rootfibres

Nucl, VII mot.
Nucl, X mot,

Fig. 7. Fig. 8.
Myxine glutinosa. Magn. 20: 1. Myxine glutinosa. Magn. 20: 1
Frontal Section through the mot. Vil nucl., Frontal Section through the mot. X nucl.
caudally from Fig. 6.

Dorsal.Sp no-occipital rootfibres

Nucl, X mot. ee

é
2
=
Fig 9: Fig. 10.
Frontal Section through the Nucl. X mot. Myxine glutinosa. Magn 20:1.
Magen. 20:1 (caudally from Fig. 8). Frontal Section through the spino

occip. column.

Proceedings Royal Acad. Amsterdam. Vol. X VII

Hotm') on this subject in 1902, which is certainly the best de-
scription as yet given of the motor nuclei in Myxine glutinosa.

Horm points out that tie motor column ef the spinal cord (comp.
our Fig. 10) can be traced frontally in the bulb.

Laterally from it lies the posterior extremity of what Sanpers has
called the lateral or latero-ventral cell group (comp. our. Fig. 9).

Hotm divides this latero-central column of the bulb, which we
shall call the viscero-motor column, into two divisions, a frontal and
a caudal one.

He again divides the frontal division into two, the caudal one
into three subdivisions.

We can only follow him in so far as we also divide the viscero-
motor column into two divisions (see Fig. 2 and Fig. 3) of which
however only the frontal one is again divided into two subdivisions.
The caudal viscero-motor division, in our Opinion, is continuous (see
Fig. 2 and 3 nucl. X mot.) and does not exhibit subdivisions.

Apart from this column Ho_m mentions a group of cells located
next the ventricle in the rostral part of the oblongata from which
he thinks that a part of the motor trigeminus originates. Another
part of the motor trigeminus should originate from a nucleus in the
lateral part of the oblongata on the level of the acusticus ganglion.

The nuclei of the trigeminus thus would be located at a fairly
great distance from each other, one lying near the ventricle, the other
near the perifery of the bulb. (Comp. lis Fig. 20 on Plate 21:
NeIm.N V and Nell m.N Y).

We do no agree with this description, nor with his statements
concerning the motor facialis.

Also the facialis — according to HoLm’s opinion — should have two
nuclei (i.e. p. 389) and from his description it clearly appears that
he considers our frontal motor V nucleus as a VII nucleus, for the
axones of this nucleus — as shown in his drawings — (Fig. 21
Plate 21) constitute the most frontal root of the bulb.

No doubt the two VII roots deseribed by Hom (VIIa and VI1I16)
are V roots, since only this nerve leaves the bulb with two motor
roots *), whereas the motor VII root is single and very small. Our
opinion is confirmed by his description of the corresponding nuclei.

The first Vil nucleus described by this author lies in the frontal
part of the bulb near the perifery, and consists of large cells. His

1) J. EF. Hotm. The finer Anatomy of the nervous system of Myxine glutinosa.
Morpholog. Jahrbuch Bnd. 23, 1902.

*) This separation of the motor V in two roots is only visible near the en-
trance. Soon after it they unite.

second V nucleus according to his description is located in the caudal
elongation of the first, is not completely separated from it and
consists of smaller cells, which description is perfectly in accordance
with the two V nuclei (see Fig. 8) of which the second, con-
sisting of smaller cells and not completely separated from the frontal
nucleus, gives also rise to the VII root. (Comp. also Fig. 4—7).

Like Hotm we were first inclined to consider the second (caudal)
nucleus only as a VII nucleus, but a more scrutinous examination
of the V fibres showed that in this nucleus also the second motor V
root found its origin.

Summarizing we state that the motor V nuclei mentioned by
Horm are no motor V_ nuclei, and that of the two VII nuclei
mentioned by this author the frontal one is a pure V_ nucleus,
whilst the caudal more parvocellular one contains root cells of
the V and VII.

This union of motor V cells and VII cells is in perfect harmony
with the condition found in Petromyzon (comp. Fig 1), where the
motor VII cells also form the caudal continuation of the V nucleus
and are a little smaller.

Since we only wish to deal with the motor nuclei in this de-
scription, we shall pass the acustico-lateral system, which for the
American Myxinoid Bdellostoma dombeyi has been so minutely
described by Ayers and Worrnineron *) and proceed to the motor
X nucleus of Myxine.

It is obvious that, without an examination of the periferal nervous
system and its muscles, the question of the presence or absence of
a motor glossopharyngeus cannot be settled.

We can only state that our researches show a reduction of the
number of root fibers of the motor X group, which in Myxine only
consists of 3 of 4 rootlets, whereas in Petromyzon it contains
together with the glossopharyngeus at least 5 rootlets.

This combined with the fact that the posterior visceromotor column
has suffered a reduction in its frontal part is in harmony with the
opinion defended by Jounsron *) that the glossopharyngeus and perhaps
even the first motor X root sensu strictiori are either very much
reduced or absent. A comparison of Fig. 1a and 2a shows that this
reduction is only probable for the frontal pole of the column,

1) Ayprs and WortHINGToN: They finer anatomy of the brain of Bdellostoma
dombeyi. I. The acustico-lateral system. American Journal of Anatomy Vol. VIII,
1908.

*) Jounsron: Note on the presence or absence of the glossopharyngeal nerve
in Myxinoids. Anatomical Record Vol. Il, 1908,

2a.

“u~
DC SOC

Showing the reduction in the frontal part of the vagal column.

since the overlapping of the caudal part of the vagal column and
spino-occipital column, as well as the topography of the posterior
extremity of the vagal column to the spino-occipital roots, are the
same in both Petromyzon and Myxine.

The reduction of the roots and of the frontal part of the vagal
column in Myxine is also in harmony with Srockarpb’s observation
that in Myxinoids, at least in its American form Bdellostoma, the
branchial sacks behind the hyomandibular arch are atrophied. *)

The vagal column begins fairly near the posterior extremity of
the mixed V—VII nucleus, lying in a somewhat more dorsal position
(Comp. Fig. 3,7 and 8). A few seattered cells lie between them, thus
constituting a sort of broken link.

The size of the vaguscells is considerably smaller than that of
the frontal V nucleus, more like the cells of the mixed V—VII
nucleus, specially the smaller caudal cells of the latter.

In its frontal part.the vagus nucleus is rather small and the cells
do not attain their largest size here. The nucleus as well as the
cells attain their maximum development in the middle part. We
have not been able however, to state a division of the nucleus in
three parts as Hoxm did.

1) SrockarRD: The development of the Mouth and Gills in Bdellostoma Stouti.
American Journal of Anatomy Vol. V 1906, specially p. 511 and fig. 35—3s6.
Compare also for further knowledge of these animals :

Ayers. Bdellostoma dombeyi. Woodshole lectures for 1893.

WortTHINGTON. Centribution to our knowledge of the Myxinoids. American
Naturalist Vol. 39, 1905.

On the other hand we agree with Hotm that the small ventro-
lateral root that leaves the bulb in the posterior part of the vagal
region and is considered by SanpErs to be a vagalroot, is certainly
a spino-oceipital one (Cf. Hotm p. 395), as much on account of its
position as on account of its central connection. —

That the spino-occipital column extends for a short distance in
the vagal region is a general feature in vertebrates and has been
shown before to occur also in Myxine by Epinerr *) (I. ¢. p. 28).

We also agree with Hoim that the dorsal sensory root entering on .
this level is a sensory spino-occipital or spinal root and not a sensory
Vagusroot, as results from the facts 1. that the size of its fibres
corresponds with those of the sensory spinal rootfibres, 2. that the
line of entrance and the ascending character of the fibres during
their intramedullary course are the same as in the spinal sensory
roots and 3. because they are joined by the latter during this
course.

Finally we wish to call attention to the fact that not only the
topography of the uuelei, but also the general morphology of this
brain shows the compression which the brain has suffered.

Similar to the other ventricles of the brain the 4" ventricle is
reduced to a minimum. This is complicated by the peculiarity that
the caudal end of the midbrain (a cerebellum does not occur in this
animal) protrudes a considerable distance between the dorsolateral
walls of the oblongata and is so closely adjacent to it that ouly the
pial membrane can follow it. Behind the caudal extremity of the
midbrain the dorsolateral walls of the oblongata unite.

One cannot speak here of a real calamus scriptorius caused by a
widening of the ventricie itself. The lateral deviation of the walls
takes place only under the influence of the midbrain, but the 4t
ventricle itself remains a small split underneath it. The dotted arrow
in figure 2 indicates the place of this pseudo-calamus. Since in this
animal, with atrophic eyes, there is no question of an enlargement
of the midbrain being the cause of this telescoping, the only reason
of it can be found in the compression of the whole brain in its
longitudinal axis, which is also exhibited by the approach of the
vago-occipital part of the oblongata to the trigemino-facial part.

This longitudinal compression probably finds its chief reason in
the pressure exercised on the frontal part of the brain by the
olfactory pit and dorsal lip, the influence of which on the form

1) Epryaur: Das Gehirn von Myxine glutinosa. Abhandlungen der Preussischen
Akademie der Wiss. 1906.

11 ‘

of the brain in Cyclostomes is already mentioned by Scorr ‘) in
Petromyzon.

As stated above, the telescoping is the more obvious in the
oblongata on account of the reduction in the acustico-lateral system
of the bulb.

Everything indeed shows that in Myxine we have to do with
considerable secondary modifications.

Also the topography of the motor nuclei is by no means a primi-
tive one.

The primitive location of the V, VII, and X nuclei in Cyclostomes
is near the ventricular ependyma where the matrix of the nerve
cells is, and where they are still found in Petromyzon. In Myxine,
however, the V—VII nucleus has a ventro-lateral periferal position
and the X nucleus a lateral periferal position, a condition that can
only be caused by secondary influences originating in the functional
reflectory relations of this animal.

The influence which has caused this secondary position is certainly
the considerable development of the descending sensory V, which
has a dominating influence on the structures of the oblongata, an
influence which is the more prevailing since the other sensory and
reflectory paths are either atrophied or poorly developed in this
animal. We know that in animals with a well-developed dorsal
viscero-sensory nucleus the motor vagal column generally has a
dorsal position, adjacent to its sensory grey (Selachians), which is
still the case even in Petromyzon.

On account of these facts we cannot agree with Hotm in his
statement that Myxine has a more primitive character than Petro-
myzon.

Summarizing our results we conclude :

In Myxine the eye-muscle nuclei are absent.

The motor V nucleus is incompletely divided into two parts corce-
sponding to the central division of the motor root into two parts.

In the continuation of the caudal V nucleus also the motor VII
cells are found, as is also the case in Petromyzon. These nuclei have
a ventrolateral position very near the concomitating grey substance
of the sensory root. A central V nucleus (Hotm) has not been found.

The posterior viscero-motor column, and also the spino-occipital
motor column has shifted considerably frontally. By the adjacency
of the earecapsule this shifting could only be partly followed, by
the motor X roots, which are crowded together on the earcapsula.

') Scorr. The embryology of Petromyzon. Journal of Morphology Vol. 1, 1887

The spino-oceipital roots have, however, followed the shifting of their
nucleus and have come very near the vagus roots.

The posterior viscero-motor column is considerably shortened at
its frontal extremity, which most probably results from the
absence or extreme reduction of the motor IX, and perhaps even
of the frontal motor X root (JOHNSTON) in connection with the absence
or reduction of the two posthyomandibular branchial sacks (Stock aRD).

Physics. — “Further experiments with liquid helium. J. The imitation
of an Ampbee molecular current or of a permanent magnet by
means of a supra-conductor.” Communication N°. 1046 from the
Physical Laboratory at Leiden. By Prof. H. KamErtinen OnnEs.

(Communicated in the meeting of April 24, 1914).

§ 1. lntroduction. If a current is generated in a closed supracon-
ductor, from which no other work is required than what is necessary
to overcome the possible remaining micro-residual resistance of the
conductor, it follows, from the small value that the micro-residual
resistance can have at the most, that the current will continue
for a considerable time after the electromotive force that set it in
motion has ceased to work. The time of relaxation + in which
the current decreases to e-!t of its value is given by the ratio

of the self-induction Z and the resistance 7 of the circuit. When
s
r approaches zero, this period may rise to very high values. Whereas
the time of relaxation is extremely small in ordinary cases (for the
coil with which we are about to deal for instance, of the order of
a hundredthousandth of a second) when the resistance in the supra-
conducting condition becomes say 1,000,000 or even 1,000,000,000
times smaller it may increase so much, that the disappearance of
the current can be observed ; it may even take place extremely slowly.

From the moment that [ had found in mercury a supra-conductor
at the lower temperatures which can be obtained with liquid helium,
I was desirous to demonstrate the persistence of a current in a con-
ductor of this kind, and amongst other things to take advantage of
it in the further investigation of the microresidual resistance of the
supra-conductor '). But it was only after the previous study of various

1) For the sake of brevily we use the word resistance here in the sense of
quotient of potential difference and current strength. In supra-conductors (see
Comm. No. 133) we can at present only speak of current and potential difference ;
whether the relation between these two can be expressed by means of the concep-
tion of specific resistance, has still to be investigated. (Comp. note 1 § 3),

problems, which were also of value for the knowledge of the con-
ditions which had to be considered, that I arrived at the simple
experiment which I am now able to deseribe, and whieh confirms
what I have adduced in a convincing way.

For this experiment a conductor was available whose constants,
in so far as they were needed in designing the experiment, were
known: I refer to the coil of lead wire Phx which has several
times been mentioned in previous papers. A thousand turns of lead
wire of ‘/,, sq. mm. in section are wound on a small brass tube
of 8 mm. in diameter in a layer 1.1 em. thick and 1.1 em. lone.
At the ordinary temperature the coil has a resistance of 734 2 and
as the inductance is I milli-henries, the relaxation time may be put
at about 1: 70000 of a second. The micro-residual resistance at 1°.8 Kk.
had been found to be more than 2 > 10°° times smaller than the
resistance at the ordinary temperature ; the relaxation time therefore
must be at least of the order of a day. The limit to which the current
may be raised before ordinary resistance is suddenly generated, had
also been determined ; at 1°.8 K. this limit was 0.8 amp.; it is clear
that a lower current than that is sufficient to make the coil into a
powerful little magnet. Finally the threshold value of the magnetic
field, below which no resistance is produced in the coil was known :
at 1°.8 K. it had been found to be about 1000 gauss. It was ascer-
tained (ef. § 3), that if was unnecessary to use a field of that strength
to be able to make the experiment by means of generating a current
by induction in the conductor. The conductor after having been tested
as to its superconductivity had to be closed in itself in a supereon-
duetive way. This was effected by fusing the ends of the lead wire
together: in previous experiments it had been found, that this treat-
ment did not lead to the production of ordinary resistance. In view
of all the data I could be assured, that all the conditions necessary
for the suecess of the experiment were fulfilled.

§ 2. Arrangement of the experiment. The coil was fitted up in
the same eryostat which had served for the previous experiments
with the plane of the windings vertieal in such a manner, that it
could be raised and lowered, as well as turned round a vertical
axis. Fig. 1 shows the arrangement diagrammatically.

As the coil was closed the current in it was generated by induction.
A large Wuiss-electromagnet, at hand for the experiments of Comm.
N". 140d could be moved on casters towards the cryostat to a position
in which the cryostat with the coil was in the interferrum,

In order to obtain an unambiguous result it is advisable to be

able to test the magnetic condition of the coil while no other magneti¢e
objects are in the neighbourhood; it is also necessary to prevent the
induction currents which are generated when the field is produced
and when it disappears from partly or completely neutralising each
other (cf. § 4). .

It can therefore be easily seen that the follow-
ope ing procedure is advisable: the field is put on,
while the coil is in the cryostat at the centre of
- the interferrum, everything being prepared for
|| siphoning the liquid helium into the eryostat.
| The current generated at the production of the
field is then immediately dissipated by the ordinary

| | resistance of the coi before the helium is poured
over. Care is taken to keep the field below the
threshold-value of the production of ordinary
resistance, which holds for the temperature at
which the experiment is going to be made. The
coil is then cooled by letting in liquid helinm,
the field remaining unchanged. In this manner a
supra-conducting coil is obtained, closed in itself
- without a current placed in the magnetic field.
If the field is now put off and the apparatus
which have produced it are removed, a current

a will remain in the coil which is smaller than or
in the limit equal to the threshold-value corre-
sponding to the temperature of the coil. The presence of this current
can be established by its magnetic action outside the cryostat.

In order to obtain a strong current it is advisable te cool the
coil as far down as possible, as thereby the threshold-value of the field
to be used for the induction and the threshold-value of the current
are both made as high as possible. Fer that reason the first experiment
was made at a temperature of 1°.8 kK, the towest temperature which
can be reached comparatively easily and maintained for a long time.

§ 3. Culeulation of the experiment. Assuming that the field
diminishes proportionally to the time ¢ from //, to O and ealling J/
the magnetic potential of the coil in the field //, “will be constant

during the period of the disappearance of the field and the equation’)

!) Here is supposed that 7 is independent of 7 below the threshold value ip of 7.

with 70 at the beginning gives

1 dM — 3
EAM bites ).
r dt

‘i
and for small values. of and ?¢, as lone as J/ has not reached

zero, With sufficient: approximation
| 1 aM

= (Fe)
Ts it

so that, if M/ reaches O while ¢ is still small,

will be the final value of the current.

In our experiment the constants were //, = 400, J/,= 1,26 10°,
L=10', so that 2 could rise to 0,126 C.G.S. or 1.261) Amps.
The current can therefore reach the threshold-value 0.5 Amp. even
with a field of rather more than half the strength assumed in the
caleulation (cf. one of the experiments in § 4). From the moment
at whieh this value is reached ordinary resistance appears and i
will be no longer small; the further increase of 7 above the threshold
value zp follows a different law from below 7p.

For an aecurate calculation of the process above 7p, it would
be neeessary to take into account the complicated law of imerease
of the resistance with the current beyond 7p. For our purpose it
is sufficiently accurate to assume, that when 7p is exceeded by a
small amount, the resistance becomes suddenly 7 of the order of
magnitude above the vanishing point.

dM .e
In that case, a remaining the same as before, the current will
aL
aw \duw
be able to rise by a small amount ¢—ip = — a whieh will soon
yr

dM
be reached, will then become constant and, on J/ and ar becoming
td

zero, disappear again in a short time. In view of the value of J/
and r’ we may, if J/ does not change very rapidly, disregard <—7p,
unless we intend an explanation of all the details of the experiment,

We therefore come to the conclusion, that, J/, being sufficiently

') The more accurate data given here differ somewhat from those in the Duteh
text.

large, the current (Fig. 2) on M diminishing to O will reach the
threshold-value, belonging to the temperature of the experiment, and

Fig 2. Fig. 3.

after the induction being completed will continue, while only after
a long time /# according to the relation

in accordance with the large value of the time of relaxation —
T

an appreciable diminution of 7 will be observed.

The ease, that the initial value of J/ is above the threshold-value
of the production of resistance Mp, is represented in Fig. 3, which
after the foregoing needs no special elucidation. The result is ap-
parently again dependent on the threshold-value of the current (see
also one of the experiments in § 4).

As appears from the values given above an initial field much
smaller than J/, was sufficient in our experiment.

According to the above calculation it was to be expected, that
the examination of the magnetic action of the coil could be per-
formed with a simple compass-needle broughi near the eryostat.

§ 4. Details of the observations. The result proved the correctness
of the discussion contained in the previous sections. The field was
taken at 400 gauss. In 10 seconds it was reduced to 200 gauss
and immediately afterwards the electromagnet was rolled away in
5 seconds. The compass-needle which was then placed beside the
cryostat to the East of it on a level with the coil and ata distance

from it of 8 ems pointed almost at right angles') to the meridian.
When the action on the magnet was compensated by means of a
second coil placed on the other side (West) of it of about the same
dimensions as the experimental coil and of 800 turns, it was found
that the coil was carrying a current of about 0.5 to 0.6 amp. *).
This was further confirmed by turning the coil and by moving the
compass-needle to various positions about the cryostat *). During an
hour the current was observed not to decrease perceptibly (as far
as could be judged by the deviation of the needle with an accuracy
of 10°/,). During the last half hour the coil was no longer at
1°.8 Kk. but at 4°.25 K. the temperature of helium boiling under normal
atmospheric pressure. Undoubtedly even at this temperature the
observation might bave been continued much longer without much
diminution of the current. A coil cooled in liquid helium and provided
with current at Leiden, might, if kept immersed in liquid helium,
be conveyed to a considerable distance and there be used to demon-
strate the permanent magnetic action of a supra-conductor carrying a
current. | should have liked to show the phenomenon in this meeting
(Kon. Acad. Amsterdam), in the same way as I brought liquid
hydrogen here in 1906, but the appliances at my disposal do not
yet allow the transportation of liquid helium.

Whereas the experiment, so far as described, shows, that a current
when started in a supra-conducting wire continues to flow, the
process is immediately stopped as soon as ordinary resistance is
generated in the circuit. When the coil is lifted out of the helium,
the current is instantaneously destroyed. The temperature of the
coil is thereby very quickly raised above the vanishing point of
lead (6° K) and the very long relaxation-time is replaced by a very
short one. Reimmersion of the coil, if not too soon after the lifting
out, does not again produce magnetic action.

If the experiment is made with the windings of the coil parallel
to the field, no effect *) is to be expected. This expectation was in so
far confirmed as only a slight effect was observed: this effect cau

1) The field of the earth being distorted by machinery the action of the latter
was compensated by magnets and there resulted a weaker field (note added in
the translation.)

2) [Calculated from the moment, comp. N®. 140d § 8, end. Added in the trans-
lation}. The coil has a magnelic moment of about 180 C.G.S. and behaves as if the
lead possessed remanent magnetisation of some 200 C.G.S. units.

8) On repeating the experiment at 4°.25 K. nearly 0.5 amp. was obtained; a
later experiment with larger initial field at 2°.3 K. gave 0.7 amp. (see further down).

') Nearer consideration points to a small effect Comp. N°. 140c (Note added in
the translation).

Proceedings Royal Acad. Amsterdam. Vol. X VIL.

be sufficiently explained by assuming that the attempt to place the
windings exactly parallel to the field had not sueceeded. *)

If the initial value of the field is higher than the threshold-value,
Mp the result is the same. Tlus case is represented in fig. 3. In
one experiment the initial field was 5000 gauss and the observed
magnetic moment corresponded to a current ¢ = 0.7 amp.

If the field through the supraconducting coil is first put on and
subsequently put off again by bringing the excited electromagnet
to its position at the cryostat and then removing it, according to
the above reasoning (disregarding the exceedingly slow diminution
with the time) no resultant current ought to remain, if no account
had to be taken of the threshold-value of the current. Indeed for
Gre Sa! gale ; :
the second period the relation 7—7,e ° = a holds, if ZL is

7 the current obtained in the
) 3 5 .
3 first period during the gene-

ration of J/,. This case will
be realized, if care is taken,
that the threshold-value of
-ig fa -==--b == 7 ~- = the current is not exceeded.
7 It is represented in fig. 4
by the lines which give the
field J/5 and the current

7, as funetions of the time.
If during the increase of

M = the threshold-eurrent is
reached, the current will not

grow appreciably on further

Fig. 4.

rise of J/; from the moment,
that the inerease of J/ stops, the current assumes the threshold-value
and stays there, until J/ begins to decrease: it then begins to fall
and becomes zero, before the field has disappeared; on the further
diminution of the field, the current assumes the opposite sign and
the resultant current will be that whieh has been formed at the
moment that J/=0, if it remains below the threshold-value, or the
threshold-current itself, if that is reached before J/ has disappeared.
In the latter case the current will exceed the threshold-value by

') This expériment had been made some says before the main experiment, although
it had not been the intention to make it with that position of the coil. So far it
has not been repeated. At the moment of making this first communication it had
not been repeated. [It has been repeated since; again a rest was found, (Note
added in the translation. Comp, Gomm. N°. 140c)].

a very small amount from the moment, that the threshold-value is
reached, until J/ = 0. In fig. 4 this case is represented by the lines
which give the relation between the field J/, and the current Za.

An instance of the case represented by a is given by an experi-
ment, in which the field brought to the eryostat was 400 gauss. A
strong resultant current was observed as in the ease, when the coil
was first free of current in the field of 400, was then made supra-
conductive and was finally charged with current by the removal of
the field. An instance approximately corresponding to case was
obtained, when the same experiment as @ was carried out with a field of
190 gauss. Even in this case the compensation was not quite complete
and a little more favourable. when the field was made to approach
slowly, than with a rapid approach.

With a rising field account has to be taken also of the compli-
cation arising out of the influence of the field of the current itself on
the threshold-values of the field and current. In fact this was not the
only feature in the experiments which could not be fully explained
yet: naturally as they were performed for the first time, the arrange-
ments were still imperfect '). Taken together however they may be
said to confirm the main experiment which shows that it is possible
in a conductor without electromotive force or leads from outside *)
to maintain a current permanently and thus approximately to imitate
a permanent magnet or better a molecular current as imagined by
AMPERE.

The electrons once set in motion in the conductor continue their
course practically undisturbed, the electrokinetic energy, represented
by Maxwet1 by the mechanism of the rotating masses coupled to
the current, retains its value, the rotating fly-wheels go on with
their velocities unchanged, as long as no other than supraconductors
come into play: the application of a small ordinary resistance
however stops the mechanism instantaneously. Although the experi-
ment mainly confirmed my deductions as to what had to be expected,

1) One of the first questions still to be answered is, what part a possible magnetisation
of lead or brass may have played in the phenomena: so far no proof las been
given, that this may be neglected. However, even now from the experiment, in
which the windings were parallel to the lines of force, we may draw the conclusion,
in view of the small amount of the action in that case, that the magnetisation
of the material of the coil can only play a very subordinate part compared to the
electromagnetism of the current, to which I have above ascribed the deviation of
the compass-needle.

*) It may be mentioned here, that it will be possible, by a change of tempera-
ture of a small part of the conductor, to insert a resistance in the circuit which
can be very delicately regulated without touching it.

)%*

a deep impression is made by the very striking realisation which
it gives of the mechanism imagined by MaxwrLi completed by the
conception of electrons.

It is obvious that the subject will lead to further discussions *)
and plans, but in this paper 1 may be allowed to confine myself to
the simple description of the experiment carried out.

Physics. — “The chemical constant and the application of the
quantum-theory by the method of the natural vibrations to the
equation of state of an ideal monatomic gas.’ By Dr. W.

H. Kuvsom. Supplement N°. 364 to the Communications from
the Physical Laboratory at Leiden. (Communicated by Prof. —

H. IK AMERLINGH ONNws). -

(Communicated in the meeting of March 28, 1914).

§ 1. In Suppl. N°. 33 (Dee. 1913) the expression for the entropy,
S, of a gas was discussed, as it follows from the application of the
quantum-theory to the molecular translatory motion by the method
of the natural vibrations. Molecular rotations and intramolecular
motions were not taken into account there. As was observed, the
chemical constant is connected with the additive constant which
occurs in the development of S for high temperatures. The object
of this paper is to show that the value of the chemical constant,
which in that manner is deduced from the expression for the entropy
(an expression which had already been given by Trrropg), is in
satisfactory agreement with values of this constant which correspond
to the experimental data concerning vapour pressures of monatomic

OAcaS
gases.

§ 2. We shall confine ourselves in this paper to the consideration
of monatomic gases. If for the energy distribution one of the tem-
perature functions is assumed which occur in the quantum-theory,
one may suppose that the molecular rotatory motion, particularly
for the molecules of a monatomic gas, is in thermal equilibrium
say with the translatory motion. If in particular that temperature
function (given by Pranck) is assumed which implies a zero point
energy, the molecular rotations in a monatomic gas also, at the
temperatures at which they have been investigated, represent a con-
siderable amount of energy in proportion to the molecular trans-

1) Compare also MAXWELL, Electricity and Magnetism Il, Ch. VL.

latory motions. The characteristic temperatures (@,, ef. Suppl. N°. 382),
which according to that hypothesis govern the rotatory energy, are,
however, owing to the small moment of inertia of the monatomic
molecules, so high, that at the temperatures mentioned the energy
of rotation of the molecules does not yet deviate appreciably from
the corresponding zero point energy. The same applies to the motions
within the atom. The contributions to the entropy due to these
rotations of and motions within the atom may then be counted as
zero. We limit ourselves to the temperature range within which this
is the case’).

We shall further assume that we are dealing with an cdeal
monatomic gas, so that terms due to the influence of the real
volume or of the mutual attraction of the molecules need not to be
considered.

The entropy of such a gas is then, on the basis of the hypot
of Suppl. N°. 30a, determined by the expressions given in Suppl.

N°. 33 § 2a.

heses

§ 3. In the first place, as was already observed in Suppl. N°. 33
§ 2af8, the introduction of the zero point energy makes no change
in the value which is found for the chemical constant. Hence a
comparison of the value calculated for this constant, e.g. with the
value which was found by Sackur to agree with experimental data,
cannot furnish a test between PLANck’s formula with or without
zero point energy ’*).

§ 4. If the development of S for high temperatures: equation (14)
Suppl. N°. 338, is written in the form

S=C,4+ Nklnv + */, NklnT +

1
-+ terms of smaller order of magnitude ()

then
C= Na(4 a Ina), Tera ees (2

1) According to measurements by Pier of the specific heat of argon, this tem-
perature range extends for this gas to at least 2300° C. As Prof. Euysrein pointed
out in a discussion, the investigation at high temperatures of the specific heat of
a monatomic gas with high atomic weight, such as mercury, would be of great
interest.

2) Prof. SOMMERFELD asks me to say, that he wishes the sentence: “Nebenbei
sei bemerkt etc. on p. 139 of: Vortriige tiber die kinetische Theorie der Materie
und der Elektrizitét,’” Leipzig und Berlin 1913, to be omitted.

From equation (13) of Suppl N°. 83 with equation (187) of Suppl.
N’, 30a it follows that

3k? (42 7s
(= saa (Gx) oh Oe re
Krom these formulae. follows for the entropy constant
C, = NE 4 a eee (aa) {- oo, ul On Re
9 Nh? \5Nk

With the values V = 6.85.10** (according to Perrin), 4 = 1.21.10 1°,
h

kh
(4) with WA = PR passes into

= 4.86.10°"', which were accepted in Suppl. N°. 30a, equation

0, =n |= in M— 7.48) . se Sees

If we take MiiiKan’s?) values V=6.06 .107, £=1.87 .10-“,
h
; — 183.107 "", we find

M — 7.285 (5b)

For the chemical constant Cyp, which is derived from C, by
means of the relation *)
é C, — 2.5R + R In Nk
CAS ae Rint

we find

Oni = log M +- 3.60 Pee) el ee (6a)

and in ¢.g.s. units

Crus = 5 log M + seal SE SG (60)

respectively.

These values differ from those which Sackur has compared with
the vapour pressures of mercury and argon and which he found
fairly well confirmed, only by 0.85 and 0.28 respectively. This
agreement may be called very satisfactory considering the uncertainty
which yet exists with regard to several of the quantities used in
that comparison on the one hand, and the approximate character of
some of the hypotheses on which the deduction of the expression
for the eninopy was founded on the other hand.

1) ne aa Miuurkan, Physik. ZS. 14 (1913), p. 796.
2) Gf. O. Sackur, Ann. d. Phys. (4) 40 (1913), p.

§ 5. The relation (4) also follows from equation (19a) of the
paper by SommurreLp (p. 134), quoted in note 2 p. 21, if@ occurring

10
there is put equal to ioe as has been supposed in the relations (3)

and (4) given above, and if in SomMmrrELD’s expression /: is replaced
by 4 A'). The latter change is connected with the fact, that in
deriving the expressions given here the supposition was made that
in considering the molecular translatory motion in an ideal monatomic
gas we have to deal with energy elements of a magnitude } hy, as
we tried to make probable in Suppl. N°, 30a § 2.

The fact that in § 4 a satisfactory agreement with experimental
data was obtained, may, if the validity of the other hypotheses is
admitted as sufficiently approximate, be regarded as a confirmation
of the above supposition concerning the magnitude of the energy
elements.

Astronomy. — “On Sevnicer’s hypothesis about the anomalies in
the motion of the inner planets.” By J. Wourinr Jr. (Com-
municated by Prof. W. pe Srrrer).

(Communicated in the meeting of April 24, 1914).

To explain the differences between observation and calculation in
the secular perturbations of the elements of the four inner planets,
SEELIGER *) worked out the hypothesis that these are caused by masses
of matter, which by reflection of sunlight offer the aspect of the
zodiacal light. He imagines these masses to have the form of a flat
dise surrounding the sun and extending nearly in the direction of
the orbital planes of the planets and reaching outside the orbit of
the earth; the density of the matter within the dise has its greatest
value in the proximity of the sun, though it is very small even there.
For the calculation of the attraction of the mass of matter special
hypotheses on its constitution are introduced; we imagine a number
of very flattened ellipsoids of revolution with the sun at the centre,
the inclinations of the equatorial planes to the orbital planes of the
planets being small. It is evident that by the superposition of a number
of such ellipsoids we get a flat dise within which the density varies

1) This confirms at the same time the fact, that the introduction of the zero
point energy does not produce a change in the value of the entropy constant.

2) Das Zodiakallicht und die empirischen Glieder in der Bewegung der innern
Planeten, Sitzungsberichte der Bayerischen Akademie, XXXVI 1906,

after a certain law from the centre outwards. SeenigEr arrived at
the conelusion that two ellipsoids suffice, one of which is wholly
contained within the orbit of Mercury, the other reaching outside
the orbit of the earth. There appears to exist a certain liberty in
choosing the values of the ellipticities and the quantities determining
the position of the second ellipsoid. As quantities to be determined
so as to account for the differences which are to be explained
SrvLiceR introduces the densities of both ellipsoids, the inclination
and the longitude of the ascending node of the equatorial plane of the
first ellipsoid with reference to the ecliptic, and a quantity not con-
nected with the attraction of the masses of matter, but relatiug to
the deviation of the system of coordinates used in astronomy from
a so called “inertial system”.

Last year Prof. py Sirrek drew my attention to the necessity
of festing Sepiicer’s hypothesis by calculating the influence of the
masses admitted by Seeriger on the motion of the moon and the
perturbation of the obliquity of the ecliptic, which Srerierr did not
consider’). | performed the calculations and arrived at the conclusion
that the perturbation of the ecliptic changes the sign of Nswcomp’s’)
residual and makes its absolute value a little larger; further that
the perturbations of the motion of the moon are insensible. I may
be allowed to thank Prof. pr Srrrer for the introduction into this
subject and the interest shown in its further development. — One could
take the formulae required for the last mentioned purpose from
Surnicur’s publication; I did not do so, but developed them anew.
I give them here on account of small differences in derivation. First
I shall give this derivation and the results; after that I shall do
ihe same for the motion of the moon.

I. Perturbations of the ecliptic.

Let x,y,z be coordinates in a system the origin of which is at
the centre of the ellipsoid, while the axis of rotation is the axis of
z, kh? the constant of attraction, g the density of the ellipsoid, a, a
and ¢ its axes, then the potential V at the point w, y,z is given
by the expression :

f= barge | 1.— = == ———y
‘ Vtu c+u/) (a+tuwye +u

1) See pe Sirrer, the secular variations of the elements of the four inner
planets, Observatory, July 1913.
2) Astronomical Constants p. 110,

No
ur

for a point outside the ellipsoid 4 is the positive root of the equation

vty? ae P
qa ee = 0; for a point inside A is zero.
ata c aE

Z* 77 we have:

Putting V = k’nqa’c2 and #+y?'+2=r

ae > 1 rT z*(a?—c’) du
ae, =| ( atu “Sass, (7+ SE ana a
" aa’ —c*)

Ta) Gea)

Perturbations caused by the jirst ellipsoid.
I develop in powers of 27 =, § being a small quantity ; for that

purpose we need (neglecting terms of the third order) :

(= Ey An of du ks
OS) hae (a* (a? +-u)? (c? +u)'l2

r—a*

?Q Pe (a?—c’)?
0c? es r(r?—a? + cy ile :

I put r=a,(1+ 8) and develop the part of $2 independent of
$ besides the coefficients of the different powers of § in powers of §

Introducing the quantities :

o.=f- = du C of du
(a? +- eae @+ wu)” Vay : (a° + w)*(c? --u)"h
a,*—a* ;2—a? a,?—a?
a 2 A oe} a," —=
a*— a’+c=p ax 7
we get
>) y 5° 2 2 3°
2=C,—4/C, — str@rerarG) Oh —gats tile
1 1 1 NES _v—c* eA Anes A eas
aMGachia Yate ach 6 Cee pp ost (- 9 —3y)s +
2 2 P a,"p
Per z 27 1) SOLE Ns
ae (Esa On ae Wace ar i= a a a ag ee 8 sla
1 JG Cu)a
bh
2 Co Ie

Let v be the true anomaly of the planet, y the angular distance
between the ascending node of the equatorial plane of the ellipsoid
on the orbital plane of the planet and the perihelion of the orbit

J ihe inclination of the equatorial plane to the orbital plane, then
we have
z= — a, (14+ §)sin(v + W) sin J
S=a,?(1 4 §)? sin? (v + wy) sin? J.

For the ecaleulation of the secular portion of the perturbative
function we thus need the secular portions of §”, §? sin? (v + yw) and
sin'(v-+ wp) for different values of p. I get (denoting the secular

portion by the letter S):

mt é 4 é? Aye 3 bs 3
co Si 5 SS re Se
sin? (v + w) =~ — Ge + gt ore
8 6
§ sin® +m = pe(1—perrw) + Georre
2

1 1 1
S § sin? (v + yw) = rn é? (: — 5 008 2 v) =6 e* cos 2 wy
@ za 3 1 A
538 , =— i — 0) S Z
S §* sin? (v + w) = e* 6 are cos 2 W

3 1
S § sin? (v + pw) = e* ae:

S sin’ (v + py) =

Substituting in the expression for £2 we find :

ae e? 3 ee ée 1 1 ome
Soars ae ae e ace ) > ( io. 6a aa

P a
: v—ec oe i 1 a A A 3 3 3 aa
| at sin? J 15) Ci ap +e To ae Y— i C,a,7p* +
v 3 5 j ‘ ae 9 ee)
tyr CO8 SDI agate pn sae aa gat t+ go?

105

1 ee 3 25 35 ‘| 3 (w@’—c?)? ip
= cos2y | — = 4
rie tn 39° ral Tete a sin

Let 7, © and § be the inclination, the Ne: of the perihelion
and the longitude of the ascending node of the orbital plane of the
planet, /, and ® the inclination and the longitude of the node of
the equatorial plane of the ellipsoid all with reference to a fixed
fundamental plane, e.g. the ecliptic of a certain epoch ; then we have:

sin J cos (W-— w + 9) = — cos J, sini -} sin J, cos i cos (§4 — P)

sin J sin(w — & + QQ) = sin (84 — &) sin J.

E ; Ad Ee ; 0S OJ Ow Oy,

From these expressions we can determine ag a Ope i the
quantities required for the computation of the derivatives of 2 with
regard to these elements. In view of the calculation of the perturbation
of the obliquity of the ecliptic I do not use the elements 7 and {),

but the elements p and gq thus defined :

p=tanisin §% 7 = tani cos §%
I get:
ay Z ale 2, Seat) )
— = cost | cos? — sin (yw -— @) + sin? — sin (w — wo + 2Q)
Op 2 2 {
Oc
ca ae 3? = e083 (wy — @) — sin* = cos ( — @ + 29)
q
Ow
Shae =sin Ftan © eosieos Qt cosJeosi cos + cosy )-+sin? “ cos(tp- 0+29)) \
P
mee, Pt ee Ree eerie aay eee See
stn. eae tan Sie aac! cost} cos ee SO) ae 5 eintp-O+ 28) ;
The differential equations for p and q are’):
dp _ 1 OV
dt na,2V 1—e*cos*i 99
dq l OV
dt na,*V 1—e’?cos*i Op

To verify these formulae I have used them for the computation
of some of the perturbations of 7 and §), which are given by
SEELIGER °).

To compute the perturbation of the obliquity of the ecliptic I take:

Sued

V = — k*xqa’e (a*—c’) C,a,’

According to SeeiicEr’s data a= 0.2400, c = 0.0239, J=6°57'.0
I get C,=0.426; taking as unit of mass the mass of the sun, as

unit of time the mean solar day I get log ¢ = 0.7119 — 5 and |
find :

') TisspRAND, Traité de Mécanique Céleste I p. 171.

, di : ete AG) ’ . :
*) For Mercury I get: — =+0%.573; sini —-? — — (049; SEELIGER gives:

li 1°),
+ 0.574 and — 0.049. For Venus I get: - = + 0".163; sin is. = + 0”.091;
¢

SEELIGER: + 07.159 and + 0.088; the small difference is owing to the value I
get for C; = 2.286, while from SsELIGER’s data follows Cy = 2.217.

OV 2) C. ain J au 0.5986-8 OS
= — 53 3 ge 20 (—Ca O 8 108 — = od 5 y— ;
) mrga7e (a°—e 4, Sued C 3 [0.5 | 3
where the number within brackets is a logarithm.
Further:
0d ; 0d
——— sn Bb; —=—cosD®; ©=—40°1'8;
Op 0g
therefore
OJ 0d
F~ = =- [0/8083 —1]; === — [0.88414]
Op 0g
therefore
oR : OR ;
~—= 4 [0.4069—8]; — = + [0.48278];
Op 0q
from which follows, taking as unit of time the century :
Uy I
P — + 9".065; — = — 0".054.
dt dt

Perturbations caused by the second eltipsord.

Here the caleulation is much simpler. Introducing :
ie) ioe)

Ek du r= > du EB =f. du

i =| (@+tu)Vcit u + =| (a? + u)? Vetu oJ (8 +a)? (2+ wu)"
0 0 0

we find:

i 3 Ike 5
S2 = H,—a,*B, — 4, be — (a?—c?) a,°E, sin | Fide cos2yp

As a verification I have here also computed the perturbations of
the inclination and longitude of the node for some of the other
planets *).

To compute the perturbation of the obliquity of the ecliptic I take:

sin? J
V = — Faga’e (a? —c’) E,a,? oi
According to Srenieer’s data a= 1.2235 and c= 0.2399; I get
di slat a REO :
1) For Mereury I find: 7 = A060 sie a = — 0”.013; SEELIGER gives:
€ f

s di d
— 0.057 and — 0.016. For Venus I find: = -+ 0’.007; sinz =>) sills)
d ¢

SEELIGER: + 0”.009 and + 0”.144; the results differ somewhat; however, cal-

dS
culating according to SEELIGER’s formulae, for Venus I find: siz 2 = -+ 0”. 154.

B, = 2.445, log g = 0.8582—9 ;

OV oJ e
= [0.3401—7] ae @ = 74°22! (1900.0), J = 7°15’;
therefore
OS A OS
— — [0.98361]; — = — [0.48051];
Op 0g
therefore
V ry QoQ co] OV Ne »
a = + [0.3237 —7]; ag = + [0.7706—8] ;
from which, taking as unit of time the century, | get:
dp A dq ,
— == + 0".125; — = — 0".447.
ay t at

Therefore the perturbation caused by both ellipsoids together is:

dp " dq
— = + 0".190; — = — 0".501.
dt dt

Let « be the obliquity of the ecliptic for the time ¢, ¢, the same

for the time ¢,, ¢ and Q inclination and longitude of the node of

the ecliptic for ¢ with reference to the ecliptic for ¢,, then:
cos & = cos i cos &, — sini sin &, cos Sb,
from which, differentiating, we get:
de Cs ib We red ih)
— sme dt = — smicosé, ae sin &, a (sin 2 cos S%)
therefore for t= t,:
de dq
Gendt
The perturbation of the obliquity of the ecliptic thus is = = — 0".507-
cd

The difference between observation and theory given by Nprwcoms
is —0".22 + 0.18 (probable error); this thus becomes + 0".28. The
addition to the planetary precession a is given by:

da 1 dp a
=— — = + 0".478.

H. Perturbations of the motion of the moon.

We shall now proceed to the formulae for the computation of
the perturbation of the motion of the moon. As the perturbative
foree in the motion of the moon we have to take the difference
between the attractions of the ellipsoid on the moon and on the
earth. Suppose a system of coordinates, the sun at the origin, the
axis of z perpendicular to the eliptic; let a, y,2 be the coordinates

of the earth in this system, 7+ § y+, 2+ those of the moon,
then the projections of the perturbative force on the three axes

are given by the expressions:

OV OV OV OV OV ove
& ir, idee © er dy | & ee Oz

The ratio of the distances sun-earth and earth-moon being very
large, IL develop in powers of §, 7,6, neglecting second and higher
powers. Then the expressions for the perturbative forees are:

OV VE Ve Oy eV OV 02V, eV a ¥.
Oa? SD dd cps Oxdz = dxdy if dy” tints oon dxdz a dy0z ts Oz?
and one can introduce as the perturbative function the funetion

parler et a ee
eae ons eel oe a ea loss ak fen age ,

det | bady |? dade

Here for v2, y,2 are to be substituted their expressions in elliptic
elements and then the secular portion of F is to be taken. Since
the powers and products of §, 4,6, contain only the elements of the
orbit of the moon, the coefficients on the contrary only the elements
of the orbit of the earth we can take the secular portion of each
separately and multiply these together.

Besides the system just mentioned suppose another system a’, y/’, 2’,
the sun also being at the origin, but the axis of 2’ perpendicular to
the equatorial plane of the ellipsoid. Then we have

z =asin Psind, — y cos PsinJ, + zcosJ,,
therefore
de! 02! dz!
a = sin P sin J,; a = — cos sind; a COS eee
Perturbations caused by the jirst ellipsoid
V
From the expression given for £2———-— we deduce, negleet-
aga
ing the terms having sin? J as a factor:

0 :. ~ du 42”
Oia ay | (@tu(etuh | (apap bay

72 4uy

dady (a? 2) (+A)

oO
072 4u2' ot Ue geet! : du
— (a°—c’?)— 2 (a?—c’?) sin D sin J, | -

dede (@ Lay a) | pw? (puis

72 ae 2 du |! Ay?
Oy? i 4 (a? +-u)? (c?+u)le — (a?+2)? (ce? +4)'b

os)

072 Aye! °
= = (a7 —c¢7) + 2i(a? cos P re
OyOz (a? A)? (c? +-a)*2 te Jase oN coe rie Se uy? u)? (c?-Lu)t2

du du
<1 A OE ea ee) Oe
(a? tu)? (c2 + up'e AC +u)? (c? + u)'h

Substituting the elements of the oibit of the earth for a, y, 2 and
neglecting the second and higher power of the excentricity I get:

72 2 C72 072
=— ere N) 2
0a? Ly °p Oy dady
0°2 = 2(a*—c?) :
a a J, — 2 (a’—c’) C, sin B sin J,
Owdz a, Pp
072 2'a? —¢?) ; : J
aa _=— Tape cos D sin J, + 2(a?—c?) C,cos B sin J,
inte 1
072

—_ == — 20, — 2(a?—c’) Cy.

Let o be the radius vector, v the true anomaly, © the longitude
of the perigee, §% the longitude of the node, 2 the inclination of the
orbit of the moon, then we have :

§ = 0 [cos (v + © — §{Q) cos §}, — sin (v +0 — Sp) sin S% cost]
4 =0 [cos (v+- O—§h) sin [ + sin(v+O — Sb) cos Hh cos 7]
$= osin(v+@—Jy) sini.

1 write these expressions thus:

= 0 (A cos v + Basin v)

y= 0 (Cocos v + Dsinv)
= 0 (Leos v + F sin v),

Vas

A, B,C, D, FE, F being expressions not containing the true anomaly.
For the formation of the required products we need the secular
portion of 0° cos? v and 9? sin’? v; I get:
So? cos? v=a',* (4 + 2e?) Sg? sin? v= ka’? (1—e’)
a, being the semi-major axis of the lunar orbif.
Thus we get expressions as :

eee (ae

* 92 v a . v
Neglecting terms hke ¢* svn* >, e* sin‘ we get:

2 2
— —— — —— sin® (1—cos2 {X) + e? + — cos 20
a, 2 4 4 4
i
3) le Fo me Sh io <
— = — sin® isin2. 4+ — e? sin 20d
es 4
a,
EO ee rey,
= — sure sin \% 4- e@ su s 20)— \/ )— — sin
73 5 sini sin 9) 1. ¢ hee in (2 \)) 9 oy
Cf 1 =_ ~ =
ve l i eC 2A) ee 3 5 ne
— — —— sm" i(1 4+ cos2't) +e —— cos 2M
Ge. 2 4 4 4
75 ye ie hy 5 £ 3 ,
~~ — = sini cos () e* sin ————=COs(2@— a) cos Q,
1g 5 9 5 ‘ 9
ay, “ 2 a a a
G le
— == — sin* 4
a Te 2

Substituting in FR these expressions we get :

Kagqate 1 a," 2 1 ey eel
ees — “A -2C,a,?+—+ de? —C,a,* )+4sin" -—-C,(a°-c*)a,?
R Cais zi P p 2 p

: : 1
+ 2(a?-—c?) sin J sin 2 cos ({i— ®) (2¢,— 4 j
Pp

The only perturbations to be considered are those of the longitude
of the perigee and of the node.
The differential equations required are :
Ia 1 OR - dsl, 1 OR

e— = - - sin 1 — == ——_ —.

dt na,” Oe dt na," 07

One easily perceives that the last term in the expression for
gives no sensible perturbation on account of the factor a*—c’, the

as 6 : ‘ :
value of whieh is about Te. and of the facet that $2 has a period
(
of 18'/, years so that the coefficient we get by integration is about
thirty times as small as would have been the case if {f had been
absent. In the same way | omit the term (C,(a@’—c’*)a?, in the coeffi-

cient of s7m>— and thus we have the following expression for FR:

: <3 i f :
I get C, = 0.678 ; — = 1.080 from which follows taking as unit
PR
of time the century :

Se arog: ©) ae Roh 33,
dt dt
- Perturbations caused by the second ellipsoid.
I find:
e2 d2 72
SSS SS SS SS I =
Ox? Oy? a dwdy
2 Rpt ee : 072 Pay s
—— == — 2 (a?—c’) E, sin B® sin J; ——— == 2(a? —c’) E, cos ® sinJ ;
Oude ; Oy0z 5
072
== 2E, 2(a*—« a) Wee

from which follows:
R 1 a,"

k@mgase | 2.0,"

| == 2H ,a,”

3h ,a,*e? — EB, (a®*—c?*)a,* sin? 2

+ 2(a?—c¢?) a,” E,,sin J sin t cos (\i — ?)|.
Although the term @*—c* is not small, yet it is. allowed to omit
the periodic term.
I get H, = 0.684, LH, = 2.445 from which follows taking as unit
of time the century :

do ; di. is
SSS (IMEI 9 SS (J
dt dt

Thus both ellipsoids together give :
UE iio oe.
dt dt

both insensible amounts.

Astronomy. — “Remarks on Myr. Wourier’s paper concerning
Seenieer’s hypothesis.” By Prof. W. pe Srrrer.

(Communicated in the meeting of April 24, 1914).

SeeLiger’s explanation of Newcoms’s anomalies in the secular
motions of the four inner planets consists of three parts, viz :

a. The attraction of an ellipsoid entirely within the orbit of Mercury
The light reflected by this ellipsoid is, on account of the neighbour-
hood of the sun, invisible to us.

6. The attraction of an ellipsoid which inecloses the earth’s orbit.
The light reflected by this ellipsoid appears to us as the zodiacal light.

c. A rotation of the empirical system of co-ordinates with reference

Proceedings Royal Acad. Amsterdam. Vol. XVI

to the “Inertialsystem’’. This rotation is equivalent with a correction
io the constant of precession. The value of this constant which is
implied in Newcoms’s anomalies is that used in his first fundamental
catalogue (Astr. Papers Vol I). In “The Observatory” for July 1913
I have shown that this constant requires a correction of + 1.24
(per century). Consequently, of SretiGer’s rotation 7 only the part
r, =r—1".24 ean be considered as a real rotation.

The position of the equatorial plane of the ellipsoid @ was deter-
mined by Serricer from the equations of condition: he found it not
much different from the sun's equator. For the ellipsoid 6 the sun’s
equator was adopted as the equatorial plane.

It is important to consider the part which is contributed by each
of the three hypotheses towards the explanation of the anomalies:
By the way in which Sernicer has published his results this is very
easy. It then appears that the ellipsoid a is practically only necessary
for the explanation of the anomaly in the motion of the perihelion
of Mercury, and has very little influence on the other elements.
Similarly the ellipsoid 6 affects almost exclusively the node of Venus.
The rotation 7 of course has the same effect on all perihelia and
nodes. In the following Table are given Newcoms’s anomalies together
with the residuals which are left unexplained by Segicer’s hypothesis.
In addition to Seriicer’s residuals I also give residuals which are
derived: A. by rejecting the rotation 7,'), and C. by omitting the
second ellipsoid. The constants implied in the three sets of residuals
are thus
SEELIGER g,=2.18 X10 ¢,=0:31 K 105% 77a ee

A 2.42 0.93 0
C 2.03 0 + 6.85,
where g, and g, are the densities of the two ellipsoids expressed
in the sun’s density as unit.
di

Seeiicer did not compute the value of rr for the earth. The resi-
dual given in the table is derived from the preceding paper by
Mr. Wor Tder.

From the table it appears that the residuals C are quite as satis-
factory as those of Srxiicer. Consequently the ellipsoid 6 is not a

1) The residuals A have already been given im the above quoted paper in “The
Observatory”. The density g, is there erroneously given as 0.37 instead of 0.93
(the correction to Seeticer’s value having been taken-as 0.2 limes this value,
instead of 2.0). | have used the figures as published by SeeLiger. The small
deviations found by Mr. WoLtsER are of no importance.

: bys)

necessary part of the explanation. Of the residuals A on the other
hand there are, amongst the 10 quantities which were considered

Mercury Venus | Earth | Mars
de
Fi NeEwcome | —0”.88 +0”.50 | --0/.21 +0”.31 | -++0/”.02 +0”.10 | +-0’.29 +0”.27 |
| | |
Newcoms | +8 .48 +0 .43| —0 .05 +0 .25/-+0 .10 +0 13) +0 .75 +0 35
dw Ci, —0 .01 | —0 10 | +0 .03 | +0 .16
“dt [/ 0 .00 0 .05 |+0 .18 0 52
Cc -—0 .02 |—o 12 —0 .04 | 0 .00
Newcoms |-++0 .61 +0 .52;+0 .60+0 17). ..... | 40 .03 +0 .22
|—o 04 +0 .02 ona Men area |—o .20
sin paels
+0 .55 +0 .01 —0 .11
—O0 31 +0 .05 —0O .24 |
NEWCOMB | +0 .38 +0 .80 | +0 .38 +0 33)—0O .22 +0 .27 | —0 .O1 +40 .20)|
a (seni |—0 .14 ‘| +40 .21 (40 .28) |+40 .01
dt )4 =) 2 | +0 aN al He) +0 .05
& —0O .15 +0 .23 —0 17 —0 .01

by Srrnicger, 3 residuals exceeding their mean error. This in itself
would not be sufficient to condemn the hypothesis, but the residual
for the secular variation of the inclination of the ecliptic (+ 1'.18)
is entirely inadmissible. We conclude therefore that the rotation 7,
is a vital part of the explanation.

The great influence of the ellipsoid 4 on the ecliptic is, of course,
due to the large inclination of its equator. If this equator was e.g.
supposed to coincide with the invariable plane of the solar system,
instead of with the sun’s equator, this influence would be much
smaller. It is impossible to decide a priori whether it will be found
possible so to adjust the position of the equator and the density of
this ellipsoid that it has the desired effect on the node of Venus
without appreciably affecting the earth’s orbit.

The motion of the node of the earth’s orbit is the planetary pre-
cession. Calling this 4, we have, for t= t,

36
ne dp
=a

where p is the quantity so called by Mr. Wortser. We thus find
for the three hypotheses

Ad. sine

SEELIGER Ah = + 0".47
A +1 13
Cc +0 15

Newcoms did not include a deviation between observation and
theory for this quantity. At the time of the publication of the
“Astronomical Constants” (1895) it was of course entirely correct
to consider a determination of the planetary precession from obser-
vations as impossible. Since that time however very accurate invest-'
igations of the precession have been executed by Nrwcoms himself
(Astr. Papers, Vol. VIII) and by Boss (Astr. Journal, Vol. XVI,
Nrs. 612 and 614). Now the precession in right-ascension depends
on the planetary precession, but that in declination does not. We
have

m = lcos €—)
n=lsine
/ being the lunisolar precession.

Newcoms determined / from the right-ascensions and the declina-
tions separately, and found a large difference in the results. If this
were interpreted as a correction to the planetary precession, we
should find

A= 0747.

Boss determined m and 2 separately, the latter both from right-
ascensions and from declinations. From his results I find (applying
the correction of the equinox Ae — + 0.30, adopted by both Boss and
NEWCOMB) :

Ah = + 0".85 + 0".22
The mean error does not contain the uncertainty of the correction
Ae. Its true value probably is about = -+ 0".25. The mean error

of the value of 42 derived from Nrwcome’s work is difficult to
estimate; we may assume it to be equal to that of Boss. The mean
of the two determinations would then be
Aa = + 0".66 + 0".181).
1) Also L. Srruve (A. N. Vol. 159, page 383) finds a difference in the same
sense. Neglecting the systematic correction », | find from his results
Ar = + 0".93 + 0".80.
The m. e. again is too small as it does not contain the effect of the uncertainty
of the correction ».

Now it is certainly very remarkable that this correction is of the
same sign and the same order of magnitude as the planetary preces-
sion derived from the attraction of Srenicmr’s ellipsoids. It must however
be kept in mind that it is very weil possible to explain the disere-
paney between the determinations of the constant of precession from
right-ascensions and from declinations (or from m and from 7) by
the hypothesis of systematic proper motions of the stars. Thus Hoven
and Haum (M. N. Vol. LXX page 586) have from the hypothesis of
unequal distribution of the stars over the two streams derived a
systematic difference which is equivalent (for Newcoms) ‘) to a correction

Ai = + 07.56.

As the effect of the attraction of SepricEr’s ellipsoids on the motion
of the moon Mr. Wortser finds a secular motion of both the perigee
and the node. Both of these are due chiefly to the inner ellipsoid
and are thus not much altered if Seeticur’s hypothesis is replaced
by either of the hypotheses A or C. We find

dw ASG et

SRELIGER a SL OTL SS = HN)
dt dt

A 4+. 2.04 135.30

C + 2 10 —-2 .06

All these quantities are well within the limits of uncertainty of
the observed values.

Chemistry. — “Vhe application of the theory of allotropy to electro-
motive equilibria.” Ul. By Dr. A. Smits and Dr. A. H. W. ATEN.
(A preliminary communication). (Communicated by Prof. J. D.
VAN DER WAALS).

(Communicated in the meeting of April 24, 1914).

1. In the first communication *) under the above title it has been
demonstrated that the theory of allotropy applied to the electromotive
equilibrium between metal and electrolyte, teaches that a metal that
exhibits the phenomenon of allotropy and is therefore built up of
different kinds of molecules immersed in an electrolyte, will emit
different kind of ions.

The different kinds of ions assumed by the theory of allotropy,
need not be per se different in size, as was remarked before. They

1, For Struvn’s stars the correction would be + 0”.77. For Boss the corre-
sponding computation has of course not been executed by HouaH and Hats.
*) These Proc. Dec. 27, 1913, XVI. p. 699.

may be equal in size, but different in structure. There can, however,
be another difference besides, viz. in electrical charge. In the preced-
ing communication the molecule kinds J/ and J/, were assumed,
and for simplicity’s sake the circumstance that part of these molecules
are electrically charged also in the metal, was not mentioned. This
circumstance need not be taken into account, because the electrical
charge of the atom J/ in one ion JJ/,*) was put equal to that in
the other ion (J2-*). If it had then been our intention to indicate
the total equilibrium in the metal, we might have drawn up the
following scheme :

2M@M°+602M=+60 (1)
QV eo
2M Fe M, (4)
from which follows that the system would then be pseudoquaternary.

For an explanation of the electromotive disturbances of the equi-
librium mentioned in the preceding communication, a consideration
of the equilibrium (1) or (4) sufficed. Then equation (4) was chosen
and 2M and M, were therefore called the pseudo components,
though of course we might as well have taken 2M: + 66 and
MM. + 60.

Now it is clear that when in the metal ions of equal structure
occur, but of different value, the scheme of equilibrium can be as
follows.

M-+202M-:-+30 (1)
(2) XS [ Ly (3) . i

The system is then pseudo ternary, but in most of the cases it
will be sufficient to consider the pseudo binary system, indicated by
equation (1), and assame MW: +20 and M--+30 as pseudo
components. A similar equilibrium will have to be assumed, when
the metal can go in solution with different valency under different
circumstances. This case is probably of frequent occurrence.

Of course the metal phase is already complex, when metal ions
occur by the side of uncharged molecules, but this complexity does
not suffice to explain the peculiar electromotive bebaviour of the
metals, whereas schemes I and II are competent to do so.

In connection with the foregoing considerations it could be shown
that the unary electromotive equilibrium finds its proper place in
the 4,2 figure of a pseudo system, which ean clearly appear under
certain circumstances, when we namely sueceed in bringing the
metal out of the state of internal equilibrium. Thus it was e.g. shown

that when a metal is brought to solution by an electrolytic way, so
when it is made into an anode, the internal equilibrium will be
disturbed, and the metal will become superficially enobled, at least
when the velocity of solution is greater than the velocity with which
the internal equilibrium sets in. In this case therefore the dissolving
metal will have to become positive with respect to an auxiliary
electrode of the same metal which is superficially in internal equi-
librium. If reversely the metal is made to deposit electrolytically,
the reverse will take place, and the separating metal will be less
noble and therefore negative with respect to the auxiliary electrode.

The anodie disturbance of equilibrium being attended with a dimi-
nution of the more active kinds of molecules, this process will bring
about a diminution of the chemical activity. This is therefore the
reason that this anodic state of disturbance is a more or less passive
state of the metal.

At the eathode the disturbance lies exactly in the other direction,
and a more active state will be brought about.

The degree in which a metal is thrown out of its state of equi-
librium in case of electrolytic solution or deposition, will depend
on the current density at constant temperature, and it was therefore
of importance to study the discussed phenomenon at different current
densities.

What may be expected is this that the internal equilibrium will
generally be able to maintain itself for very small current densities.
Then the tension with respect to the auxiliary electrode will be
zero, both when the metal is anode and cathode. With greater
current densities the metal will get superficially more and more
removed from the state of internal equilibrium on increase of the
current density, and the tension with respect to the auxiliary elec-
trodes will greatly increase.

As the metal surface gets further removed from the state of
internal equilibrium, so becomes more metastable, the velocity of
reaction which tries to destroy the metastability, increases however
in consequence of the change of concentration in the homogeneous
phase; and we may therefore expect that the potential difference
between metal and auxiliary electrode will vary with the current
density in the way indicated in Fig. 1.

When the velocity with which the internal equilibrium sets in,
is small, the part a) will lie at exceedingly small current densities,
and if the measurements are not exceedingly delicate, we shall get
the impression that this piece is entirely wanting.

lt is clear that the tension which is represented here as function

of the current density means the tension with respect to the auxiliary
electrodes. This tension, which is also called polarisation tension, is

Polarisation.

Fig. 1.

positive when the metal is anode, and negative, when it is used
as cathode.

Further this possibility was still to be foreseen that when the
metal assumes internal equilibrium very slowly a distinct change of
the potential difference would have to be demonstrated even after
the current had been interrupted.

Now it shonld be noted here that when a base metal has become
noble during its use as anode, and the difference of potential between
the metal and electrolyte has risen to the tension of liberation of
the oxygen, at the anode two processes will begin to proceed side
by side; besides the going in solution of the metal we get also the
discharge of the OH’-ions and the possible formation of oxide skins,
the influence of which should be examined.

We get something of the same kind at the cathode. When viz.
the difference of tension metal-electrolyte at the cathode has become
ereater than the tension of liberation of the hydrogen, besides dis-
charge of metal ions, also discharge of H’-ions will take place there.

Method of Investigation.
The measurement of the polarisation tensions took place in the

following way (see Fig. 2). Two electrodes of the metal that is to
be investigated, in the shape of wire or rods, were placed in a solution

of a salt of the metal, generally the nitrate. The two electrodes
were connected by a variable resistance and an Amperemeter with
a number of accumulators, so that the strength of the polarizing
current is easily changed and measured. To measure the tension of
polarisation at one of the electrodes a beakshaped bent glass tnbe
was brought into the solution, whose capillary point was placed as
close. as possible ‘against the polarized electrode. In this glass tube
a third (auxiliary) electrode of the same metal was brought. This
auxiliary electrode, which is currentless, exhibits the normal potential
difference with respect to the solution. As there is no loss of tension
in the liquid of the auxiliary electrode, and its point is close against
the polarized electrode, the potential difference between the auxiliary
electrode and the polarized
electrode gives directly the
deviation which the potential
difference of the polarized
electrode presents from the
normal potential difference,
so the polarisation tension.

The measurement of this
potential difference took place
by reading the deviation
which was obtained by con-
necting the auxiliary electrode
and the polarized electrode

by means of a resistance of

_ Fig. 2. some meg. ohms with a gal-
vanometer. The value of the scalar divisions in Volts was determined
by connecting the galvanometer with a normal element.

Silver, Copper, Lead.

2. The investigation of different metals, undertaken in this direc-
tion, has shown us that as was to be expected, they represent the
most different types.

There are metals which in contact with an electrolyte, assume
internal equilibrium very quickly ; there are those that do so very
slowly, and there are those that lie between these extremes.

Beginning with the metals which quickly assume internal equili-
brium, we may first mention the metals: sé/ver, copper and lead.

The result of the investigation of these metals is found in the
following tables.

After the current had been interrupted, no potential difference with
the auxiliary electrode was to be perceived.

In the first column the current density is found expressed in milli-
amperes per em*®. In the second column the potential difference with
the auxiliary electrode is indicated in Volts, the metal serving as
anode (anodic polarisation tension); and in the third column the
same is given for the case that the metal served as cathode (cathodic
polarisation tension)

AB Es
Silver electrode immersed in 1/, N, Ag NO3-solution.
l

: = ne V-anode V-cathode
25 + 0.03 — 0.006
50 + 0.03 —— 0.012
100 + 0.04 — 0.014
200 + 0.05 — 0.015
300 + 0.05 — 0.016
400 + 0.06 — 0.018
750 + 0.09 — 0.020

It is seen from this table that the silver is not materially nobler
during the solution, and not materially baser during the deposition
than the auxiliary electrode, which is entirely in internal equilibrium.
The polarisation is therefore exceedingly slight here, from which we
may deduce that the metal silver very quickly assumes internal
equilibrium. Under these circumstances it is of course out of the

TABLE 2.
Copper electrode in '/. N.Cu(NOs))-solution.

|
= = uae V-anode V-cathode
14 + 0.016 — 0.016

29 + 0.026 — 0.026
57 | + 0.032 — 0.035
114 + 0.048 — 0.063
171 + 0.048 — 0.082
930 + 0.050 — 0.088

43
question that a potential difference could sull be demonstrated after
the current had been broken, which accordingly was by no means
the case.
For copper the following values were found. (See table 2 p. 42).
This is, therefore, the same result as was obtained for silver, and
lead behaves in an analogous way, as appears from the following table.

TAB EES 3:
Lead electrode in 1,.N.Pb(NO3)-solution.

2 — ne V-anode | V-cathode
36 + 0.010 — 0.006

140 + 0.033 — 0.010
280 -L 0.046 — 0.013
510 | + 0.082 — 0.017
1000 «=| «40.126 =| . — 0.020

After the current had been interrupted no potential difference with
the auxiliary electrode could be demonstrated.

Nick ‘el °

3. A splendid example for an internal equilibrium setting in very
slowly is furnished by nickel, as appears from the following result.

TABLE 4.
Nickel electrode immersed in '/, N . Ni (NO3),-solution.
5 | V-anode V-cathode
| ——.
21— | +1.61 — 0.95
ra Nigel hg
Cine 4 SET GES ES ho
180 + | + 1.77 — 1.40
360 | +4 1.83 | 1166
540 | STEER |b eles yg

Nickel shows therefore an enormous anodic and cathodic polarisa-
tion, which we must ascribe to the very slow setting in of the
internal equilibrium, the more so, as we found that even after the

current had been interrupted a great potential difference with the auxili-
ary electrode could still be demonstrated viz. an anodic polarisation
tension of 0,95 Volt. and a cathodic polarisation tension of 0,5 Volt.
These tensions decreased with diminishing velocity to 0, as a proof
that the metal assumes internal equilibrium by the aid of the
electrolyte. As on account of the osvillations of the mirror of the
galvanometer the said tensions could not be observed quickly enough
after the current had been interrupted, the above values give the tensions
some seconds after the interruption of the current. Immediately after
the interruption they willhave been + 1,88 V resp. — 1,77 V. Hence
nickel, used as anode, becomes superficially a metal nobler than
platinum as we know it.

Cadmium.

4. Cadmium is a metal lying between silver, copper, and lead
on one side and nickel on the other side with regard to the velocity
with which its internal equilibrium sets in.

For this metal we found what follows;

TABLE 65.

Cadmium electrode in !/> N. Cd (NO3)o-solution.

d | V-anode V-cathode
21 |) 220h093) | —n027
et Stats | — 0.186
144 | + 0.290 | — 0.220
286 | + 0.380 | = 0.220
428 | + 0.507 | — 0.220

Besides that the polarisation is smaller here than for nickel, it is
noteworthy that while for nickel the anodic and cathodic polarisa-
tion tension differ little, this difference becomes pretty considerable
for cadmium, at least for large current densities. This peculiarity
may be explained in a simple way by means of the A,z-figure given
in the preceding communication. (See Fig. 3.")

Suppose that with unary electromotive equilibrium at the given
temperature the electrolyte 4 and the metal phase S coexist, then the

1) Here the potential difference of the metal with respect to the electrolyte has
been given.

metal phase in case of anodic polarisation will move from S to 6,
dA

and over this range — is great.
Ae

In case of cathodic polarisation the metal phase moves from S§
upwards along the line SC, but here we see now that the quantity
END ee : :
= will continually decrease and can become very small in consequence
of the ever increasing curvature of the line SC, which can be even
a great deal more pronounced than has been drawn here.

It now follows from the observations that the metal cadmium
assumes internal equilibrium pretty rapidly, and in harmony with
this is the fact that after the current had been broken the polarisa-
tion had soon entirely vanished.

It was besides noticed in this investigation that the metal which

Served as anode, was gradually covered with a skin of basic salt.
It was, however, easy to demonstrate that this skin could not have
caused the observed phenomena through increase of the resistance,
for the phenomena remained the same also when this skin, which
could be very easily removed, was taken away during the electro-
lysis. Moreover it appeared that when this metal with skin was
made to cathode, the cathodic polarisation was the same as in the
absence of this skin. The formation of the skin is therefore a secon-
dary phenomenon, as was also expected (see under 1).

bismuth.

5. bismuth is a metal that very clearly seems to be catalytically
influenced, as appears from the following table.

TABLE 6.
Bismuth in '/9 N Bi(NO,)-solution.

5 | V-anode | V-cathode
35 AE S02 a = 0802
G0) ie OROL en OF08
133 © |) St eDs050 le =aulov03
2600) | Zeal S14el =. 50803

The anodie polarisation presents this particularity that though it
is exceedingly small up to a current density of 133 milli Amperes
per cem*, as for silver, it becomes pretty considerable for a current
density of 260 milli Ampeéres. Now it is worthy of note that the
anodic polarisation was at first also small for a current density of
260, but if increased slowly, so that it amounted to + 1.14 volts
after a few minutes. For smaller current densities, however, no rise
of the polarisation tension took place in course of time. The explanation
of the observed phenomenon is probably as follows. The Bismuth,
which gets positively charged in the used solution, assumes internal
equilibrium very quickly at first. At the greatest density of current,
however, this internal equilibrium is no longer able to maintain itself,
and then generation of oxygen seems to take place, which oxygen
evidently exercises a negative, catalytic influence, which renders the
metal still nobler. This phenomenon being attended with the formation

of a white skin (probably of basie salt) we have again examined
what influence this skin exercises on the phenomenon. For this pur-
pose the current was suddenly reversed, after a thick layer of the
basie salt had formed, in which however, only a cathodic polarisation
of 0,18 Volt was observed as a proof that this skin, indeed, increased
the resistance somewhat, as was expected, but that this could have
been only of slight influence on the amount of the anodic polarisation
tension’). What the negative catalytic influence here consists in,
cannot be said with certainty, but as has been stated, it seems
probable to us that the oxygen, dissolved in the metal to an exceed-
ingly slight degree, retards the setting in of the internal equilibrium.

Tron.

6. If we now proceed to the metal iron we meet again with
phenomena, and very pronounced ones too, which in our opinion
point to catalytic influences.

We found the following result :

TABLE i:

Iron electrode immersed in !/) N.FeSO,-solution.

0 | V-anode

50 0.026
100 | 0.038
130 0.044
160 | 0.064
199 0.075
250 | 0.113
300 | 0.164
400 2.25
600 2.47
800 2.53

from which it appears that in this transition of a current density
from 300 to 400 the iron has suddenly become very noble. This

1) For it ean hardly be assumed here that the skin offers a different resistance to
currents of different direction.

phenomenon, whieh has been already often observed, and is called
the becoming passive of iron, has not been accounted for in a
satisfactory way.

In the light of these new considerations the explanation, as was
already observed, is not difficult.) The iron, which shows. this
sudden increase of the anodic polarisation, is entirely free from so-
called annealing colours and_ perfectly reflecting, so that an oxide
skin is out of the question.

If we, however, assume that the metal dissolves a little oxygen,
and this oxygen retards in a high degree the setting in of the
internal equilibrium, the sudden considerable enobling of the metal
is explained in a simple way.

Up to now it has been lost sight of too much that the pheno-
menon of passivity, arisen by an electrolytic way, and that called
into existence by a purely chemical way, must be explained from
one and the same point of view. By a purely chemical way iron
is made passive by being simply immersed in strong nitric acid for
a few moments. If then the iron is put in a solution of copper
sulphate, the copper does not deposit. By a shght shake, the appli-
cation of a magnetic field ete. this passive state can, however,
at once be destroyed, and the iron is covered with a coat of
copper.

If we consider the passive iron to be iron that is superficially
very far from the state of internal equilibrium, in which super-
ficially the easily reacting molecules are practically entirely wanting,
and assume that this state can be maintained for some time on
account of the negative catalytic action of oxygen under certain
circumstances, which state, however, outside the cell, can be destroyed
by vibrations, a magnetic field ete., the phenomenon of passivity
of iron becomes less unintelligible. *)

Returning to the experiment, we will show in the first place
what was found when smaller current densities were worked with
after the iron had become “passive” at higher current density.

This table exhibits therefore the great difference between the passive
and the active iron. As appears from the last table but one, the
active iron yields a difference of tension with the auxiliary. electrode
of 0,026 Volts for a density of current of 50; the passive iron yields
a difference of tension of 2,18 Volts for the same current density.

i) Suits, These Proc January 25, 1913, XVI. p. 191.

2) We have probably to do here with metal ions of different valency. (We shall
return to this later on.)

49
; TABLE 8.

iron electrode, immersed in ''5 NFeSQO,-solution.

‘ V-anode | V-cathode
800 DOS 0 50
600 2.47 | 0.47
400 2.40 0.44
200 | 2.30 | 0.42
100 2.24 | 0.37

50 | 2.18 0.27

It is now remarkable that, as has also been found by others,
contact with hydrogen can annihilate the passivity. When we reversed
the current and made the passive anode the cathode for a moment,
and then reversed the current again at a density of 400 m.A., the
difference of tension with the auxiliary electrode amounted at first
only to 0,12 Volt, but this tension rose at first rather slowly to
0,6 Volt and then rapidly to 2,27 Volts.

It therefore appears from this experiment that hydrogen is a
positive catalyst for the setting in of the internal equilibrium of
iron. which also accounts for the fact that the cathodic polarisation,
as appears from the last table, is extremely small in comparison
with the anodic polarisation. The difference between anodic and
cathodic polarisation is therefore so great here, because for the
anodic polarisation a negative catalyst, and for the cathodic polarisa-
tion a positive catalyst come into play.

That for nickel the anodic and the cathodic polarisation are about
the same proves that the oxygen and the hydrogen do not act
noticeably catalytically on this metal.

It should finally still be pointed out that when at the moment
that the passive iron had veached an anodi¢ tension of polarisation
of 2.27 Volts, the current was broken, still a tension of polarisation
was observed of 1,07 Volts, which tension, however, pretty quickly
fell to O. So it appeared just as for nickel that the iron without
passage of the current soon assumes internal equilibrium by the aid
of the electrolyte, and becomes active. We see from this that the
hegative catalytic action is maintained by the current; when the
current is broken the active iron above the liquid will, however,

Proceedings Royal Acad. Amsterdam. Vol. XVII.

promote the setting in of the internal equilibrium in the at first
passive part, and this will be the explanation of the fact that the
iron becomes active after the current has been broken.

Also after the use of the iron electrodes as cathode the current
was broken, and as was to be expected, the much smaller cathodic
polarisation tension of + 0,15 appeared to run very rapidly back to 0.

Aluminium.

7. As far as ifs electromotive behaviour is concerned, aluminium
is undoubtedly one of the most interesting metals. For anodie pola-
risation the current density decreased regularly, and the tension

increased, as is shown in the following table.

TAB EE V9:

Aluminium electrode in !y NAlo (SO4)3-solution.,

; L
0 V-anode
0.8 + 2.56
0,53 Ly
0,46 | + 3.84
0,36 = | ate ASD

Accordingly we find anodie polarisation tensions of about 4 Volts
for this metal already at very small current densities, which points
to the fact that here a layer of great resistance must have been formed.

Up to now it has been tried to explain this strong anodic polari-
sation for aluminium by the formation of an insulating skin of Al,O,.
With greater densities of current the anode is really covered with
an oxide skin, and it is therefore natural to assume the formation
of this skin also for smaller densities of current, and attribute the
observed phenomenon to this skin of Al,O, with great resistance.
There are however objections to adopting this explanation, for in
our experiments no trace of annealing colours was to be observed,
and the metal remained beautifully reflecting.

To ascertain whether in our experiments a skin of great resistance
had formed round the anode, we made the following experiment.

The bottom of the vessel with the Al?(SO,), solution was covered
with a layer of mercury, and the aluminium electrode was anodi-

éally polarized. When this electrode was now covered with a skin
of great resistance, an immersion of one extremity of the aluminium
electrode in the mereury should not exert any influence on the
difference of tension between the aluminium anode and the auxiliary
electrode. If, however, this skin does not exist, the aluminium elec-
trode will get into contact with the mercury during the just described
manipulation, and the said difference of tension will be modified.

The result was that when during the anodic polarisation the
aluminium anode was immersed in the mercury, and the current
was then broken, the difference of tension with the auxiliary elec-
trode was absolutely unchanged, which proved therefore that the
aluminium electrode did not get in contact with the mercury, but
was surrounded with a coat of electrolyte. This appeared to be no
specifie property of the anode, for the same thing was observed after
cathodic’ polarisation. An unpolarized Al-wice, immersed from the
electrolyte in the mercury layer, immediately assumed the potential
of the mercury, from which therefore follows that the gas layer on
the aluminium retains the electrolyte with great force.

In this way the question of the skin could therefore not he solved.
What is remarkable is this that the skin formed during anodic
polarisation, immediately seems to disappear again by cathodic
polarisation. The assumption of a film of Al,Q, is attended with
great difficulties, in the first place this oxide cannot be reduced
under these circumstances by H in status nascens, and in the second
place it appears, that nothing is to be perceived of this skin, at
least with the naked eye, as no annealing colours are to be observed,
and the metal remains clearly reflecting. It seems therefore not too
hazardous to us to conclude in virtue of this that the skin cannot
be an oxide layer, and the only thing left to us is to assume, as
we did for iron, that the oxygen dissolves in the aluminium during
anodie polarisation, and that this solution possesses a great electric
resistance for aluminium. In this way we come to the assumption
of a layer with great resistance, of which it is, however, to be
understood, that it entirely disappears on cathodic polarisation to
make room for a solution of hydrogen and aluminium. Accordingly
this layer is metallic, and can amalgamate in course of time when
in contact with mercury, through which the resistance disappears.
The result at which we arrive is therefore this that the anodically
measured tension is so extraordinarily great for aluminium, much
greater than the liberation tension of O, can be here, because the
dissolved oxygen not only retards the setting in of the internal
equilibrium, but also a layer of great electric resistance is formed.

At greater current densities Al,O, can separate from this solution
of oxygen in aluminium, but then the electrode is no longer reflect-
ing, and it cannot be made reflecting again by cathodic polarisation.
This layer of Al,O, can also possess a great resistance, but the
primary feature of the phenomenon is in all cases the formation of a
solution of oxygen in aluminium, which possesses a great resistance.

If we now proceed to the description of the experiments with
amalgamated aluminium, we will begin with stating that when in
the just deseribed experiment the aluminium electrode was. raised
ont of the mercury, after amalgamation had set in, and the lower
opening of the auxiliary electrode was placed against the extremity
of the aluminium wire, this part of the aluminium had undergone
a great change, and had become negatively electrical with respect
to the auxiliary electrode. The tension difference amounted to —0.9
Volt, and still increased slowly. At the place where the aluminium
had been in contact with the mercury, it had therefore become
much baser, and had visibly become somewhat amalgamated.

That amalgamated aluminium is baser than the non-amalgamated
metal, was known, but the exact value of this difference in tension
was not met with in the literature. To determine this difference in
tension, an aluminium electrode was amalgamated by immersion in
a solution of HgCl,, after which this electrode was compared with
the auxiliary electrode. We found that the amalgamated Al obtained
in this way was still baser than the just mentioned Al, for the
tension of this electrode with respect to the auxiliary electrode
amounted now to —1.27 Volts.

That the amalgamation for aluminium has a very particular effect
follows moreover from this that amalgamated aluminium possesses
a much greater chemical reactive power than the ordinary alumi-
nium. Amalgamated aluminium immersed in water gives a very
considerable generation of hydrogen, and it oxidizes so rapidly when
exposed to the air that the metal is immediately covered with a
layer of oxide, the liberated heat raising the temperature of the metal
very noticeably.

In consideration of all this it seems more than probable to us
that the action of mercury is here positively catalytic, and that mer-
cury therefore, when dissolving in aluminium, brings the metal in
internal equilibrium, which condition corresponds to a greater con-
centration of the simpler, so more reactive kinds of molecules.

The anodic polarisation of the amalgamated state is almost as
slight as for silver, as a proof that the internal equilibrium sets in

53
much more quickly here than for pure Al, but not yet so rapidly
as for Ag.

Amalgamated Aluminium.

Lo leaned V-cathode

2 | + 0.03

5) |) 420.07), |) = 0:05

Ne a= ONS |= 0120

33 | +018 | --033 i
a7), 0.34 1 |

That the amalgamated aluminium goes into solution much more
rapidly than the non-amalgamated aluminium also appears from
what follows. If a new aluminium electrode is put in the just men-
tioned mercury layer, which covers the bottom of the vessel with
the Al,(SO,),-solution, this electrode assumes the mercury potential.
The tension difference with the auxiliary electrode is then namely
+ 0,6 Volt, which tension difference is also found when a plati-
num electrode is used instead of an aluminium electrode. If the same
experiment is, however, made with an amalgamated Al-electrode,
the tension difference with the auxiliary electrode is — 0,78 Volt.
It follows from this that if the ordinary aluminium partially immer-
sed in mercury, failed entirely to maintain its potential difference
with respect to the electrolyte in consequence of too slow solution,
the amalgamated aluminium does not quite succeed in this either,

but it almost sueceeds, for instead of — 1,27 Volts its tension with
respect to the auxiliary electrode has namely become — 0,78 Volt.

lt is perhaps not superfluous to elucidate this phenomenon in a
few words. With immersion of the aluminium electrode in the mer-
cury a short circuited element aluminium-electrolyte-mercury is obtai-
ned, in which the aluminium is the negative pole, and therefore
sends ions into solution. If now the setting in of the internal equili-
brium took place with great rapidity, the aluminium would be able
to maintain its unary potential difference, and in this case the ten-
sion of this electrode with respect to the auxiliary electrode would
have remained — 1.27 Volts. Now we find —-0,78 Volt, proving
that the state of internal equilibrium was disturbed to a certain
extent after all, and the metal has become a little less base by
dissolving. If, as was described, the same experiment is made with

ordinary aluminium, which is therefore an enobled state of aluminium,
we get what fellows.

The ordinary aluminium is at first the negative pole with respect
to the mercury. It becomes, however, noble by the dissolving, and
it is soon as noble as mercury. Nobler than mercury it can, howe-
wer, not become then, since in this case, the current would be
reversed, which would change the state of the aluminium again in
the base direction. This is the reason that ordinary non-amalgamated
aluminium immersed in mercury, assumes the potential of the mer-
cury. This experiment can however not be continued for any length
of time, because the aluminium in contact with mereury slowly
amalgamates, as we have seen, in consequence of which finally also
the part which is not in contact with the electrolyte, will become
active, so that the same things will be observed as in case of well-
amalgamated aluminium.

In a following communication the investigation of the other metals
will be treated, after which a critical summary will be given of the
theories which have been proposed by others up to now as an ex-
planation of some of the facts discussed here.

SUMMARY.

In the foregoing pages the theory of allotropy was applied to the
electromotive behaviour of the metals Ag, Cu, Pb, Ni,Cd, Bi, Fe, Al.

We have come to the conviction that the newly obtained point
of view, as we hope to prove further, enables us to survey the
widely divergent cases, and gives a deeper insight into the signifi-
cance of the observed phenomena.

Anorg. Chem. Lab. of the University.
Amsterdam, April 23, 1914.

Chemistry. — “The Allotropy of Cadmium.” Il. By Prof.
Ernst Conen and W. D. HeELpEerMAN.

(Communicated in the meeting of April 24, 1914).

1. In our first paper on this subject') we concluded from measure-
ments with the pyknometer and the dilatometer that cadmium has
a transition temperature at 64°.9 and that this metal as we have
known it until now, is a metastable system in consequence of the
very strongly marked retardation which accompanies the reversible

1!) These Proc. 16, 485 (1913).

change of these allotropie modifications both below and above their
transition points. As we pointed out in our papers on the allotropy
of copper and zine, the possibility that there might be present at
the same time more than two allotropie forms had to be taken
into account.

If this were the case, a variation in the previous thermal history
might have an influence on the transition temperature.

The samples which had given 64°.9 as their transition point
(Vide § 11 of our first paper) only differed by the fact, that the
second one had been in the dilatometer at 100° in contact with
paraffin oil for 36 hours after having given 64°.9. At the end of
this time the measurements were made, which are given in Table II.
On continuing our investigations we got the impression that this
difference in the thermal history of the samples might not have been
large enough to determine whether a third modification can be
formed. As a result of the following considerations we carried out
some new experiments.

2. If in our sample A, (first paper) there had been present
originally more than two modifications, it might be possible that
the greater part of the modification(s) which is (are) stable at higher
temperatures had been changed into the ;“-form, as the sample
had been heated at 101°C. for 24 hours in contact with a solution
of cadmium sulphate. In this case the heating at 100°, which
followed the first experiment with the dilatometer, might have had
no perceptible influence on the transition point which is in accordance
with the results given in tables I and II.

3. We now varied the previous thermal history of A, very
markedly. For this purpose the metal was taken out of the dilato-
meter and chilled by throwing it into water. After this it was put
into a new dilatometer without previously treating it with a solution
of cadmium sulphate at 101°. The dilatometer was then kept at
70°.0; the temperature remained constant within 0.003 degrees. The
meniscus fe// in 3°’, hours 143 mm. while we observed formerly
(first. paper) a strongly marked increase of volume at the same

temperature.

4. In order to control this result, we carried out the following
experiment :

A fresh quantity of the metal (‘‘KanLBaum’ — Berlin) weighing

about 300 grams (A,) was melted and chilled. We then turned it
into thin shavings on a lathe and put it into a dilatometer ; the bulb

was filled up with paraffin oil and a quantity of small glass-beads.
(Vide our first paper § 10). At no temperature between 50 and 100°
(vide § 4 of our first paper) did any change occur. We then added
100 grams of the same material A, which had been in contact with
a solution of cadmium sulphate (at 50°) during 12 hours. We now
observed that the meniscus of the dilatometer

fell 167 mm. in 54 hours at 50°.0
ped Ss Tw pa aia eee meter OO:

This result is in perfect accordance with the observations of § 3.

5. The following experiments prove in a more quantitative way
that the previous thermal history of the metal has an influence on
the transition temperature.

A fresh quantity of the metal (4) was divided into two parts
[(K,)r and (K,)77| of 500 grams each.

(Kj. was reduced into turnings on a lathe and immediately put
into a dilatometer. At 69°.9 we observed a decrease of volume
(456 mm.) in 257/, hours.

(K,)j) was converted into turnings in the same way and kept
for 5 days and nights at 100° in a solution of cadmium sulphate.

After having it put into a dilatometer (bore of capillary tube 1 mm.)
we made the following readings (Table 1).

TABLE I.
|

Temperature. Dee euaee ae \ Hee orth sib Beat: is
hours. , in mm. per hour

49.6 : — 100 | — 600

60.4 ; — 125 — 250

62.5 3 | ats ed

63.1 ; ae its) + 45

63.7 r + 83 | + 249

69.6 " | + 225 | + 2700

The transition point is 62°.8.

6. The metal was now kept at 100° in contact with a solution
of cadmium sulphate for 7 days and nights. After this it was put

57
again into a dilatometer which was heated for 24 hours at 145°,
then for 24 hours at 270° (that is only 50 degrees below the melting
point of the metal).
We only succeeded in ‘bringing it into motion” by heating it for
48 hours at 50° in a solution of cadmium sulphate.
We then got the following results (Table IT):

. TABLE Il.

Duration of the Increase of the

Temperature. observations in | pacueaee eae: level
hours. : in mm. per hour

60.0 "Vo — 105 — 210

63.0 ES — Il — 33

63.5 | 1g — 8 | — 6

64.0 | 11g | at 22 | ae 18

|
69.0 | Vg + 58 | + 348

The transition point has been changed to 63°.4.

7. In this way we carried out a great many experiments with
samples of different previous thermal history *). The extreme limits
which were found for this (apparent) transition temperature were
69°.3 and 61°.3.

8. As it is almost impossible to fix the real transition point
of the pure modifications in this way, we tried to prepare a sharply
defined modification of cadmium avoiding high temperatures. For
this purpose we electrolyzed an ammoniacal solution of cadmium
sulphate between an electrode of platinum and one of pure cadmium.
(40 Volt, 20—25 Ampere ; surface of the electrodes 26 em?*.).

We kept the temperature of the solution below 40°, cooling the
vessel with ice. The solution was kept homogeneous by a glass-stirrer
(Wirt), which was kept in motion by a small motor. The cadmium
which was formed at the electrode was washed with dilute sulphuric
acid, then with water, alcohol, and ether. After this it was dried at 40°.

170 grams of this material were put into a dilatometer. As it is
very finely divided, great care must be taken in order to remove the
air from the dilatometer. We used a Garpr-pump for the purpose.

1) The details will be given in full in our paper in the Zeilschrift f. physik. Ghem,

The paraffin oil was boiled on this pump with finely divided ead-
mium. If there had been formed during the electrolysis only one
modification of cadmium, we might expect that no transformation
would occur in the dilatometer, in consequence of the absence of
germs of a second form. From our earlier experiments (first paper
§ 4) we know that even if a second modification were present the
retardation may be very strongly marked.

We found in our first experiment that neither at 50°, nor at
80°, nor at 100° did any change occur.

After having removed the paraffin oil we washed the metal with
ether and brought it into contact with a solution of cadmium sul-
phate (12 hours at 100°; 48 hours at 50°). After this the dilato-
meter gave the following results (Table III).

TABLE II.
Téaperatuze | Digaiontoties. | Ieease obievel | dnsecas Oh a
|

71.0 | 34 — 351 — 468
94.8 | Yq He5132 + 528
70.5 | 53/4 — 267 = 5
70.5 | i | Bea | ny 6
60.0 24 | — 138 | — 6
70.0 | 11), a7 0 + 46
65.0 1p =) 853 | gs

There is a change in the direction of motion of the meniscus at a
constant temperature (7O°.5). The transition point is now between
65 and 70°.

This change proves therefore that now (viz. after the treatment
at 100° and 50° with a solution of cadmium sulphate) there are
simultaneously present more than two modifications.

9. Finally it may be pointed out here that the pyknometer cannot
be used to determine with exactness the density of the moditications
of cadmium formed by electrolysis, as this material always includes
constituents of the solution which has been electrolyzed. The water
may be driven out by melting the metal; the salt will then flow
on to the surface of the metal and may be washed away, but for
exact determinations this material cannot be used.

Utrecht, April 1914. van “tT Horr-Laboratory.

Chemistry. — “The allotropy of Zinc.” Il. By Prof. Erxsr Conny
and W. D. HeLperMan.

(Communicated in the meeting of April 24, 1914).

1. In our first paper on the allotropy of zine’) we called attention
to the “atomized” metals which may be prepared by the new method
of M. U. Scnoop of Zurich.

We then pointed out that this method forms an ideal way of
producing chilled metal. As a result of our investigations on the
metastability of the metals as a consequence of allotropy we may
expect that ‘‘atomized” zine will contain two or more allotropic
forms at the same time.

From a technical standpoint we thought it interesting to prove
this more directly : if the “atomized” metal really contains two or
more modifications at the same time, it will disintegrate in the long
run when stabilisation occurs.

2. Mr. Scnoop supplied us with one kilo of zine, which had been
“atomized” in the way described in our first paper on the subject.
As the material is very finely divided one would expect that an
eventual change would proceed in such a way that it could be
measured easily. On the other hand much care must be taken to
remove air from the very finely divided material after having brought
it into the dilatometer.

3. About 750 grams of the metal and a small quantity of glass-
beads which had been heated beforehand*) were put into a dilato-
meter. The material had not been in contact with an electrolyte. The
capillary (bore 1 mm.) was bent horizontally and put in connection
with a GarpE pump. In order to remove the air as completely as
possible the dilatometer remained in connection with the pump
for 1—1'/, hours. After this the paraffin oil was filled in; it had
been carefully boiled on the pump at 200° in contact with some
“atomized” zine. In this way the instrument was made perfectly
free of air as many experiments proved.

4. In a_ preliminary

of the metal occurs at 25°.0. We then carried out a fresh one, the

experiment we found that a contraction

“atomized” metal having been kept at 15° in a dry state for three

1) These Proc. 16, 565 (1913).
*) These Proc., 16, 485 (§ 10) [1913].

months. We used a_ special thermostat, which will be before long
described. The temperature was determined by means of a BrckMANN
thermometer. It remained constant within some thousandths of a
degree.

The results are shown in Table I,

TAUB LE we
Temperature 25°.00.

Level of the
meniscus (mm.)

Time in hours |

0 526
I 425
22/, 252
2/3 219
112/5 181

A strongly marked contraction at constant temperature occurs.

5. As the metal contains a certain amount of zine oxide in
consequence of its fine state of division, the question might arise
whether the contraction observed may be attributed to some chemical
reaction between the oxide and the paraffin oil.

In order to investigate this point more closely we filled a dilato-
meter (100 ec.) with zine oxide and the same paraffin oil we had
used in the experiment described above. After having evacuated it
at the GarpE pump we put it into a thermostat at 25°.00. The
meniscus did not show any change in 24 hours. The contraction
observed in our first experiment has consequently to be attributed
to a change in the metal. We intend continuing our investigations
on the different modifications of zine present in.the “atomized” metal.

Utrecht, April 1914. vAN 't Horr-Laboratory.

Chemistry. — “The allotropy of Copper’. UU. By Prof. Ernst Coney
and W. D. Henperman.

1. We have also continued our investigations on the allotropy
of copper in the direction indicated in our second paper on the
allotropy of cadmium.

The dilatometer had shown (§ 4 of our first paper) that there is
a transition point at 71°.4. We used the same method described in
our second communication on cadmium in order to determine if

this point changes by a change in the previous thermal history of
the metal.

2. The sample the transition point of which had been fixed at
71°.7 ($6 of our first paper) had not been treated with an electrolyte.
It was removed from the dilatometer, washed with ether and kept
in contact for some days with a solution of copper sulphate. This
material (Cu,,) then gave the following results:

TABLE I.

| Duration of Rise of level

Rise of level

Temperature. measufements in | ie a ae
61.7 ie | — 78 — 468
14.6 | lg | 4.225 41350
69.6 | Iq | 38 | — 152
72.1 tg | + 67 | + 402
70.3 | \poiassss [es
11.6 2/5 + 84 4. 126
70.8 | ip | Te aae | LL O7
10.6 1g | — 10 — si
70.7 | Big | 4. 36 fe

The transition point has thus been altered from 71°.7 to 70°.65.

3. As far as the measurements we carried out with samples of
very different previous thermal history are concerned, we only
mention here that we found as upper limit of the transition tem-
perature 71°.7, as lower one 69 .2. *)

4. We merely give here some details concerning a sample (Cuz)
which had been made by mixing a certain weight of Cuyy (Transi-
tion point 70°.65) with an equal anantity of the original material
(Kupfer-KanLBaum, Elektrolyt, geraspelt), which as we were told
when purchasing it, had heen melted after electrolysis. Curr had
been at 50° for 10 days and nights in contact with paraffin oil.
The results are given in table II.

1) The description of our experiments will be given in full in our paper in the
Zeitschr. f. physik. Chem.

TABLE II.

Rise of level

At constant temperature (69°.5) the direction of motion of the
meniscus has changed. This change proves that also in this case
there are more than two modifications present at the same time.

5. How. extraordinarily marked the retardations are which may
oceur, is shown by the behaviour of a sample Cury (comp. § 7 of
our first paper); it was not possible to “bring it into motion” even
after treating it with a solution of copper sulphate. However, it
ought to be pointed out that there was no finely divided powder
present, which was the case with the other samples we investigated.

Utrecht, April 1914. van ‘t Horr-Laboratory.

Botany. — “nergy transformations during the germination of
wheat-grains’. By Luerm C. Dover. (Communicated by Prof.
F. A. B.C. Went).

(Communicated in the meeting of April 24, 1914).

The reserve materials of seeds represent a large quantity of che-
mical energy. In germination these substances are split into com-
pounds with a much smaller number of atoms and partly by the
process of respiration completely oxydized to carbon dioxide. In
consequence of these exothermic processes a considerable quantity of
energy is set free, which can be used for the various vital-
processes.

In order to obtain a conception of these transformations of energy
during germination, | have made some observations on germinating

wheat-grains, on which I now wish to make a short preliminary
communication.

The germination of the wheat-grains under observation always
took place at about 20° C. in the dark, there couid therefore be no
energy taken up from without by assimilation of carbon dioxide ;
all the energy needed for the processes of germination had therefore
to be provided by means of the reserve materials.

At the commencement of germination imbibition chiefly takes
place, in this way heat is already liberated, therefore energy ; then
there follow very soon a series of exothermic processes, in wheat-
grains more especially decomposition of starch to sugars and com-
plete oxydation of this material of respiration to carbon dioxide.
The energy set free in this manner is now applied to various ends :
1st. for all kinds of synthetic processes by means of which plastic
materials are formed for the growing plant, 2". for the production
of osmotic pressure, 3". for the overcoming of internal and external
resistances, and 4'>. energy is given offin the form of heat-radiation.

The methods used to obtain an insight into these various energy-
relations were the two following :

1s'. Determination of the heat of combustion before germination,
and after the germination had been progressing for some time.

2-4. Determination of the quantity of heat produced during ger-
mination.

As regards the first point, it must be pointed out that the internal
chemical energy during a certain length of germination must decrease;
a measure of this loss can be found by determining the difference
in the heat of combustion. The energy which will no longer be
shown by this heat of combustion, is that which is utilized osmoti-
cally, for overcoming resistances and which is lost by the giving out
of heat. The energy, however, which is used up during germination
for synthetic processes is again fixed as chemical energy and is
indeed represented by the heat of combustion.

The loss of energy, that is found by determinations of the heat of
combustion, does not give therefore the total amount of energy,
which has played a part during germination, for a considerable part
of this energy has again been withdrawn from observation by the
synthetic processes.

The Brrtue.ot-bomb was used for determining the heat of com-
bustion. In it a weighed quantity of wheat-grains, germinated or
ungerminated and previously dried for a long time at 100°, were
burnt; by the rise of temperature of the water in which the bom

was placed, in combination with the water-value of the respective
parts, the amount of energy which was set free by combustion,
could be caleulated.

This heat of combustion was always calculated for the weight of 1
eram of ungerminated wheat (initial-weight) ; this was done in the case
of both germinated and ungerminated wheat. In this way comparable
values were obtained; the difference in heat of combustion after a
definite period of germination gave therefore the loss of energy
above referred to.

Heat of combustion of wheat calculated per gram of the initial-weight,

expressed in gram-calories.

The germination took Average
place at + 20° C. | | values |

| |
————— ———————— .

Ungerminated 3748 — 3774 — 3778 —3794—3797!)| 3778

Loss of energy ~

Sudtin; 0.6 Ist day
After 1 day’s germin: 4
Me wewic 2nd day
meet ay ” 3756—3793 3774 )
lise OE eigemrenpaies 3rd day
Pog : 3740 3740}
? ; 94 4th day
ye ey " 3653—3681—3682 —3707—3707 | 3686 j
| ( Year O62 5th day
” 5 » ” 3594 3594 | )
' OG). mentee 6th day
” 6 ” ” 3498 3498
180) eee Ith day
” 7 ” ” 3318 3318 |

It is clear from these values, which were found for the heat of
combustion, that the loss of energy during germination steadily
increased. The loss of energy in the first two days was slight ;
probably imbibition had chiefly taken place at this stage, whilst the
chemical transformations had then only subsidiary importance.

It can be further deduced from the figures that between the 2"4
and 38" day especially the loss of energy greatly increased, and after
that continued to rise.

If these values for the loss of energy after different lengths of
vermination are summarized graphically, a curve is obtained, whieh
begins almost horizontally, and rises more and more steeply.

The loss of energy per hour per kilogram of initial-weight can be
roughly ealeulated from the loss of energy during the different days.

The loss of energy per gram of initial-weight was after two days
4 calories.

1) The figures are arranged in ascending values, and not chronologically.

During the 1s* and 2.4 days the loss of energy per hour per kilogram of
g i 8. | $s

1000
the initial-weight was therefore roughly is = oom, cals
LOOG
The same for the 3'¢ day aie pq et ==141'7...;,
9 ” ” ” 4th ” ” S< 54 —= 2250 as
We. 2 Bees Ol aes su Jn S833 |,
”? ” ” ” Gt ” ” << 96 — 4000 an
” ” ” ”» oh ” ory < 180 SS 7500 5

This amount of lost chemical energy corresponds therefore in all
DO.

probability to that which is applied to osmotic purposes, to the over-

coming of resistances and to the evolution of heat.

In a second series of observations | aiso attempted to determine
directly the amount of heat that is given off. The principle, that
underlay these determinations, was briefly as follows: air, saturated
with water-vapour, which had been brought to a constant known
temperature, was passed over germinating wheat-grains at a constant
velocity ; these acted as a continuous source of heat; the air which
passed over it therefore rose in temperature.

If the difference of temperature between the air streaming in and
out were measured, when the latter passed at a known rate, then
in the ideal case when absolutely no other heat conduction took
place, the amount of heat set free could be calculated from the
known heat-capacity of the air. Moreover for this the space in which
the seedlings were placed would have to be completely saturated with
water-vapour ; if this were not so, evaporation would take place on
germination, in whieh way heat would be withdrawn from the
observation.

The apparatus: with which | conducted these experiments consisted
of a copper vessel placed in a waterbath of constant temperature.
Through this copper vessel, in which a large number of germinating
wheat-grains were placed, a current of air was directed at the rate
of % litres per hour; the air had had for a large part of its course an
opportunity to take up the constant temperature of the water. A set
of thermal needles served to measure the difference between the tem-
peratures of the air entering and leaving; the current resulting
from this difference in temperature was led through a very sensitive
mirror-galvanometer, whilst a spot of light was thrown by the mirror
on a seale and so made it possible to compare accurately the deflections,

The apparatus was for the most part composed of materials which

Proceedings Royal Acad. Amsterdam. Vol. XVII.

conduct heat very easily, thus making the ideal case described above
very far from being realised.

If a source of heat were introduced into the vessel while a regu-
lated stream of air was passed through, only a part of the heat
liberated could be used to raise the air-temperature ; the remainder
would pass into the surrounding water by conduction.

It was to be expected that, when a definite source of heat was
present, a maximum difference of temperature between the in- and
out-sireaming air would arise after some time; with the given rate
of passage of the air this difference of temperature caused by this
source of heat, could not become greater. A calculation as to how
ereat this maximum difference of temperature would be for different
amounts of heat, would be very complicated, if not entirely impos-
sible. For this reason the simplest way was to calibrate the apparatus
by introducing a source of heat of known magnitude. For this
purpose a manganin-wire was placed inside the apparatus over as
wide an extent as possible, in the place where later the germinating
wheat-grains were to be put. This wire formed a metallic contact
with two copper rods which projected above the lid of the appara-
tus. An electric current could be passed through the manganin-wire
by connecting these rods with the two poles of an accumulator.
The resistance of the manganin-wire was accurately determined, whilst
a milliamperemeter, placed in the cireuit, served to measure the
strength of the current. By taking the current from 1, 2, and 3
accumulators alternately, sources of heat of different magnitude could
be introduced into the apparatus.

When in this way a source of heat of known magnitude occupied
the apparatus, air was passed through and at regular intervals the
(double) deflection of the spot of hght on the scale was read till
this ultimately remained constant and therefore had reached a
maximum. These observations were conducted at temperatures of
20°, 30°, and 40° of the surrounding water, and also therefore of
the entering cr.

These calibration-experiments showed: 1st that the maximum
deflection of the spot of light, or in other words the difference of
temperature between the in- and out-going air was roughly in
proportion to the source of heat which was placed in the apparatus,
2e¢ that this proportionality was maintained at a surrounding
temperature of 20°, 30°, and 40°, 3" that the absolute magnitude
of the deflection was independent of this temperature, 4'", that a
deviation of 1 centimetre corresponded to a development of about

11.5 calories per hour.

As the apparatus was now calibrated it was possible conversely,
by reading the deflection of the spot of light, to calculate the
magnitude of any source of heat, which was in the apparatus. For
such an unknown source of heat germinating wheat-grains were
used. (The number of these was always 500).

In the course of the experiments however it became plain that
in this ease the deflection of the light spot could not be looked
upon as showing exclusively the heat-evolution which took place in
germination. For when 500 germinated wheat-grains, which had
previously been killed by heating to 106°, were placed in the
apparatus, then it was seen that the spot of light inevitably
passed the zero; in various experiments of this kind a deflection of
about 8 centimetres was always found.

In order to ascertain whether the dead seedlings did not after
all give off some heat possibly as a result of a continued enzyme-
action, the apparatus was filled by way of control with quantities
of filterpaper previously soaked in water. In this case there could
be no question of heat-evolution by the filterpaper. Also with this
arrangement of the experiments the spot of light invariably passed
the zero, reaching finally a maximum deflection corresponding to
that obtained when dead seedlings were placed in the apparatus.
The extent of this deflection was independent of the temperature of
the surrounding water (fixed at 25° and 35°), in other words, with
this arrangement of the experiment there arose always a constant
difference of temperature between the in- and out-going current of air.

Since in these cases no direct evolution of heat by means of the
substances used was possible, another cause for the rise of temperature
in the experiment described had to be found. The most probable
thing was that condensation of water-vapour must have taken place
in some way and that the heat thus set free caused an increase of
temperature in the out-going air and in consequence of this of the
upper thermal needle. In the calibration-experiments the spot of
light had remained at zero when there was no heat-source in the
apparatus; the difference in conditions then and during the experiments
just described was, that the space within was in the latter case for
a great part filled with a completely imbibed mass.

The many efforts made to eliminate this irregularity were practically
without results; I was therefore compelled, in experimenting with
living seedlings, to adopt a correction, the amount of which was
experimentally fixed while theoretically it had to be left partly
unexplained,

Since it was therefore found that by filling the apparatus with

very moist substances a difference in temperature between the two
needles arose when the current of air passed through, it had to
be assumed that this would be also the case when living seedlings
were present. The deflection found in that case would have to be
attributed partly to this physical cause, partly to generation of heat
which actually took place in germination. It was therefore necessary
to subtract from the deflection found in this arrangement the amount
of deflection found in the experiments with dead seedlings, the
remainder then being the measure of the heat generated in germination.
This latter was observed at different temperatures and in different
stages of germination. In consequence of the complications mentioned
higher up the sources of error were relatively very numerous’ and.
this was. especially noticeable in’ the few parallel-determinations
which were carried out, so that in the values summarized in the
table below an approximation to the amounts of heat given off
must be expected rather than an exact measure thereof. These
influences are proportionately very large in the lower values.

Number of calories given off per hour calculated per kilogram
of the initial weight.

eee

| | | |
a. | On the 2nd} On the 3rd | On the 4th | On the 5th | On the 6th | On the 7th
5 day of | dayof | day of day of day of | day of
f | germination) germination germination | germination | germination | germination
| | | |
20° | 710 "2143 2790 | 2869
: : : St is | ates
25° 363 540 | 2938 2977 4341
3455
30° | | | 4999 «| = 6790 |
6313
Boe 752 7326 | 71575
|
io MiMi se | -
40° | | 5689 6847

It appeared therefore from the values found that the generation
of heat on the 2™¢ and 3° days was still small in comparison to
that in later stages of germination. The generation of heat shows
a great and sudden increase between the 3'¢ and 4 day and it
is probable that it continued to increase slowly during the following

days, but the relatively small differences from the 4 to the 7! day

justify the calculation of an average for this period of germination.

Number of calories given off per hour calculated per kilogram

of the initial weight.

The generation of heat, therefore,

surrounding temperature; by arise

Temp. leery aa 5th day | 6th day | 7th day, Average
20° 2143 | 2790 | 2869 2601
|
| harness |
25° | 2038 | 2977 | 4341 3428
| 3455 |
30° 4999 | 6790 | | 6034
6313 |
|
35° 7326 | 7575 | 7450
——— + — ~~ —~
40° | 5689 | 6847 6268
| | |

was much influenced by the
of 10°, the quantity of heat

evolved, increased to more than double. The generation of heat was

diminished at 40°, a proof of the harmful influence of this temperature.
| |

Finally a comparison can be made between the number of calories

pro kilogram of initial weight given

off as heat and the loss of

energy deduced from the heat of combustion. This comparison could

only be made for a temperature of 20°

because at this temperature

germination had always taken place, so that the heat of combustion
referred to processes at this temperature only,

Loss of energy per hour per kilogram of the initial weight.

At 20° By heat given off

On the 2nd day |

' Calculated from the
| heat of combustion

83 Cal.
f4i7' .

py oils 710 Ca.
ee ee 4th 3 2143,

Sy iw eOUnue 5 2790 ,

re pa Melos a

en i pithien 2869 ,

2250,

3833
4000
7500

The total amount of chemical energy which was set free in
evermination was therefore always larger than the quantity of energy
given off as heat to the surroundings. A part of the free energy
which became available in the process of germination was therefore
evidently used for other purposes (osmosis ete.) than for heat-evolu-
tion only.

This was however doubtful only on the second day, the evolution
of heat on that day was not determined; the loss of energy, cal-
culated from the heat of combustion, was however so small in this
period that it is very possible that the evolution of heat at that
moment was larger. If afterward it should appear that this is really
the case, it would be very intelligible. For in the beginning of
germination imbibition will principally take place so that in this
case evolution of heat is not at all necessarily connected with chemical
transformations.

The results of this investigation may therefore be summarized
as follows.

The loss of energy calculated from the heat of combustion as
well as the evolution of heat increase with the duration of germination.

Both are small at the beginning of germination and greatly increase,
chiefly on the 34 day.

The evolution of heat is greatly dependent on the surrounding
temperature.

The optimum of beat-evolution is roughly 35°,

The total loss of energy during germination at 20° exceeds the
loss of energy by evolution of heat at the same temperature.

Utrecht, 1914. Botanical Laboratory.

Chemistry. — “Lyquwilibria in ternary systems XV”. By Prof. F:

A. ,H. SCHREINEMAKERS.
(Communicated in the meeting of April 24, 1914).

In our previous considerations on saturationcurves under their own
vapourpressure and on boilingpointeurves we have considered the
veneral case that each on the three components is volatile and
occurs consequently in the vapour. Now we shall assume that the
vapour contains only one or two of the components. Although we
may easily deduce all appearances occurring in this ease from the
general case, we shall yet examine some points more in detail.

The vapour contains only one component.

We assume that of the components A, 6, and C' the first two
are extreiaely little volatile, so that practically we can say that the
vapour consists only of C. This shall e.g. be the ease when A and
/ are two salts and Ca solvent, as water, alcohol, benzene, ete.

Theoretically the vapour consists always of A+ B+ C; the
quantity of A and 4, however, is generally exceedingly small,
compared with the quantity of C, so that the vapour consists prac-
tically completely of C.

When, however, we consider complexes in the immediate vicinity
of the side AZ, circumstances change. A complex or a_ liquid
situated on this side has viz. always a vapourpressure, although
this is sometimes inmeasurably small; consequently there is also
always a vapour, consisting only of A+ 45 without C. When we
take a complex in the immediate vicinity of the side AZ, the
quantity of C' in the vapour is, therefore, yet also exceedingly small
in comparison with the quantity of A+ Sb.

Considering equilibria, not situated in the vicinity of the side
AB, we may, therefore, assume that the vapour consists only of C;
when, however, these equilibria are situated in the immediate
vicinity of the side AA, we must also take into consideration
the volatility of A and # and we must consider the vapour as
ternary.

Considering only the oceurrence of liquid and gas, as we have
formerly seen, three regions may occur, viz. the gasregion, the
liquid-region and the region L—G. This last region is separated from
the liquid-region by the liquid-curve and from the vapour-region
by the vapourcurve.

As long as the liquid-curve is not situated in the immediate
vicinity of AZ, this last curve, as a definite vapour of the vapour-
curve is in equilibrium with each liquid of the liquid-curve, will
be situated in the immediate vicinity of the anglepoint C. Therefore,
the gas-region is exceedingly small and is reduced, just as the gas-
curve, practically to the point C. Consequently we distinguish within
the triangle practically only two regions, which are separated by the
liquid-curve, viz. the liquid-region and the region L—G ; the first
reaches to the side AZ, the last to the anglepoint C. The conjugation-
lines liquid-gas come together, therefore, practically all in the point C.

When, however, the liquid-curve comes in the immediate vicinity
of the side AA, so that there are liquids which contain only exceed-
ingly little C, then in the corresponding vapours the quantity of
A and & will be large with respect to C. The vapour-curve will

then also be sitnated further from the anglepoint C and closer to
the side AB, so that also the vapour region is large. At a sufficient
decrease of pressure or increase of temperature, the vapour-region
shall even cover the whole components-triangle. Consequently it is
absolutely necessary that we must distinguish the three regions, of
which the movement, occurrence, and disappearance were already
formerly treated.

When the equilibrium “+ 2+ G occurs, we may now deduce
this in the same way as it was done formerly for a ternary vapour.

a) The solid substance is a ternary compound or a binary com-
pound, which contains the volatile component C.

For fixing the ideas we shall assume that in the triangle ABC
of fig. 1 which is partly drawn, the point C’ represents water, /’an
aqueous doublesalt, #4” and /” binary hydrates. In accordance with
our previous general deductions we now find the following.

The saturationcurves under their own vapour-pressure are circum-
or exphased at temperatures below 7’, (7’,—= minimum meltingpoint
of the solid substance under consideration). The corresponding vapour-
curves are reduced to the point C. When these substances melt with

Fig. 1,
increase of velume, the points //, H’ and //’ are situated with
respect to /, #”’ and F" as in fig. 1; when they melt with decrease

of volume, these points are situated on the other side.

In fig. 1 different saturationcurves are completely or partly drawn ;
the pressure increases along them in the direction of the arrows.
Further it is apparent that along the saturationcurve of /’ the pressure
is maximum or minimum in its points of intersection with the line
CF; the point of maximumpressure is situated closest to C. On
the curve bcdihg of fig: 1, which is only partly drawn, c is,
therefore, a point of maximum-, 4 a point of minimumpressure.

The pressure along a saturationcurve of the binary hydrate /”
(or #'") is highest in the one and lowest in the other end, without
being however in these terminating points maximum or minimum.
On the curve abg/f of fig. 1 which is only partly drawn, the
pressure in @ is the highest and in / the lowest.

This is also in accordance with the rule, formerly deduced, that
the pressure is maximum or minimum, when the phases /’, 4, and (
are situated on a straight line, but that this is no more the case
when this line coincides with a side of the triangle.

As the vapour has always the composition C here the point of
maximum- and that of minimumpressure of the saturationcurve of /
are, therefore, always situated on the line C#’; the saturationcurves
of F’ and F" can, however, not have a point of maximum- or
minimum-pressure.

As we may obtain all solutions of the line Ch (CB and CA)
by adding water to / (F” and F'") or removing water from /’ (/”
and F'"), we shall call the solutions of Ch (CB and CA) pure
solutions of # (#” and Ff"). Further we eall the solutions of C H/
(CH’ and CA") rich in water and those of Hh (H’B and H"A)
solutions poor in water. Consequently in fig. 1 a, ¢ and e represent
pure solutions rich in water and f, 4 and & pure solutions poor in
water. We may express now the above in the following way :

Of all solutions saturated at constant 7’ with a binary or ternary
hydrate, the pure solution rich in water has the greatest and the
pure solution poor in water the lowest vapourpressure. Therefore,
the pressure increases along the saturationcurve from the pure solution
poor in water towards the pure solution rich in water. When the
solid substance is a ternary hydrate, the highest pressure is at the
same time a maximum- and the lowest pressure also a minimum
pressure,

We see that this is in accordance with the direction of the arrows
Vay jot Ale

6) The solid substance is the component A or / ora binary com-
pound of A and £4; therefore, it does not contain the volatile com-
ponent C.

In fig. 2 some saturationcurves under their own vapourpressure
of A (ak, blem,on) and of B (hi,g lfm, pn) are completely or
partly drawn. When in one of the binary systems, e.g. in CB, there
exists a point of maximumtemperature H’, then also there occur
saturationcurves as the dotted curve gi. As long as we consider
solutions, not situated in the vicinity of AB, the vapour region is
represented by point C. When we consider, however, also solutions
in the vicinity of A 4, the vapour region expands over the triangle.
Consequently, when we de-
duce the — saturationeurves
under their own vapour-pres-
sure, assuming that the
vapour is represented by C,
we may do this only for
solutions, not situated in the
vicinity of AB. For points
of the curves in the vicinity
of AL we take the case,
treated already in communi-
cation XIII that the vapour
is ternary. The same applies,
as H’ is situated in the vicinity of 5, also to the curves in the
vicinity of H’.

If follows from the deduction of the saturationcurves that the

pressure, e.g. along a, continues to decrease from a; only in the
vicinity of 2, a point of minimumpressure may perhaps be situated.
As the pressure in 6 and consequently also in the minimum possibly
occurring is exceedingly small and practically zero, we can say:
along tae saturationcurve of a component the pressure increases
from the solution free from water (4) towards the pure solution (q).
The pressure of the solution free from water is practically zero.

Let us now take a binary compound of A and # (for instanee
an anhydric double-salt); it may be imagined in fig. 2 to be repre-
sented by a point # on AL. When we leave out of account satura-
tioncurves in the vicinity of #, we may say that the saturation-
curves under their own vapourpressure have two terminatingpoints,
both situated on AS. As the pressure is again very small in both
the {terminatingpoints, it follows: along the saturationcurve of an
anhydric doubdle-salt, the pressure increases from each of the solutions
free from water towards the pure solution.

c) The solid substance contains the volatile component C' only.

This is for instance the case when an aqueous solution of two

salts is in equilibrium with ice; the saturation- or icecurve under
its Own vapourpressure has then, as curve ed in fig. 2, one ter-

minatingpoint on C A and one on C4. We find further: along an

icecurve under its Own vapourpressure the pressure is the same in
all points and it is equal to the pressure of sublimation of the ice.

We may deduce the previous results also in the following way.
As the vapour consists only of C, we equate, in order to find the
conditions of equilibrium for the system /-+ 4+ G in (1) (Il)
Zo—OLand 7v— 0. We then find:

Z—3

Z IZ WA
a eet and Z.-pe. apipey sr aa Fey se ee GL)
y

For the saturationcurve of / under its own vapourpressure we
find :

(Gop saa (Gist) O,j—— Giddens by (2)

(art Bs\de+t(astBddy=—(A+tOdP .. .¢

which relations fellow also immediately from 8 (II) and 9 (II). In

order that the pressure in a point of this curve should be maximum
or minimum, dP must be = 0. This can be the case only, when

COP SS MRS oe ee ere eo (GH)

This means that the liquid is situated in the point of intersection
of the curve with the line CF’, consequently, that the liquid is a pure
solution of /’. Consequently we find: along a saturationcurve under
its Own vapourpressure of a ternary substance, the pressure is
maximum or minimum in the pure solutions.

In order to examine for which of the two pure solutions the
pressure is maximum and for which it is minimum, we add to the
first part ef (2) still the expressions :

1 Or 108 1 Or Os snd : Ose SOL sy?
3’ pas +y = a 1 (stots I, 7) vdy +-— 2( 1 Lo 5, } ye.

and to the first term of (38):

1 Or ac is ony ate Pedy 1 Ose me ee
3 Biv + | a da~ +- oy +- { a dudy +4 9 («5. + | 5.) dy? +

Now we subtract (2) from (3), after that (2) is multiplied by «& and
(3) by w. Substituting further their values for A and ¢

" we find:

1
5 (rda* +- 2sdedy + tdy’) = [(e—a) V, + a V—avjdP. . (5)

Representing the change of volume, when one quantity of vapour

arises at the reaction between the phases F, LZ and G, by AV,
(5) passes into:

5 @(rde* 4 Asdady + tdy*) = (c—a) AV, X<adP a un)

Let us consider now in fig. 1 the pure solutions of F, therefore -
the solutions of the line Ch. For points between Cand f «—a<0,
for the other points «2 —e > 0. Considering only the solutions of
the line Ch, we can consider the system “+ L-+ G as binary.
Imagining a P,7-diagram of this system, // is the point of maximum-
temperature. From this it is apparent that AV, is negative between
H and F, positive in the other points of the line Ch. From this it
follows: :

(e—a) AV, is negative in points between C and H, therefore for

the solutions of /” rich in water.

(a—a) QV, is positive in the other points of this line, therefore,

for the solutions of /° poor in water.

The same applies also when the point // is situated on the other

side of

Let us take now a pure solution rich in water of /’, for instance
solution c of the fig. 1; as the first term of (6) is positive and
(a—a) AV, is negative. it follows: dP is negative. This means that
the pressure is a Maximum in ¢.

When we take a pure solution poor in water of /’, for instance
solution h of figure 1, (e—a)AV, is positive, therefore, the pressure
is a minimum in h.

In accordance with the previous considerations, we find, there-
fore, that the pressure along the saturationcurve of a ternary com-
pound is a minimum for the pure solution poor in water and a
maximum for the pure solution rich in water.

When the solid substance is a binary compound, as /” in fig. 1
or 3, we must equate «=O. (Of course 3 =O for the compound
F’"). (2) and (3) pass now into:

(wr + ys) dx + (as + yt)dy=-—CdP . . . 2)
Bsda + pidy = —(A + @)\dR, 2 2 es)

From this we find:

Bu (rt — s*) da =[(as + yt)(A + C) —BC))dP . . . (9)

From this it is apparent that dP? can never be zero or in other
words: on the saturationcurve of a binary hydrate never a point of
maximum- or of minimumpressure can occur.

In the terminatingpoint of a saturationcurve on BC« =0; as

j 7
Lim it while ¢ and s remain finite, it follows, when we
&
replace also A and C' by their values:
Bee da — || — 8) Veep —yoee. s 2=. (10)

Representing by AV, the change of volume, when one quantity
of vapour arises at the reaction between the three phases (#”, L
and (G), (10) passes into:

BRL edec — (y — PB) A VeriOve b= gee eeeaNes. 6 (1h)

For solutions between C and /” is y— <0, between /” and
B is 1—gs>O0. Imagining a P,7-diagram of the binary system
hr t+L+G, H’ is the point of maximum temperature; A’, is
consequently negative between //’ and /”, positive in the other
points of C4. From this it follows: (y — Bp) AV, is negative in points
between C' and //’, therefore, for the solutions rich in water; (y—~)
AV, is positive in points between //’ and #, therefore for the
solutions of #” poor in water.

From (11) it now follows: dP is negative for liquids on CH’,
positive for liquids on H’. In accordance with our former results
consequently we find: along the saturationcurve of a binary hydrate
the pressure increases from the pure solution poor in water towards
the pure solution rich in water.

When /° is one of the components, which are not volatile, e.g.
B in fig. 2, then a=O and B=1. From (11) then follows:

RT .d«e =(y — NN AWA 5 CHE arama oo (12)

We now imagine a P,7-diagram of the binary system B+ 1+G;
this may have either a point of maximumtemperature //’ in the
vicinity of the point 4 or not. When a similar point does not exist,
AV, is always positive; when a similar point does exist, AV, is
positive between C’ and #1’, negative between H’ and B. As we
leave, however, here out of account points, situated in the vicinity
of B, AV, is positive. As y—1 is always negative, it follows
from (12) that dP is negative. In avcordance with our former results
we find therefore: along the saturationcurve of a component the
pressure decreases from the pure solution towards the solution free
from water.

When F is the volatile component, as for instance in the equili-
brium tce+ L+G, then «=O and B=O. The second of the con-
ditions of equilibrium (1) passes now into: Z =. This means that
not a whole series of pressures belongs to a given temperature, but
only one definite pressure, viz. the pressure of sublimation of the
ice. Therefore we find again: along an icecurve under its own

ke)

Vapour pressure the pressure is the same in all points and equal to
the pressure of sublimation of the ice.

Now we shall consider the boilingpointcurves; in general the
same applies to them as to the saturationecnrves under their own
vapourpressure, which we have considered above.

Now we assume that the curves in fig. 1 represent boilingpoint-
curves; the point /7 no longer represents a point of maximum
temperature, but a point of maximum pressure ; consequently it is
always situated between C and #. This point of maximumpressure
His always situated closer to C' than the point of maximum tem-
perature /7; the same applies to the points #7’ and #" in the figs.
2 and 8. Wishing to indieate by arrows the direetion in which the
temperature increases, we must give the opposite direction to the
arrows in the figs. 1—3s.

We saw before that on the side CB of fig. 2 a point of maxi-
mumtemperature /7/’ may either occur or not; on this side, however,
always a point of maximumpressure is situated. The same applies
to the side C'A. We now find the following.

a) of all solutions saturated under constant P with a binary or
ternary hydrate, the pure solution rich in water has the lowest —
and the pure solution poor in water the highest boilingpoint. There-
fore, the boilingpoint inereases along the boilingpointeurve from the
pure solution rich in water towards the pure solution poor in water.
When the solid substance is a ternary hydrate, the highest boiling-
point is at the same time a maximum- and the lowest at the same
time a minimumboilingpoint.

6) along the boilingpointeurve of a component or of an anhydrie
double-salt the boilingpoint increases from the pure solution. When
the solid substance is an anhydrie double-salt, the boilingpoint of
the pure solution is at the same time a minimum.

c) along the curve of the solutions saturated with ice under a
constant pressure the boilingpoint is the same in all the points and
it is equal to the sublimationpoint of the ice.

The icecurve under its Own vapourpressure of the temperature
7’ and the boilingpointeurve of the ice under the pressure P coincide,
therefore, when / is the pressure of sublimation of the ice at the
temperature 7.

The following is amongst others apparent from what precedes.
We take a pure solution of a solid substance (component, binary or
ternary compound). Through this solution pass a saturationcurve

Us)

under its Own vapourpressire and a boilingpointcurve. Generally we
now have: when the vapour pressure at a constant 7’ decreases (or
increases) from the pure solution, the boilingpoint under a constant
P will increase (or decrease).

This, however, is no more the case for solutions between the
point of maximumpressure and the point of maximumtemperature.
The point of maximumpressure is situated viz. closer to the point
C than the point of maximumfemperature. When we take a solution
between these points, it is a solution rich in water with respect to
the saturationcurve under its own vapourpressure, & solution poor
in water, however, with respect to the boilingpointeurve. Consequently
as well the pressure along the saturationcurve as the temperature
along the boilingpointcurve will decrease from this solution.

We may express the foregoing also in the following way: the
vapourpressure (at constant 7’) and the boilingpoint (ander. constant
P) change from a pure solution generally in opposite directions.
When, however, the pure solution is situated between the point of
maximumpressure and the point of maximumtemperature, then as
well the vapourpressure as the boilingpoint decrease from this solution.

Formerly we have already considered the saturationcurve under
its Own vapourpressure of two solid substances (viz. the equilibrium
P+ Fk’ + L+ G); now we shall discuss some points more in detail.
It should be kept in niind in this ease that all deductions apply
also now to points, which are not situated in the vicinity of AB.
The deductions discussed already formerly apply to points in the
vicinity of this line.

Let us take the solution m of fig. 2 saturated with A+B, ihere-
fore, the equilibrium A+ 6-+ Z,,-+ G. As the pressure increases
from m towards ¢ and towards /, we may say: the solution saturated
with two components has a smaller vapourpressure than the pure
solution of each of the components separately.

When we consider the solution p of fig. 2 saturated with ice +A
and when we imagine curve np to be extended up to CA, it appears:
the solution saturated with 7ce-+ A has a greater vapourpressure
than the solution saturated with A—+ / and a smaller vapourpressure
than the metastable pure solution of A.

In the previous communication we have already discussed the
curves zu, 2v,and zw; 2 represents the solutions of the equilibrium
A+65+L+G, zw those. of the equilibrium tee + A+ L+ G
and zv these of the equilibrium tce+ B+ + G, w and v are
binary, < is the ternary eryohydric point under its own vapourpressure.

Let us now contemplate the solution m of fig. 3 saturated with
the hydrates 7+ /”; it is apparent from the figure that solution m
has a smaller vapourpressure than 7 or n. When we take however

Cw wn eek aa Cc

the solution 4, saturated with these hydrates, this has a larger
vapourpressure than the solutions @ and ce.

Curve pq represents the solutions of the equilibrium #4 #”-++-L-+G;
point HZ is the point of maximumtemperature of this curve. In
accordance with our previous definitions we call the liquids of branch
pH vich in water and those of branch //q poor in water. We then
may express what precedes in this way:

the solution saturated with two components or with their hydrates
has in the region rich in water always a smaller vapourpressure,
in «he region poor in water always a greater vapourpressure than
the pure solution of each of the substances separately.

Let us now take a liquid saturated with a double salt and one
of its limit-substances. [In fig. 1 the series of solutions saturated
with /’ of curve bed is limited in 6 by the occurrence of F” and
in d by the occurrence of /'". Therefore we shall call 7” and #"
the limit-substances of the double-salt /’). Curve po represents the
solutions of the equilibrium /’-+ 4” + L-+ G, curve og those of
the equilibrium #” + F+ + G and curve o7 those of the equili-
brum F"+F+4+2-+G. M and M’ are points of maximum-
temperature of these curves. In accordance with previous definitions
we call solutions of o//7 and oJ’ rich in water and those of Mg
and J//7 poor in water.

The following is apparent from the direction of the arrows in
how AP

a. In the region of the liquids rich in water. When a doublesalt
is soluble in water without decomposition, the solution saturated
with this double-salt and with one of ifs limit-substances has a
smaller vapourpressure than the pure solution of the doublesalt and
also than that of the limit-substance.

When a double-salt is decomposed by water, the solution saturated
with this double-salt and one of its limit-substances has a smaller
Vapour pressure than the pure solution of the limit-substanece. The
solution saturated with double-salt and with the limit-substanee, which
is not separated, has a smaller vapour-pressure than the solution,
saturated with double-salt and with the limit-substance, which is
separated.

6. In the region of the liquids poor in water the opposite takes
place.

As a special case a liquid can be saturated with two substances
of such a composition, that one of these may be formed from the other
by addition of water. They are
represented then by two points /”
and #”, which are situated with C
on a straight line. In fig. 4 this line
CF does not coincide with one
side of the triangle. In this figure
aec f is a saturationcurve under
its Own vapourpressure of /’, curve
bedf one of F’; the arrows
indicate the direction, in) which

the pressure increases. Both the

Fig. 4. curves can be circum- or exphased
and they either intersect or they do not. In fig. 4 they intersect
in e and f/f, so that the equilibria #” + #” + L. + G and
F+ Ff’ + Lr+G occur. Now we can prove that the vapour
pressure of those two equilibria is the same, therefore P= Pr.
When we remove viz. the liquid from both the equilibria, we retain
r+ Fk’ +G. As between these three phases the reaction */’+G
is possible, we can consider /’+ #” + G as a binary system. We
then have two components in three phases, so that the equilibrium
is monovariant. At each temperature /’+ /” +- G has, therefore,
only one definite vapourpressure, from which immediately follows :
ips ad ee

6
Proceedings Royal Acad. Amsterdam. Vol. XVII.

Curve gehfk in fig. 4 indicates the solution of the equilibrium
FtrF+t+L+G; when in a P, 7-diagram we draw‘the curve
r+ F’ + G@ (consequently the curve of inversion /Z /” -+ G) and
eurve /} + 7” + L+ G, then they coincide.

In fig. 5 the line CFF” coincides with the side BC of the triangle ;
We assume viz. that the component B and its hydrate /” occur as
solid substances; further we have also assumed that the component
A occurs as solid substance. The curves be, fy and th are saturation-
curves under their own vapourpressure of A, th and ef of B, ab
and de of the hydrate /’; the arrows indicate again the direction
in which the pressure increases.

It is apparent from the figure that vz represents the solutions of
the equilibrium A+ /+ L4G, cw those of A+B+L+4G

B and zu those of b+ F+4+L-+4G.
Consequently in 2 the invariant equili-
w brium A+ 6+ F+ 2+ 4 occurs.
; Curve zu terminates on side BC in
the quadruplepoint a with the phases
B+ F+4 L+G of the binary system
CB. When we remove the liquid LZ,
from the equilibrium 5+ #7+21,+G

occurring at the temperature 7, and

C A underthe pressure /’., we retain the mono-

(w) a variant binary equilibrium B+ 7G.

Fig. 5 When we draw in a P,7-diagram the

curve b+F+-G (therefore the curve of inversion / 2 5+-G) and
curve B+ f+ L+G, these two curves coincide. We can say,
therefore :

the vapourpressure of a solution, saturated with a component and
with its hydrate, is equal to the pressure of inversion of the hydrate
(the pressure of the reaction 2 b-+ G).

From the direction of the arrow on de it follows that the pressure
in @ is smaller than in d. We can say, therefore :

the solution saturated with a component and with one of its
hydrates has a lower pressure than the pure solution of the hydrate,

The same considerations apply also when two hydrates of a same
component occur.

We may summarise the previous results in the following way.
Through each solution saturated with two solid substances go two
saturationcurves; when we limit ourselves to the stable parts of

these curves, we may say that two saturationcurves proceed from
such a solution. Then we may say :

1. The two solid substances are situated in opposition with respect
to the line LG.

a. The solution saturated with these substances is rich in water:

The pressure increases from this solution along the two satura-
tioncurves.

6b. The solution saturated with these substances is poor in water.
The pressure decreases from this solution along the two saturation-
curves.

2. The two solid substances are situated in conjunction with
respect to the line LG.

a. The solution saturated with these substances is rich in water.

The pressure decreases from this solution along the saturation-
curve of that solid substance which is situated closest to the
line LG; the pressure increases along the other saturationcurve.

6. The solution saturated with these substances is poor in water.

The same as sub 27.; we must take however the changes of
pressure in opposite direction.

3. The two solid substances are situated on a straight line with
the vapour.

The pressure increases from the solution saturated with these sub-
stances alone the saturationcurve of the substance with the largest
amount of water, it decreases along the saturationcurve of the sub-
stance with the smailest amount of water.

We find examples of 1¢ in the equilibria :

FAR +1,+G (fig 1), F+F"+014+4 (fig. 1), A+B+L,+G4
(figs. 1 and 2), #”+F"-+L,,4+G (tig. 3), A+ B+ ,4G4 (fig. 5) and
F+A+L;/+G (fig. 5).

We find examples of 1° in the equilibria: 7-+-/”’+-L,+4G (tig.

Feu ae et Ga(fies 2) and. P42" by iG (fe. 3):

An example of 2“ is found in the equilibrium /-+- /”+ L,+-G (tig. 1).

We find examples of 3 in the equilibria: P+/”+21,.4-G (fig. 4),
P+’ +Ljy+G (fig. 4) and B4+4+1,4 G (fig. 5).

We may deduce the above-mentioned rules also in the following
way. We shall viz., while the temperature remains constant, change
the volume of the system M+ /” + L4G, so that a reaction
takes place between the phases and there remains at last a three-
phase-equilibrium. As this reaction is determined by the position of
the four points with respect to one another, we may immediately
distinguish the above-mentioned cases 1, 2, and 3. When we eall

the change of volume, when one quantity of vapour is formed at the
reaction, AJV,, then AJ, is always positive, except when the
liquid is represented by a point of the fourphase-curve between the
point of maximumtemperature and the intersectingpoint of this curve
with the line #/”.-When we now apply the rule: ‘the equilibria,
which arise at increase (decrease) of volume, are stable under lower
(higher) pressure’, we may easily refind the above-mentioned rules.

When we take as an example fig. 38 in which the case sub 1
occurs, the equilibrium /” + /".+ L + G is represented by curve
pq, Which intersects the line A’ 7" in WS; 7 is the point of maximum-
temperature of this curve. Consequently 4’ is positive on pH and
Sq, negative on //S; the solutions of p/ are rich in water, those
of Hg poor in water. When we take a liquid rich in water, the
reaction is:

L2k+k’+4. AV,>0.
4th AG
RP’ tL +G4 PAR +G.
Retr’ E

As the reaction proceeds from left to right with increase of volume
(AV, >0), the equilibrium to the right of the vertical line occurs
on decrease of pressure and the equilibria to the left of the vertical
line oceur on increase of pressure. Therefore, from each point of
branch pQ the equilibria /”-+ 1+ G and I'"+ L + G proceed
towards higher pressures; consequently we find the rule 1¢.

When we take a liquid poor in water, this is situated on /ZS or
on Sq. When it is situated on /7S, the above-mentioned reaction
applies also, but OV, <0. Therefore, from each point of branch
HS the equilibria #’ + 1+ G and #'" + L + G@ proceed towards
lower pressures; this is in accordance with rule 1%.

When we take a solution of branch Sg, the reaction is:

+ FY’ S Lt G. AV, >0.
M+R A LE Iv tL+G
MAR’ AG | FP+AL+G

As the reaction proceeds from left to right with increase of volume
the equilibria to the right of the line oceur with increase of volume.

In accordance with rule 1° we find, therefore, that the equilibria
FtL+G and F"4+ L4G proceed from each point of the
branch Sq towards lower pressures.

Now we have deduced the rules 1¢ and 1? assuming that point #7
is situated on branch pS; we may act in a similar way when point
H is situated on branch gS. In a similar way we can also deduce
the rules 2 and 3.

Considering, instead of the saturationcurves the boiling point
curves, the same applies to these in general. We must then replace
on the fourphase-curve the point of maximumtemperature by the
point of maximum pressure. In fig. 3 besides the point of maximum-
temperature H, also the point of maximum-pressure Q is drawn.
We imagine further that the saturationcurves are repiaced in the
diagrams by boilingpointeurves. We then refind the rules 1, 2, and
3, with this difference, however, that increase of pressure must be
replaced by decrease of the boilingpoint and decrease of pressure by
increase of the boilingpoint.

From each point of the four-phase curve proceed two saturation-
curves and two boilingpointecurves. When this solution is to be
considered as rich in water or as poor in water with respect to the
saturationcurves, it is also the same with respect to the boiling-
pointeurves. Only the solutions between the point of maximum-
pressure and the point of maximumtemperature make an exception ;
these are rich in water when we consider the saturationcurves,
poor in water when we consider the boilingpointcurves. Now we
find: from a solution saturated with two solid substances the vapour-
pressure (along one of the saturationecurves) and the boilingpoint
(along the corresponding boilingpointcurve) change generally in
opposite direction. When, however, this solution is situated between
the point of maximumpressure and the point of maximumtemperature,
vapourpressure and boilingpoint change in the same direction.

(To be continued).

Physics. — “On the thermodynamic potential as a kinetic quantity”.
(First part), By Dr. H. Hunsnor. (Communicated by Prof.
J. D. VAN DER WAALS).

(Communicated in the meeting of April 24, 1914).

In a communication published in These Proc. Il p. 889 of Jan.
27 1900°) it has been set forth by me that in the capillary layer
the molecular pressure must have a different value in different
directions as a direct consequence of the attraction of the particles,
whereas the thermic pressure (the sum of the molecular and the

1) I expressly call attention to this date, because some time after, this subject
was treated in the same way by a writer who had informed me of his own
accord that he was going to publish an article on this subject in the Zeitschrift
fiir phys. Chemie, and that he should of course, cite my paper there, but who
has failed to do so.

internal pressure) must be the same in all directions. Hence a
condition oceurs in the capillary layer in which the external pressure
in the direction of this layer p, has a quite different value from the
pressure normal to this layer p, i.e. the pressure in the homogeneous
vapour and liquid phases. In the surface a tension appeared to exist:

fo. —p,)dh.

The molecular pressure could be easily defined so that the surface
tension was in agreement with the capillary energy determined by
Prof. vAN per Waats by a thermodynamic way :

fee —T,y + p,w—pM)dh,

1 : : :
in which ge—=— and v is the volume for a molecular quantity of
v

MW grams and

c, d*o Cy d‘o
2d 4) dh”

The two integrals, which must be extended over the full height
of the transition layer, are equal, and this is also the case with two

p= (6) ao

corresponding elements so that:
o(e—T\y + p\v—uM) = p,— Pp,
from which immediately follows
e—T7 yn 4+ pv=ul. *

As p,, the pressure in the direction of the capillary layer, has
the same value in the homogeneous vapour and liquid phases as
p,, it holds for the quantity

e— TI, + pyv
that i has a constant value both in the homogeneous vapour and
liquid phase and in the capillary layer. This property leads us at
once to expect that if will play an important part especially for
kinetic considerations, and that it will express that the number of
particles that two arbitrary phases will exchange in the same time,
will be equally great. It will, in fact appear that this quantity
makes the capillary layer accessible for the considerations developed
by Prof. vax per Waats in his paper on the kinetic significance of
the thermodynamical potential. Assuming that really in the direction
of the capillary layer the pressure p, is different from the pressure
p,, and besides entirely different in different layers, the neglect of
this circumstance will make it impossible to derive the thermodynamic
conditions of equilibrium for the capillary. layer from kinetic con-

siderations. A particle, namely, that begins a new path at some
place, is subjected to the influence of the pressure p, prevailing
there, and in the layer, where it terminates this path, it is subjected
to the in general entirely different pressure p, of this layer.

Van per Waals’ first equation runs:

a a
dmNu,? + pr, — — = 4mNu',? + pu» ——-. - . . (1)
v v

1 2

The expression pv, — - = G = ) is for a monatomic fluid the
2 1
heat of evaporation for the molecular weight, «, -+ pr, —(#, + pr,).
We shall now have to apply a modification to this equation, when
the layers between which the interchange of particles takes place,
are taken in the capillary layer. Here we shall have, as it were,
an evaporation from a space under the pressure p, towards a space
under the pressure p’,, and a condensation in opposed direction.

Hence our first equation becomes : =
ImNu,,? aL Cs d*9 1 Nu! an teat ' Cy d*o! 1)
<miNU p,v—ao — — — == 5mLlVu ?,v —ago — — — -

2 n Ps N 2 dh? n Ps N 9 dh? (

The equation which expresses that for a stationary state a group
of particles from one layer will be replaced by a group of particles
from the other layer becomes just as vaN DER WAALS puts:

ane Wn
1 e j 1 a i
€ tin, =——— 6 w', du'y
v—b 0
Now from (1) follows :
Un Uy 1, AU a

and our second relation becomes therefore :

Un? Dee
1 a 1 ae ‘
v—b : Ta p25 z (4)
hence :
ay Hs d*o' c, d’o
ae ee pv —ay'— ~ |—| p,v—ag— =
i v—b ImNu,?—tmNu,? 2 dh? 3 2 dh?
0 = + ___ — +
ae tmNa? MRT
or
c, 0 a cad: oO i ae
ag-— —~-MRTlog(v-b) + p,v = -ao0'-— —~-MRT log(v'—b) + pv = Mu (3)
2 dh? ‘ ™ i 2dht ; y ;

e— Ty + pe Se — Pig pe Mae

The validity of the relations (2) and (3) may be established by
means of BoLtZMaNn’s equation modified by van Der WaAats

M |(Xdx + Ydy +Zdz)

nS MRT ’
in which M | (Xde + Ydy + Zdz) represents the work done on the

be
molecular quantity on transition from a layer with density — to a
Vv

layer with density —.
in
When in a point of the capillary layer at h the energy with
omission of the constant amounts to
c,d°o ¢, d‘o
=== 00)
2 dh? 4! dh’
the molecular pressure in this point in the direction of the layer
Cems om Or eh10)

4
a 1 he Ty ay Saga

can be represented by — ee = ag? +

Vo
ag? + So. ; (enz.) =p + ag’,

in which p represents the pressure belonging to the homogeneous
phase of the density 9, we have

‘
c, do

aaa:
PPG OF

If we substitute p, from this relation in (3), the latter passes into :

1D = 1 =

do
— av —¢, Te MRT? log (v — b) + puo=ul.
ah

This equation, which we have derived by the aid of kinetie con-
siderations, is the condition of equilibrium, at which Prof. vAN DmR
Waats arrives in his ‘“Thermodynamical theory of capillarity”

Following in Prof. van per Waaus’s steps, Dr. A. vAN ELprk has
given a thermodynamie theory of the capillarity for a mixture of two
substances. By applying that the total free energy must be a minimum

for all variations of @ and a, which satisty fg dh = constant and

fe (1 — x) dh = constant, he found for the variation with respect to @

f(ex)+o af —— a, M, (1-«) — uw, Mx — ¢,, (1-«) diet ae) c, (1-2) Gee —
INS ry do ess M243 11 dh? 13 dh?
d’o(1-«) Pou
eer emi” 75 eee

In this f(@z) is the free energy of a homogeneous phase with
the w and o existing in /, and hence

— MRT log (v—b,z) — ae 4+- MRT \(1—2z) log (1—«) + «@ log 2}.
t . t v ‘ s

of
o an = pv
The energy for M, grams of the first ee amounts to
eh dc. (1—2) M.. dow
é, = C,—a,, 9 (l—2) —4,, 9@ — 3 ¢, un Fe ie a

and for J/, grams of the second component :
% d°o(1—-2) d* ow
&, = C, — a,,0(1—2) —a,, 0 e — $.¢,, ——>—__ — 36 2

dh* anes dh?

We get therefore for our equations (1) for the first component :

me. ELAN a A ig d* o(l—a ) dou
1m,Nu, ? + ——— — a,,90(1l—e# ox — te -—1¢, —_=
et it o (1-2) 118 113 Le dit 219° apa
tm, Nul, 2+ se Be Nie ni ay nme Ea OS Ney
tan Ni. a @ )—a,,.9 & —3C; Sam 2 iis =e
as AGE ian Bi eae ge dh? ;
and for the other component:
d’o(1-w) doa
$m, Nu, Le SEO —z)—a, 29 — SACts aang <a aa 2
Ut dh dh
' a 2 !
4 d’o'(1-«’) o'r
© 2 2
= 2m Nu’, ; = = 4150 0 (1-é t')—4,,0.0 — b Cis — qo)! $ Cy5— = 3 (1,)
ou dh dh

In this a represents the partial pressure so that in the homogeneous
phase ,a is the partial pressure for the first component, and ,a the
partial pressure for the second component. ,2 + ,.7 =p. In_ the
direction of the capillary layer these partial pressures are represented
Dye dean 2K... sO: that oa, a. —

a Ea)
mm ao 2 1 2 . # a
thes expressions ——_—_ (Or —, therefore, represents the work done
o(1—~) l—a
on a quantity J/, of grams of the first component when it leaves the
phase. The phase being composed of J/, (1—a) +-J/,v grams in a volume
. . . v
M, grams of the first component will occupy a volume

The equations (2) which express that for each of the components
a group of particles from one phase is replaced by a. group of
particles from another phase, become for the first component:

1 Ju. 2 nt 7; 2
tm, a din, Nu 1,
hey cay TAT ESS 1p M ee Way
Sse ty dts 3m, C= ie Git. weve aU Grae (2,)
! 1 1 1
v—by. n a v — by n n
and for the second component: :
1 Ty. 3 1 lea
tm, N tls tm, Nu’,
A aa Bal ogo ; ee nue
wv i, ipa av it 2
—u, du, e 3m,Na,* —_" —u', dui, e pm, Na,” 3 ((2,))
y—D n n — by n n

Taking into consideration that 2, dea, = wu, ds, and us, dua, =
= u's, du's,, and that 4m, Na,?=4m, Na,?= MRT, we may write
for (2,) and (2,);

7. 2 1 leis. x]
pe, Alcs bm, Nu, | — km, Nu ty
log ame = Ul = a Vy Ty
i= 05) he MRI
and *

j= Bee bm, Nu, > — Im, Nu', *

re n

log ae es ee
yb, of “URI

from which then follows for the first Component in connection with
Ge) sama yar)

pe =n) note d*o(1-«)
\T log =e +- 65) —4,,9 (1-2) -a,,0%-}¢,, 7
d* ow Ore Roce ; : Per }
— 3Cr, dh? — MRP log jaa AG o'(1-a") wane (1-a')-a,,g'@ ik (3,)
?9'(1-z') d?9'x' a v
— 3¢, dit aga Gays =e, — Tn, eg
and for the een component :
P 1? o(1-« \
— MRT log - Sow 242 a 4129 »(1-«) —a,, ow —3e paul ae
x ox dh?
dow Fa eS OE Pate a ;
—4¢,,—,,— — MRT log—__ + = 40 1-0) — oh 0
dh a Ou
d?o'(1-2') d?o'a' v
21g dhe San Cas dh? 5 Ty, + 5% 2a =o uM, .

The expressions :

Vv
é, — Ty, + 17, ae and é

v
— Ty, + .2, —=u,Y,
&

have a constant value throughout the vessel. For every component
they give us the thermodynamic potential in its kinetical signification.

When we now write the value of w.J/,(1—.«)+ yu, Je, we tind
for it, at the height of / with density y and concentration «
— MRT SU rsdeiag MRT \(1 = x) log (1L—w) + wx log x} +- pv — azo —

d*o0(1-«) ; dou ; d*o(1 x)
= $og(1—2) ell a Ge 2 Oy gt ii
ad’ ox
ba VU, (l-«) +m «;
for
iT, ay
== —— 0
Q Q

The pressure p, can be expelled from this relation when we
consider that p;-+ 4, (molecular pressure in the direction of the

capillary layer) =p--a.e*, in which p represents the pressure
belonging to an homogeneous phase of the same density and con-
centration. In general M, = — 0 fe, — C, (A-—a) — Cyz} holds, in

which ¢ = ¢, (1—w) + ¢,7, hence the energy for the quantity of the
mixture M, —2) + M,x. Now:

4 d’o(1—z)
&; = C, (l—a) + C,z — a9 — }¢,, (1-—«)

dh?
age +, d?9(1—-x) Pow

are) dh? Ne dh? — $450 dh?
hence
; Eola, do. SOE) dow
i= $C, (1-2) dh? ¥ 4c,,(1- x) — dh? mat} 2 Oya? Ae 5p Qt dh?

If this value of p, is introduced, the found relation passes into
— MRT log (v —b,) + MRT \(1 —«) log (1—a) + «log x} + pv — arg —
d° oe 2) d? ow d*o(1-«) Pox
— ¢, (I-2) 72 —¢,, (1-2) dhe ks a dhe meas ae =
= uw, (1—2) + u,M,«

This relation, which we have derived by means of kinetic consider-

ations only, is the first of the two conditions for the equilibrium
determined by van Expik by a thermodynamic way.

For the two homogeneous phases, which are in equilibrium with
each other, the following form holds:
—MRTlog(v-b,) + MRT}\(1—a)log(1-«) +- wloge} + pv-a,o=, VM, (1-2) +4, Mya
or

yw -}+ pv = "MY, (l1—2) + uM.

As the kinetie theory teaches that the pressure in the two phases

must be constant, it follows immediately from this that:
yw — J, (1—2) — vw, Ma

— Pr .

Chemistry. — “On the behaviour of gels towards liquids and the
vapours thereof.’ Il. By Dr. L. K. Wore and Dr. E. H.

Bicuner. (Communicated by Prof. A. F. Honieman).

(Communicated in the meeting of April 24, 1914).

In continuing the experiments mentioned in our first communi-
cation about this subject"), we hit upon two observations which
have given us the key to the solution of the problem. Firstly it
was found that, when leading saturated water vapour over gelatine
which at the same temperature had swollen in water, the weight
of the gelatine does not change; secondly it appeared that the
amount of decrease with the experiments made in the previously
described way — in desiceators according to VAN BreMMELEN —
depended upon the size of the desiccator, and besides that in this
way of experimenting pure water also lost in weight. These things
found, we came to the following conception of von ScHROEDER’Ss
phenomenon :

1. the state attained in water vapour is no equilibrium ; even
though the quantity of water absorbed does not visibly increase for
days and days, one must suppose an extremely slow absorption still
to be taking place, at least if the experiment is made in the exact
way which will be presently deseribed. However, it may be several
years, before the true equilibrium is reached, which in liquid water
appears within some days. So the so called vapourequilibrium is
only a ‘false equilibrium”.

2. the curve which indicates the connection between the water
content and the vapourtension, runs almost horizontally as soon as
the point which represents the vapour equilibrium, is passed; the
tension being taken as ordinate, the concentration as abscissa.

3. The observation formerly advanced by von ScHroepmur, BANCROFT,
and also by us against the hypothesis mentioned under 1, viz. that.
the watercontent of gelatine swollen in the liquid. decreased again
in vapour, (from which was concluded that the ‘equilibrium’ was
attained from two sides), is founded on an unsatisfactory way of
experimenting. This conception seems to give a satisfactory explana-
tion of the whole of the phenomena; we can support it by a great
number of experiments.

We shall now first of all treat the proof of the third thesis. As

1) These Proce. 15, 1078 (1912/18).

93
we doubted about the exactness of the method with desiceators, we
made experiments in another way. We let a piece of gelatine swell
under water until the equilibrium was attained, put it into a U-
tube with ground stopeocks, hung this tube in a thermostat, and
sucked a stream of air saturated with watervapour through it. In
order to fully saturate the air with watervapour, we let it pass
in extremely tine bubbles through four tubes of water which were
also hanging in the thermostat. We made sure of the vapour really
being saturated by placing a U-tube filled with water before the
U-tube with gelatine, and by also weighing the former before and
after the air had been led through.

Nasi Is ke
Time Weight of U-tube Weight of U-tube

++ water + gelatine

| 30.130 | 30.779 |
24 hours | 30.127 30.781 | Temp. 19°.0
267". | 30.126 | 30.779 | (in thermostat)
[Sin | 30.123 30.778
Hts wy tl 30.117 | 30.780

It will be seen, that the gelatine, coutrary to our former experi-
ments, showed no decrease of weight: if was in equilibrium and it
remained so, and there was not the slightest abnormality. Now
which method, the old or the new one, is more reliable ? The
answer cannot be dubious, for we succeeded in improving the old
method to such an extent that if gives the same results as the
new one.

Formerly we used to place little dishes of gelatine in a ScHErBl.Er-
desiccator, at the bottom of which was some water, and which
stood in a room of a fairly constant temperature. In order to exclude
the possibility that the water from the gelatine, under the influence
of gravity, should distill to the water at the bottom, we have now,
instead of pouring the water into the desiccator, placed a dish of
water at the same level as that with gelatine. And, thinking of
Foorr’s experiments mentioned in our first communication, we also
weighed this dish, expecting, of course, that the water lost by th
gelatine, should be found back here. However it appeared that
both gelatine and water equally decreased in weight; (it is to be
noticed that the desiccator was not evacuated).

DAB GE MI:
Tt a Weight of dish ranean’ Weight of dish
Time aaatar decrease + gelatine decrease
47.458 48.391 temp. 22°
(room).

24 hours 47.238 .220 48.209 . 182
24k 47.031 207 48.009 . 200
Bs 45.868 163 47.863 . 146
a || 46.5067 | .301 47.525 -338

2nd experiment (three dishes of water).

a
time weightn9l decrease weight n°2 decrease weight n°3 decrease

| |

81.129 | | 64.399 | 45.888 | temp. 22°

94 80.601 | 267 63.709 .332 45.291 | .300

We see from this that, in taking the experiment in this way, a
dish of water decreases in weight 200 to 800 mG. in 24 hours, and
that consequently the experiments thus made with gelatine, do not
prove anything whatever.

It is not quite easy to say where this water goes to. It might be
thought that if serves to saturate the whole space of the desiccator
with vapour; but for this a much smaller quantity suffices, 1 L.
saturated watervapour of 22° only weighing 19 mG. Nor are
differences of temperature probable, because the changes we have
found always go in one direction, and because we cannot think
why the water in the middle of the desiceator should always be
warmer than the walls thereof. Besides the temperature in the room
was rather high'), only varying within 0,5°, and so the dishes,
after being weighed, would sooner enter colder than warmer.
It was also controlled if a loss of weight occurred during the
weighing and the preparations for it; by working quickly however,
this loss could easily be kept under 1 mG. The only explanations
left are, either the watervapour diffuses to the outside, passing
through the layer of grease which is between the desiccator and
the lid, or water is adsorbed at the great glass surface of the de-
siccator. The latter explanation will be most probable, as in smaller

1) Except in two series of table IN), where the differences are equally great
all the same.

IpAy Bybee eit:

Small desiccator of FRESENIUS; temp. room 22°.

» 36.009

desiceators — model Fresenius — we found much smaller decreases,
and as we also found a loss of weight when making the experiment
differently. A glass bell-jar, in which was hanging a weighing-bottle
with gelatine swollen in water, was partly placed ina pail of water,
so that the gelatine remained some em. above the water surface.
There can here be no question of diffusion to the outside. Yet the
adsorption hypothesis is not without its difficulties; for in taking the
above mentioned experiments the desiccator or the belljar were first
well rinsed out and moistened with water, so that one should think
the glass surface to be entirely covered with a layer of water.
Perhaps the two last mentioned causes of decrease of weight are
cooperating.

Whatever may be the cause of decrease, we can distinctly see by this
able that both water and swollen gelatine decrease. So if we wished
to really confirm voN ScHroEDER’s observation, we first ought to have
an arrangement with which water only does not diminish in weight.

A series of experiments, undertaken in consequence of Foorr’s
communieation which has been mentioned before several times, will
illustrate how hard it is to make exact observations by the statical
method. In a glass tube were two small tubes filled with water
above one another, which had been weighed before. The tube was
closed with a rubberstopper or it was sealed in the flame, and then
placed in a thermostat; after two days the tube was opened, and
the little tubes were quickly put in weighing bottles, and were

weighed.

PAS Bees EMV:
| | “an
himey ete lowet ‘decrease | Welg BtUBper | decrease
| 22.098 24.000
48 hours 22.090 | -008 | 23.992 | 008 temp. 18°.0
48, 22.081 009 | 23.980 | .012 rubberstopper
ond experiment. |
22.060 23.923
48, | 22.051 | .009 | 23.918 | .005 | id. id.
3rd experiment.
10.108 | | 36.289 | |

AB 10.098 010 36.244 045 | sealed

So we again found a decrease of weight in all cases, be it less
than with the experiments made before. As the amounts are so much
smaller here, another circumstance, except the one of adsorption at
the glass walls, must be taken into consideration, which, as we have
found with the apparatus presently to be described, can account for
differences to an amount of some mG.!) The tubes were opened
outside the thermostat; the outer’ walls then cooled down a few
degrees, while the inner tubes remained a litthke warmer. In those
few moments a small quantity of water could distill to the wall of
the great tube, and this may be the cause of the loss of weight.

Now in order to exelude adsorption we have passed on to another
arrangement. We had a cylindrical box made of brass (measures:
diameter 7.5 em., height 7.5 em., volume 320 ¢.c.), which was
closed by an exactly fitting brass lid that could be still more strongly
fixed on by screws. Both the box and the lid were silvered at. the
inside. The apparatus was entirely plunged into a thermostat, kept
constant within O°.1. In this apparatus too we began with weighing-
bottles, which only contained water; we again had to state a loss
of weight. With these experiments the vessel was taken out of the
thermostat, and was quickly unscrewed after which the weighine-
bottles were taken out and weighed with their stoppers closed.
When a closed weighing-bottle with water was placed in the vessel,
the weight remained constant; when taking if out, some sheht
moisture was to be seen against the stopper. A refrigeration evidently
took place here, by a colder stream of air entering when the lid
was taken off. In order to avoid this as much as possible, we placed
the apparatus rather high in the thermostat; when it had to be
opened we made the water run out of the thermostat through a
siphon, so far that the lid appeared just above the watersurface.
Meanwhile the screws were unscrewed so that the lid could be
taken off as soon as it was above the waterlevel; in this way the
whole kept the same temperature until the very last moment. The
then obtained results were satisfactory (ep. table V), and we there-
fore repeated our experiments with gelatine-water, agar-water, and
celloidin-aleohol in this way.

From these experiments we learn that gelatine, agar, and celloidin
swollen in a liquid, do not undergo a loss of weight when placed
in saturated vapour, if the experiment is made rigorously. The results
with the celloidin-aleohol system are not so good as with the others,
it is true, but the decrease which reached an amount of 1O0—200

') The greater difference in the upper tube of the 5rd experiment is evidently
due to the heating during the sealing process.

Proceedings Royal Acad. Amsterdam. Vol. XVII

TAY BLEW.
Temperature 19°.0; weighings every 24 hours.
weight of weighing- |... | weight of weighing-
bottle 1 -+- water decreas] bottle 2-+- water decreas
26.045 25.096
Ist series
water | 26.033 .012 25.088 008
vessel opened
outside the 26.025 008 25.081 007
thermostat |
26.012 013 25.069 .012
2nd series ; 2
rarer 25.772 27.837
vessel opened c ; 97 @
in the thermostat 25-1168 004 ay Eos 003
| weighing- bottle |
+ gelatine
20.136 The gelatine had been
90:13 wa swelling for a fortnight in
Beit exaas Wess) ; | water at a temperature of
Pate ae 20.135 0 19°.0, and had been dried
gelatine with filter paper before the
| 20.135 | 0 experiment.
| 20.133 -002 (after 3>< 24 hours).
| | |
Temperature 21°.4.
24.575 |
Mls arine Da AN | The agar had been swel-
ALN | BOE | (+ -005) | ting for 8 days under water
agar 24.582 | (+ .002) | at the same temperature, and
had been dried as said above.
| 24.581 | .001 |
Temperature 21°.4
3 SEEEREEeaeiemeed
NO, | NO, 2 No. 3 N°. 4
| | | |
| | | | |
12.202 12.122 | | 12.389 | 11.310 |
5th series | | | | after
celloidin- | 12.200 | .002 | 12.108 | .014 | 12.379 010 304 | .006 | 42 hours
alcohol
12.095 | .013 | 12.370 Ne | 11.301 | AGO || ES
Temperature 0°,
| 12.248 12.115 | 12.397 | |
| I | |
6th series) 12.255 | (+.007) | 12.113 | .002 | 12.399 | (+.002) | after 61 hours
celloidin | 12.249 .006 | 12.109 | .004 | 12.396 20033] ins &
| |
12.249 | 0 0 12.395 | S001) 24 >

12.109 |

| {

mG. with the old method, has been reduced to some mG. only ;
we must herewith remember that the vapour tension of alcohol is
considerably greater than that of water. Therefore the 6" series of
experiments was undertaken at 0°; according to our expectations the
results were better than at 21.4°.

The experiments communicated here have taken away every actual
ground of existence from the opinion expressed first by von ScHRoEDER,
viz. that here was a conflict with the second law of thermodynamies;
the second law, as one might think, remains untouched. Of course
the phenomenon of several substances swelling more in liquids than
in vapours, remains; but we think this can be sufficiently explained
by assuming that the absorption in vapour occurs extremely slowly
in the end. We have also investigated if not totally swollen geiatine
and celloidin placed in vapour, would absorb more water in our
new apparatus, and would come to the real equilibrium. This
appeared not to be the case; e.g. with gelatine of the following
compositions: 1 gelatine to 26 parts of water (in weight); 1:24,2;
1:18,8; 1:15,8; 1:6,5, (the ‘false vapourequilibrium’” is about
1: 0.7) no change of weight was found for five days’). So it goes
without saying that the absorption takes place exceedingly slowly.

This is most probably connected with the fact that the vapour
tension of gelatine (and numerous other substances) is already very
near to that of pure water when they have only absorbed a rather
small quantity of water*); consequently all the further water absorp-
tion of any importance is only of slight inflaenee upon the vapour
tension. Or in other terms, the difference of the vapourtension of
pure water and of gelatine in “vapourequilibrium” is very small,
and consequently the absorption velocity will also be very small.
That it is yet very great in liquid water, may be easily explained
from the density which is 50000 times greater.

We just wish to state that the determinations meant here have
ail been obtained by the statical method, the deficiency of which
we have proved; a true opinion can only be possible if the experiments
are taken along the dynamical way‘), and if the real equilibrium
has been proved by placing the jellies alternately in vapour of
higher and lower tension. The values given for the composition of
the substances swollen in the vapour of pure water are never true

‘') These experiments were also made in the dynamical method with U-tubes,
yielding the same result.
») Katz, these Proc. 18, 958 (1910/11).

5) Or m the apparatus described above.

100

equilibria; one ought to state the value which is attained in liquid
water °).

The explanation of the phenomenon becomes somewhat different,
if we do not let the gelatine (ecelloidin) swell in pure water (alcohol)
but in solutions. In case of the dissolved substance being volatile
(example: celloidin-aleohol-water), the circumstances are exactly the
same as above mentioned; but, if the substance is e.g. a salt, the
thing changes. Von Scurogper has made some experiments about
this question, and he ascertains that '/,,,,,,-"norm. sulphate solution
already lowers the vapourtension of gelatine so much, that there is
not even a decrease in vapour, but an increase. After the results
deseribed above, voN ScurorpEr’s argument loses all weight, and
his result is sure to be due to chance. .

It is a fact we have repeatedly observed, that gelatine (celloidin)
which had swollen in the vapour of a salt solution (NaCl in water,
resp. HeCl, in alcohol) absorbs much more still, when brought ito
the liquid; 1 Gr. celloidin e.g. gains 1,77 Gr. in weight in a solution
of 4°/, sublimate in alcohol of 96°/,, whereas only 0.89 Gr. is
absorbed in the vapour of aleohol, and consequently still less in
the vapour of a solution in alcohol. The difference between the
swelling in a pure liquid and in a solution finds its cause in a
substance, when in the vapour of a solution, never being able to absorb
anything but the solvent, as long as the dissolved substance is not volatile;
when placed in the liquid itself, it also absorbs the dissolved substance.

This is a wellknown fact about gelatine; we have ascertained
by the experiments with celloidin mentioned above, that this substance
too had not only absorbed alcohol, but also sublimate. So in these
cases it is clear for other reasons, that a substance swollen in vapour,
when brought into the liquid) phase, must still absorb more, and
that the state attained in vapour is not a true equilibrium’). In
vapour e.g. celloidin passes into celloidin + alcohol, until the vapour-
tension of this phase has become equal to that of the liquid phase:
alcohol + HgCl,. Now if one brings the celloidin phase under the
liquid, the HgCl, diffuses into the celloidin; diminishes so to say
the vapourtension of the alcohol which is contained therein, and
consequently a furtber absorption of alcohol must take place. If we

1) Strictly speaking one must not speak of pure water, but of a saturated solution
of gelatine, agar ete. in water; of course, the difference really is exceedingly minute.

2) Cf. Totman’s views, J. Amer. Chem. Soc. 35, 307 (1913). We have
assumed with ToLMAN that every substance evaporates somewhat, no matter how
little; if one objects to this, one must speak of an equilibrium which lies differently
in consequence of passive resistances (GIBBS).

101

represent this by a figure, we obtain in the vapour a state @; and
after this the state 6 is reached in the liquid along an exactly
horizontal line, for the vapourtension remains absolutely the same ;
only the composition of the celloidin changes. @ lies of course at
a lower pressure than «@ in the figure, which stands for pure
alcohol; in the latter ab’ is only approximately horizontal.

iE : oy b

2 XK

It is evident that in this case the greater absorption in the liquid
must be connected with the solubility of the salt in the gelatine or
celloidin. According to the colloid absorbing more salt, the difference
between the vapour and the liquid equilibrium will be all the greater.
We believe a closer study of this subject may probably bear fruit
with a view to the knowledge of the behaviour of jellies in different
solutions. We intend to start experiments about this with celloidin,
which, as to stability, has great advantages over gelatine with which
suchlike experiments have been made up to the present’). We do
not consider skinpowder an ideal substance for this purpose either *).

As a summary we think, we can say that the pretended conflict
with the second law of thermodynamics has been put an end to,
and that von Scurogper’s phenomenon in the principal case is due
to a slowly coming equilibrium; one may expect it in all cases
where the vapourtension already approaches the tension of the pure
liquid very nearly, a long time before the equilibrium has been
attained. If the liquid absorbed is a solution of a nonvolatile sub-
stance, another explanation must be given.

Path. Anat. and Inorg. Chem. Lab.

University of Amsterdam.
1) HormeEIsTER, among others.
*) Herzog and Apuor, Koll. Zeitschr. 2, Supplem. heft 2, (1908).

102

Mathematics. -- “The quidruple involution of the cotangential

points ef a cubic pencil.” By Professor Jan pe Vries.
(Communicated in the meeting of April 24, 1914).

1. We consider a pencil of cubies (v*), with the nine base-points
4,. On the curve gv’, passing through an arbitrary point P, lie three
points P’,P",P", which have the tangential point’) in common with
P; in this way the points of the plane may be arranged in qua-
druples of an involution (P) of cotangential points. We shall suppose,
that the pencil is general, consequently contains fivelve eurves with
a node D,;. On such a curve dé all the groups of the (P*) consist
of two cotangential points and the point D, which must be counted
twice. Apparently the 12 points ) are the only coincidences of the
involution; as the connector of the neighbouring points of D is quite
indetinite, the coincidences have no detinite support. The points Dy
are at the same time to be considered as singular points ; to each
of them an involution of pairs P,P’ is associated, lying on the curve
J),*, which has D, as node.

2. The nine base-points Br are also singular; to each point Lb,
a triple involution of points 2”, P", P" is associated, lying on a
curve B,, of which we are going to determine the order.

To each curve g* we associate the line 6, which touches it in B;
in consequence of which a projectivity arises between the pencil of
rays (b) and the eubie pencil (*). The curve tr produced is the
locus of the tangential points of B (tangential curve of B).

The line 6, which touches a g* in £#, cuts it moreover in the
tangential point of B; this is apparently the only point that 6 has
in common with +r’ apart from B. So rt! has a triple point in By
there ave three lines 6, which have in # three points in common with
the corresponding curve g*; i.e. B is point of inflection of three
curves g*

Let us now consider the tangential curves rt‘, and t*,, belonging
to b

consequently have apart from the peints 4, three points in common ;

, and #,. Both pass through the remaining seven base-points,
so there are three curves g*, on which B, and 4, have the same
tangential point. Hence it ensues that the singular curve 3, belonging
io B,, has triple points in each of the remaining eight points Bb;
it does not pass through 2B, because (/') has coincidences in D,

1) The ¢angential point of P is the intersection of 9% with the straight line
touching it in P.

L038

only. With an arbitrary g*, 3, has moreover in common the three
points which form a quadruple with 4, ; consequently 27 points in
all. So the triplets of (P') belonging to 4, lie on a curve of order
nine, Which passes three times through each of the remaining base-points.

We found that 5, and 4, belong to three quadruples; the three
pairs, which those quadruples contain besides, belong to the singular
curves 3,’ and ~#,°. They have moreover in the seven remaining
points 5;, 63 points in common; the remaining 12 common points
are found in the singular points Dy.

3. The locus of the points of inflection / of (~*) has triple points
in Br, has therefore with an arbitrary v*, 9 x 3+ 9 = 36 points
in common; it is consequently a curve of order twelve, v?. On a
curve d* lie only 3 points of inflection ; we conclude from this, that
v= has nodes in the twelve points DY, ; in each of those points «4
and d* have the same tangents.

The points P’, P', P'", which have / as tangential point, lie in a
straight line, the harmonic polar line h of I. So e* is the locus of
the points, which in (77) are associated to dinear triplets.

The curves p,° and <«* have in the singular poiits LB and D
8 x 37-12 x 2=96 points in common; on @,’ lie therefore 12
points 7, so that B, belongs to 12 linear triplets. From this it ensues
by the way, that the involution (/*) lying on p,° has a curve of
involution (p) of class twelve; tor the line p= P’P" will only pass ~
through B, if P" is a point of inflection, while P lies in 4,. As
B, is point of inflection of three g*, (P*) has three linear triplets,
consequently (p),, three triple tangents.

The locus 2 of the linear triplets has, as was shown, 9 dodecuple
points B; as g* bears nine points of inflection, therefore 9 linear
triplets, it has with 4 9 >¢ 12-49 < 38=1385 points in common.

Consequently the linear triplets lie on a curve 2".

4. We shall now consider the curve g, into which a straight
line ¢ is transformed, if a point P of 7 is replaced by the points
P’, which form a quadruple with ?; for the sake of brevity we
shall speak of the transformation (P, P’). If we pay attention to the
intersections of 7 with ?;” and with d,°, we arrive at the conclusion
that @ has nonuple points in B, and triple points in Dy. It has
therefore with a gy in 4, 81 points in common; further these
curves cut moreover in the three triplets which correspond with the
intersections of ? and 7. Consequently 9 is a curve of order thirty.

104

On an arbitrary straight line lie therefore fifteen pairs of cotangential
poms.

By the transformation (P, ?’), the curve 2", which contains the
linear triplets, is transformed into a figure of order 1350. It consists
of twice 2 itself, three times «, twelve times the curves B® and
seven times the singular curves d*. For 2 x 45+3 «12+4+9x
12 < 91098; the points PD produce therefore a figure of order

252. From this it ensues that 4** has septup/e points in the 12 singular
points D.

The pairs P, P’, which are collinear with a point &, lie on a
eurve «*, on which / is a triple point; the tangents in # go to
the points of the triplet of the (P'), determined by /. The line HA,
cuts p,’ in 9 points P, which form with 4; pairs of the (/*) ; hence
e* has nonuple points in By.

The locus of the pairs P", P", belonging to the pairs P, P’ of

e'’, we shall indicate by «,. As # is collinear with 12 pairs of the

involution (/*) lying on 2,°, B, is a dodecuple point of &,.

On an arbitrary g* the cotangential points form three involutions
of pairs and the supports of the pairs of each of those involutions
envelop a curve of class three (curve of Cayiny). Consequently 1
is collinear with 9 pairs P, P' of ~’, and this curve contains 9 pairs
of s. As the two curves in 4; have moreover 9 >< 12 points in
common, consequently 126 points in all, e is a curve of order 42.

The curves ¢** and B,° have in the points 5,(4==1)8 x9 3
points in common; moreover they meet in 9 points of #4, and in
the 12 pairs P, P' mentioned above. The remaining 48 common
points must lie in D,; so e* has quadruple points in the 12 singular
points D.

The curves «,‘? and 8° have in By (k==1)8 x 12 <3 inter
sections; further they meet in the 9 pairs P", P", belonging to the
9 points P' lying on #B,, and in the 12 points P", belonging to
the 12 pairs P, P’ of 3,°, which are collinear with 4. So they must
have 60 intersections in Dj); &"* has consequently quintuple points
in the 12 singular points D.

The curves ¢,"* and «” have in Be 9X 123, in D,12K5K2
intersections, together 444; the remaining 60 lie in points of infleetion,
of which the harmonic polar lines pass through /. In sueh a point
of inflection /, «&,? will have a ¢rip/e point, for the corresponding
3, 80 that
T appears three times as point of ¢&,. Consequently 4 bears 20
straight lines h: the harmonic polar lines of p* envelop a curve of

polar line h contains a linear triplet, so three pairs of &

class twenty.

105

Mathematics. — “A cubic involution of the second class.” By
Prof. Jan pr Varins.

(Communicated in the meeting of April 24, 1914).

1. By the class of a eubic involution in the plane we shall
understand the number of pairs of points on an arbitrary straight
line’). In a paper presented in the meeting of February 28", 1914 °*)
I considered the cubic involutions of the jirs¢ class, and proved that
they may be reduced to sév principally differing sorts.

The triangles A, which have the triplets of an involution of the
first class as vertices, belong at the same time to a cubic involution
of lines; the sides of each 4 form one of its groups.

The cubic involntions of the second class possess the characteristic
quality of determining an involution of pairs i.e. an involutive
birational correspondence of points. For, let Y, ¥’, X" be a group
of an involution (X*°) of the second class; on the line X’ NX" lies
another pair Y’, Y""; the point VY’, completing this pair into a triplet,
is apparently involutively associated to XY. In the following sections
I shall consider a definite (Y") of the second class and inquire into
the associated involutive correspondence (\)’).

2. We start from a pencil of conies g? with the base-points
A, B,, B,, B, and a pencil of cubies ¢°
B,, CG. (h=1 to 6). The curves «* and y

arbitrary point Y, intersect moreover in two points X’, X", which

with the base-points B,, B,,

*, which pass through an

we associate to A. As the involutions /* and /*, which are determined
on a Straight line by the pencils (4*) and (¥*), have two pairs X’,
X" and ¥Y’, Y" in common, a cubic involution (X*) of the second
class avises «here.

The ten base-points are singular points, for they belong each to
1

0
point of one of the pencils.

groups; on the other hand is a singular point certainly a base-

The pairs of points which with the singular point A determine
triangles of involution A, lie apparently on the curve «* of the
pencil (~*), passing through A. As they are produced by the pencil
(¢?), they form a central involution, i.e. the straight lines.« = X’X"
pass through a point Lot a (opposite point of the quadruple
AB,B,B,).

Analogously the pairs \’,

, which are associated to C),, lie on

1) This corresponds to the denomination introduced by Capora.i for involutive
birational transformations. (Rend. Acc. Napoli, 1879, p. 212).
*) “Cubic involutions in the plane”. These Proceedings vol. XVI, p. 974.

106

the conie y,2 passing through C,, which conic belongs to (y*); the
straight lines v intersect in a point J/,, the centre of the /?.

In order to find the loens of the pairs, corresponding to B,, we
associate to each g* the gv, which touches it in B,. The pencils
being projective on this account produce a curve of order five, B,°,
which has a triple point in B,, nodes in B,, B, and passes through
A and Cy. If the straight line «= X’Y" is associated to the straight
+ and) qos niineeemes
correspondence (J, 1) arises between the “curve of involution” enveloped

line, which touches the corresponding curves »

by a and the pencil of rays B,; from this it ensues that (7) must
be a rational curve. As no other lines w can pass through 5, but
ihe tangents at 3,° in the triple point B,, (z) is a rational curve of
the third class, has consequently a bitangent; on it lie two pairs of
(X*). To the tangents of (2), belong the lines Ab, and AB,.

There are three singular straight lines b; = ABg; each of them
bears a /* of pairs Y', XY". The corresponding points X lie on the
ine nO bens

8. The curve of coincidences (locus of the points X= X') has
triple points in #; and passes through A and C;. With the singular
curve y*, it has 10 intersections in A and Sz; as it touches it in
C’, and at the same time contains the coincidences of the involution
(X', X") lying on y?,, it is a curve of order seven’), which will be
indicated by 47. It passes through the 12 nodes of (y*) and the 3
points (0; bin).

As d@ has six points in common with g*, apart from By, and Ch,
the involution /* of the A inscribed in g* possesses sev coincidences.
In the same way it appears that the involutions 7? lying on «* and
8° possess four coincidences each.

The supports of the coincidences envelop a curve (d) of class
eight; for through A pass in the first place the lines dg, each bearing
two coincidences, and which consequently are bitangents of (d) and
further the tangent in A at «@*, which will touch (d) in A.

4. To the points Y of a straight line / correspond the pairs of
points YY’ and XV" of a curve 2, which has in common with / the
two pairs of the (.Y*) lying on /, besides the points of intersection
of / and 6’; hence 2 is a curve of order eleven. By paying attention
to the intersections of / with the singular curves a‘, B;°, and yj’,
we see that 2'! passes three times through A, jive times through By
and two times through C4.

1) This corresponds to this well known proposition : the locus of the points where
a curve o” of a pencil is touched by a curve ¢” of a second pencil is a curve
of order 2(m--n)—3.

107

On 2, XN’ and X" form a pair of an involution; of the straight
lines v= NX’ X" six pass through A. Three of them are indicated
by the intersections Y of / and «'; here ’ lies every time in A.
The remaining three are the lines 6;; for each of them contains a
pair X’, Y" corresponding to the point Y = (/b,,,,).

The curve (x), enveloped by w is rational, because we can associate
w to NX; it has therefore ten bitangents. As such a bitangent bears
two pairs \’, X" and Y’, Y" it follows that the imvolution (X,Y)
contains ten pairs on /, and consequently is of the tenth class.

5. Let a straight line / be revolved round a point HL; the pairs
X', X" and Y', Y" lying on it describe then a curve «°, which
passes twice through / and is touched there by the straight lines
HE and HE". On EFA lie two points X' and Y", each forming with
Ea pair of the (X"); so A is a node of ¢°. For the same reason
é° has nodes in 4;; it also contains the points Ci. In consequence
of the existence of 5 nodes, &° is of class 20, so that / lies on 16 of
its tangents. Of these 8 contain each a coincidence of the (Y*); the
remaining 8 are represented by four bitangents, being straight lines
s, on which both pairs belonging to (X"*) have coincided. From this
it ensues that the lines s envelop a curve (s), of the fourth class.
Apparently the straight lines s, passing through A, are tangents to
a’. In the same way the four tangents out of A, to pe° are the
straight lines s, which may be drawn through By. ts
and J’ have 16 points in

Apart from the singular points ¢
common; to them belong the 8 coincidences of which the supports
d pass through #. The remaining 8 must be points Y’, coinciding
with the corresponding point Y without ¢/’s passing through 4; i.e.
they belong to the locus «, of the points Y, which complete the pairs
lying on é* into groups of (.X°).

As EF lies on three of the straight lines «= X'NX" belonging to
br, By is a triple point of e,; analogously A and C; are simple
points of that curve, so that the latter has 2+3<2<3+6= 26

intersections with ¢° in the singular points. Besides the 8 points of

7 y
' ny

J’ indicated above they have moreover the points 4’, £” in common;

so we conclude that «, must be a curve of the sivth order. To the
intersections Y of ¢°, and / correspond lines w, which pass through
HL; trom this it ensues again that v envelops a curve of the sixth
class, when Y deseribes the straight line /.

6. If # is laid in C,, &° is replaced by the tigure composed of
1 | \ :

> and a curve y,*, which has a node in C,,

the singular conic y,
and passes through the points A, 5;, C,. The two curves have apart

108

from A and Be two more points “’, 2" in common; the lines
C, £', C, #" touch y,.in C, and are apparently the only possible
lines s passing through C,; hence C, is a node on the curve (s),.

The curve ¢." belonging to C, is represented by the figure com-
posed of y,* and a curve *y,*, which has nodes in Ly. This may
be found independently of what is mentioned above. The trans-
formation replacing a point Y by the corresponding points X', X",
transforms a straight line / into a curve y1', consequently the curve
y,' into a figure of order 44. It consists of y,* itself (for this curve
bears oo’ pairs X, X'), twice ,?, the curves a’, B;° 7,’ and twice the
locus of Y"; the latter is therefore of order four.

If # is brought into the centre J/, of the 7? lying on y,?, &° passes
with node J/,. Of the latter 6 tangents
pass through J/,, whereas this point lies on 2 tangents of y,?; from

into y,? and a curve ,,*
this it ensues anew that the lines d envelop a curve of the eighth
,' four points in
common, which must form two pairs of the /?, and so determine
two lines s, J/, too is a node of the curve (s),.

If # lies’ in A, &° consists apparently of a@’*, and the three lines
b.; whereas ¢,." is the figure composed of an @ and the three lines
bun. For FE in T &* is replaced by the figure formed by a® and a

class. As y,? apart from A and 4, has with u

curve t*, also passing through 7’ and having with a@* besides the
four points A, By. two more pairs collinear with 7’; consequently
T is also a node of (s),.

For Bb, «° consists of B,° and the line BA; «,° of B,° and B,B.

7. Passing on to the consideration of the involutive correspondence
(X, 1”) we cause X to describe the straight line /, and we try to
find the locus of the corresponding points Y. On each line X' X"
lies a second pair J’, Y"; the curves ¢* and g*, which intersect
in the points }', Y" we shall associate to each other. In order to
determine the characteristic numbers of this correspondence, we
consider the involutions /°, which are formed on a curve ¢ or g*
by greups of (X*).

The sides of the 4 described in a ¢ envelop a conic; among
the 12 tangents, which this curve has in common with the curve
of involution (wv), belonging to 4'' must be reckoned the two lines
N\', X", for which X is one of the intersections of / and g*. The
remaining JO contain each a pair Y', ""; consequently each g? is
in the said correspondence associated to 10 curves gp’.

The involution /* on a y* possesses a curve of involution of the
third class; for 6, bears in the first place the line 6,, which contains

109

a pair of the 7*, then the lines joining B, to the two points, deter-
mined by the y*, which touches y* in 5,. The intersections of /
and g* procure three common tangents of (7), and (v),; there are
consequently 15 straight lines, which bear a pair )”', Y"", so that
the said correspondence associates 15 curves ¢° to y”.

By means of this correspondence the points of a straight line +
are arranged into a correspondence (30, 30). For to the gv? passing
through a point R of 7 correspond the 30 intersections A’ of 7 with
the 10 curves g* associated to g*; on the other hand the g* passing
through =f’ procures 30 points A, by means of the corresponding
15 q’. The intersections of the corresponding curves form therefore
a figure of order 60; it consists, however, of two parts: the locus
of the pairs ¥’, ¥", which lie on the tangents of the («),, and the
locus of the points Y.

The former may also be produced by. the pencil (v*) and’ the
system of rays (v),. To each y?, in virtue of the consideration men-
tioned above, a number of ten straight lines is associated, which are

each coupled to one yg’ only ; henee a (10,12) arises now on 7, so
that the pairs of points ’, Y" are lying on a figure of order 22.

For the points )” we find therefore a figure of order 38; it is
composed of the three lines 4, and a curve of order 35. For to
the intersection Y of / and 6,24, corresponds a pair XY’, VY" on AB,;

but this line bears co!

pairs ’,)"" and the corresponding points 7
of b,B, are all associated to V. Apart from these three lines the
line / is transformed by means of the birational correspondence
(X, Y) into a curve of order 35, 7**. It cuts / in 10 pairs_X, Y (§ 4)
and in 15 coincidences Y= )’. There is consequently a curve of
coincidences of order jifteen. The figure of order 22 found above
1

consists of the three lines 6; and a curve 4'', for to the conic (,, O,,)

corresponds the tangent , of (),.

8. We shall now determine the fundamental curves which are
associated to the fundamental points A, By, Ch. The curves of invo-
lution (7), belonging to ¢,° and 3,° (§ 2) have 9 tangents in common,
there are consequently 9 lines, for whieh lies in , and Vin £,.
Therefore the fundaniental curve of 2, has nonuple points in 2, and
B,. No other point VY of the line B,6, ean correspond to a point
X lying in £,; the said curve is therefore of order 18. It has a
nonuple point in 4 too and passes three times through each of the
points A and C),; for through 7 or J/;, passes one line, bearing a
pa ie, eof py and aspair YY"
then 5, = X corresponds to a point Y lying in A or C4.

of «@ or xy)”; through whien

110

The fundamental curve of A is apparently identical with the
curve &" (§ 5) belonging to the point 7; we shall indicate it by a’.
As «* has two pairs in common with t* (§ 6) A is a node of a’.
That «® passes through the points Ci, and has triple points in Bz,
ensues from the consideration of the lines 71, and of the tangents
out of 7’ to the (xv), belonging to By.

It appears analogously that the fundamental curve of C, has
triple points in 4; and a node in C,; it passes through A and the
remaining points C, and is of order six. This curve is at the same

time the «° belonging to J/,.

We can now prove once more that the birational correspondence
is of order 35. To the intersection Y of two lines /, corresponds .
the point }’, which the two curves 4, apart from the fundamental
points, have in common. As appears from what was mentioned
above 2 passes 18 times through 4; and 6 times through A and
Cy; from 1+ 3 187+ 7 6? = 1225 = #5? it appears now that
2 is a curve of order 35.

Physics. — “On the manner in which the susceptibility of para-
magnetic substances depends on the density.” By Dr. W. H.
Knpsom Supplement N°. 36c¢ to the Communications from the
Physical Laboratory at Leiden. Communicated by Prof. H.
IKCAMERLINGH ONNES.

(Communicated in the meeting of April 24, 1914).

§ 1. Introduction. In Suppl. N°. 32a (Oct. °13) an expression was
developed for the molecular rotatory energy in a system of freely
rotating molecules as a funétion of the temperature. This expression
was introduced into the theories of Laneryin and Wrauiss, on the sup-
position that, when the equipartition laws are deviated from, the
statistics of the molecules under the action of an exterior directing
field, in this ease a magnetic field, is determined by the value 2, of
the rotatory energy in the same way as for equipartition it is by
‘kT. Wt then appeared that different experimental results can be re-
presented very satisfactorily in that way ').

1) The expressions developed in the above-mentioned paper appear to be also
suitable to give a quantitative representation (as far as observations are available)
of the decrease of the temperature of the Curin-point by the addition of a dia-
magnetic metal to a ferromagnetic one, with which it forms mixed crystals, on
the supposition that the diamagnetic metal exerts no other influence than that the
vautual action of the ferromagnetic molecules is lessened in consequence of the

sale
In the communication mentioned above the system of molecules

increase of their distance, as regards the molecular field in particular according
to the supposition mentioned further on in this note. In fig. 1 the points -++- repre-

Fig. 1.
sent the temperature 7» of the Curte-point of alloys of nickel and copper as a
funetion of the mass-composilion «x of nickel according to W. GuerTLer and G.
Tammann, ZS anorg. Chem. 52 (1907), p. 25 [the quantity « introduced here is
not to be confused with thal ef equation (4)|. The carve represents the results of
the calculation. In this I started from equation (16) of Suppl. N°. 32a, applied to

the nickel molecules

Nnngu?
= Uae oteeney Nes! Wem <M (sete sci fee ah (cz)

3
The density of the different alloys of nickel and copper was assumed to be equal,
so that the density of the nickel in the alloy may be put equal to @ = 9,2 (the

index 1 indicates that the quantity concerned corresponds to «= 1, that is in our
case to nickel’. Further the coefficient of the molecular field, Nm, is assumed not
to depend on the composition. This assumption involves, that the molecular field,
the magnetisation per unit of mass being kept constant, ’s proportional to the first
power of the density of the ferromagnetic component; this relationship differs
from the result obtained by Wetss, G.R. 157 (1913), p. 1405, with alloys of the
two ferromagnetic metals nickel and cobalt from the manner in which the con-
stant of the molecular field, derived on the assumption of equipartition, depends
on the composition.
Further @, has been put (cf § 5 of this Bape proportional to 27/s :
Ay = A, 1 av : > F, = c - (d)

The equation which determimes the value of Te which cateeennaas to a given

112

was always‘) supposed to be contained in the same volume. and
in the comparison with experimental data no account was taken of
the influence which the relatively small changes of density connected
with the temperature changes exert on the parameter (/,, which
acenrs in the formulae of that communication, and which [ will
call the characteristic zero-temperature.

Since then the measurements by Prrrimr and Kaweriincu ONNEs *)
coacerning the susceptibility of liquid mixtures of oxygen and nitro-
gen have furnished very important data, which, when considered
from the point of view taken in the paper quoted above, allow a
conclusion as to the manner in which the characteristic zero-tempe-
rature @, depends on the composition of those mixtures. If it is
further assumed with Prrrmr and KamertmGcu Onnes, that to a’
first approximation the presence of the nitrogen molecules in these
mixtures does not exert a direct influence on the statistical distri-
bution of the orientations, nor on the magnetic noment of the oxygen
molecules, so that it is only the changes in density of the oxygen,
which determine the changes in the susceptibility, then those mea-
surements furnish at the same time data for a discussion of the
question how “, depends on the density.

We will in the first place treat the question whether the results
of the measurements by Perrier and Kamuriincn Onnxes mentioned
above can be represented with the aid of the relations of Suppl.

value of 2, may then be pul into the form:

Ure Urel

== ails ec, ec a . (c)

«0 UyO1

Ota
For nickel (7.1 = 633, G0,1 = 2100, cf. Suppl. N°. 32a § 4) awd 1,30. From
UyO1

‘“ the value of can be derived, and then with “/) from (b) the value of 7c

ae) 0

corresponding to «2 can be found.

A continuation of the investigation of the magnetisation of alloys such as those
mentioned above, particularly for compositions, for which the CuRt&-point lics
below O° C., would be of great interest, on the one hand for putting the appli-
cation of the quantum-theory to a test (according to this with such alloys the
different cases indicated in Fig. 5 of Suppl. N’. 326 might be realised), on the
other hand for increasing our knowledge of the molecular field [In the mean
time | nave received an article by P. Watss, Ann. de physique (9) 1 (Febr. 1914)
p. 134, in which is mentioned, that, with a view to the investigation of the
molecular field, a series of measurements concerning alloys of nickel and copper
has already been undertaken. (Added in correcting the proof of the Dutch edition)].

') With the exception of the note added in Leiden Comm. : note 2, p. 6.

*) ALB. Perrier and H. KAMeRLINGH ONNES. Comm. No. 139d (Febr. 714).

113

N°. 32a’). It is shown in § 2 that the answer is in the affirmative,
in § 3 the same appears to be the case for the measurements con-
cerning the susceptibility of liquid oxygen over a wider range of
temperatures. § 4 contains the conclusion which follows from §§ 2
and 3. Finally in the following § § are treated the consequences
concerning the dependence of 6, on the density, which follow from
the results of those measurements *).

§ 2. The susceptibility of the liquid mixtures of oxygen and nitrogen
and the application of the quantum-theory to paramagnetisin. As a
preliminary to the question whether the results of the measurements
by Prrrmr and KameriincH Onnes can be represented with the aid
of the relations of Suppl N°. 32a, in so far as these are applicable
to paramagnetic substances, the specific susceptibility of the oxygen
in the mixtures (Table [, Comm. N*. 139d) was compared with the
specific susceptibility for pure oxygen in the gaseous state at the
same temperature, which would follow from the measurements by
Weiss and Piccarp if Curim-LAnGrvin’s law remained valid down to
that temperature (cf. tabie I, Comm. N°. 139d). This value we will
call the equipartition value Zey.

On the assumption mentioned in § 1, that the presence of the
nitrogen molecules does not cause a change in the magnetic moment
of the oxygen molecules, the (paramagnetic) specific susceptibility of
the oxygen in the mixture is determined by Oostgruuis’s relation :

nu
Owmnmintre— gag Py (1)

In this relation n represents the number of oxygen molecules
in 1 gram of oxygen, uw is the magnetic moment of an oxygen
molecule, w, the mean rotatory energy (about two axes 4 to the
magnetic one) of a molecule of oxygen in the mixture at the tem-
perature and density considered. According to LanGuvin

nu?
Xeq. = 3k"
Division gives

1) For a detailed discussion of those measurements on the basis of the assump:
tion of a negative molecular field, as well as a consideration of the other cir-
cumstances which may have an influence, we refer to the paper by Perrier and
KAMERLINGH ONNES quoted above.

*) The principal results of this paper were already inserted in the translation
of Comm. No. 139d; p. 915 note 2

Proceedings Royal Acad Amsterdam. Vol. XVII

114

eq. Ur
ee es me et CD
kT

Xo, in mixture

If for w, we assume the temperature function, developed in Suppl.
N°. 32a, and determined by

- (4)

where
2
0
Ct —— g ké, ’ . : . . . . . . (5)
: : Skip r
at each value of « the mutually corresponding values of Ep ae
r 0

can be calculated. The value of ae corresponding to the value of
: / j
0
u/kT given by equation (3) can then be found by graphical inter-
polation, after which @, immediately follows.
From the data of Table [| Comm. N°. 139d by Perrier and
KAMERLINGH ONNES the following values of 6, were in that way

obtained :
TAREE |
Values of J, |
Oi) vs Sehr aaie |
| 2
| y \f=— 195.65|f = — 202.23) = — 208.84) Mean | A (= a 9.)
pera) Gob! | |
1 | 0.7458 165 161 159 162 21.6
I | |
» HW 04010 | 975 99.5 | 971 98.0 13.1
| WI | 02304 | 53.9 55.1 [61.0] 54.5 7.3
SIV: s|Dlas0ele we 250 EYE || SPAN 23.3 3.1
Vo 0.0801 7.55 10.6--} 91 1.2
| | | |

From the fact, that the individual values of 6, vary irregularly
about the mean values, the conclusion may be drawn that the obser-

115

vations can be represented with suflicient accuracy by the equations
(1) and (4). This is confirmed by Table Il which gives. the values of
xy calculated with the aid of the mean values of 4, given in table I.
Table II also contains the deviations ( C' between observed and
calculated values.

IPAS ELE II

Calculated specific susceptibilities of oxygen.
Comparison with observed values.

| +i | 4 | i l
| t= — 202.23) O-C || t= — 208.84, O—C

0 |t=—195.65) O-C
SS | ! ——— —— ———
1 |o7458 |} 2962 |—17 3139, | 06)| 2345. | £20
eet hozofor! aa62) (|= 0.2\||" “s6l20 J 161) 300m - | 205
| : MM | 02304 | 3636 |+ 05) 3038 |—os|| 4292 | [—5.7)|
|= 1 | 01380 | ~ 384.6 |— 10] 4188 | + 1.6 || 460.1 | —03 |
|v /ooso | 3037 | +12/| | WP a yaiey alleen pe |

Table II confirms the conclusion that the observations concerning
the specific susceptibility of oxygen in the liquid mixtures of nitrogen
and oxygen can be represented within the degree of accuracy of
those observations by substituting the expression 4:7’ in Lanarvin’s
theory by an expression for the molecular rotatory energy which is
derived from the quantum-theory with the assumption of a zero-
point energy *).

These observations do not therefore furnish a decision between the
assumption just mentioned and that, in which the expression £7" in
LanGEvin’s theory is left unchanged, but the assumption of a negative
molecular field is added, which was found by Perrine and Kamernincu
Onnes (Comm. N°. 139d) to be in sufficient agreement with the
observations. In the mean time it must be mentioned that on the
assumption investigated in this paper the inclination of the y~1, 7-
lines for the mixtures with small density of the oxygen approaches
to the equipartition value for oxygen, which follows from the measure-

1) Dr. OostERHuts tells me, that calculations made in the way indicated above,
but in which for a the expressioa is taken which was assumed by him in Suppl.
N° 31, lead to the same result Cf. note 2 p. 915, Comm. N°. 139d

116

ment by Wetss and Piccarb, whereas, as was found by Prrrier
and KampriincH Onnes, on the assumption of a negative molecular
field with unchanged molecular rotatory energy a correspondence of
the inclinations can only be obtained by the aid of a new hypo-
thesis (unless the difference in inclination should be ascribed to a
systematic difference of experimental origin).

§ 3. The susceptibility of liquid oxygen and the application of
the quantum-theory to paramagnetism. The susceptibility of liquid
oxygen being measured over a considerably larger temperature range
(from 65.°25 K. to 90.°1 K.: Kamertinch Onxes and Perrier, Comm.
N°. 116; from 70.°2 kK. to 90°.1 K.: KAMERLINGH ONNuS and OosTERHUIS,
Comm. N°. 132e), than was possible for the mixtures treated in § 2, -
it is important to investigate whether the data which are available
about liquid oxygen can be represented also with the aid of the
relations (1) and (4). In table II] the corresponding data have been
put together.

As Perrier and Kamertincuo Onnns observe, account has to be
taken of the change in density of liquid oxygen. For the reduction
of 7, to the same density use was made of the result whieh will
be derived in § 5 from the observations concerning the above mix-
tures considered in connection with those concerning oxygen, viz.
that at these large densities 7, is proportional to @”s.

Tt AGB AE slita

| Specific susceptibility of liquid oxygen
(KAMERLINGH ONNES and PERRIER). |
i | Keale.’ 1 |
PI NEYR LOSE.) “ON TEC ore—=nio3. 3| O—-C
| | Boal ey \with @, = 232. (ao
| 4 (Gee)
64.25 | 284.9 | 232.5 | 1.267 229 282.6 + 2.3
70.86 | 271.4 | 232.7 | 1.235 | 233 | 271.7 70m
| 77.44 | 259.6 | 231.3 | 1.204 | 238 | 261.3 =e
| | | |
0h i Watt 22012 | 1.143 | 232 | 240.9 ALO
i | i : | a
mean 232,

The agreement between observation and caleulation may be con-
sidered sufficient. This conclusion is supported by the observations

117

of KAMERIINGH ONNES and OosTERHUIS:

TABLE Ilo.

Specific susceptibility of liquid oxygen
(KAMERLINGH ONNES and OOSTERHUIS).

§ 4. Conclusion. The data treated in §§ 2 and 3 lead to the
following conclusion :

The susceptibility of oxygen in liquid mixtures of oxygen and
nitrogen as well as that of liquid oxygen can be represented within
the degree of accuracy of the observations with the aid of the
application of the quantum-theory to paramagnetism as expressed
by equations (1) and (4).

The agreement between observation and calculation (particularly
if the susceptibility of liquid oxygen is also considered over the
whole range of temperatures) is somewhat better with the application
of the quantum-theory than with the introduction of a negative mole-
cular field alone: indeed Perrier and KamernincH Onnes find it
necessary for the mixtures of oxygen and nitrogen also to change
the value of the Curtm-constant. Calculations made for liquid oxygen
support this conclusion. Nevertheless it is quite possible that for liquid
oxygen also if a changed Cvrin-constant is assumed just as good an
agreement may be obtained by the introduction of a negative

molecular field.

§ 5. Dependence of the characteristic zero-temperature on the
density. Table 1V shows more particularly the manner in which /,
depends on the density 9 of the oxygen.

From the last column the conclusion may be drawn that for the

, 4, 2 log 9, rs

higher densities ——- approaches to #/,. For those densities we
7 0g Oo

may therefore write as a limiting law:

G00; smn pay etch) << evel ete te. (Ol)

118
TABLE IV.

| | A log @,

oO 4 ———
: sl) eAYogio
San nn EE :
0.0801 Oneal
| ss
0.1381 | 23.3
| \) eale66
0.2304 || 54.5 | |
| | 1.06
0.4010 | 98.0
| 0.82
0.7458 | 162
| | Osan

12235 ea) N2S2 un
|

where a is a constant (for a definite substance, This dependence
of O, on the density quite agrees with that, which in Suppl. N°. 30a
was derived for the molecular translatory motions from the hypo-
theses assumed there, cf equation (184) of that paper.
This result can be interpreted as indicating, that the proportionality
factor in the relation
C= eh,
(ef. Suppl. N°. 32a § 2), in whieh e¢ represents the velocity of the
“rotational waves” considered in the paper mentioned, is independent
not only of the temperature but also of the density, as aceording
to Suppl. N°. 80a equation (7) is the case for the corresponding
“translational waves”.
In Fig. 2 the points indicated by small circles represent the values
of 6, derived from the observations as a function of e. The curve
6—<— — Se pivese@o29) Sram
| | | “| chosen so as to obtain agree-
{| |} 6hcment for the higher valiies jor
| | | | | | vy. This agreement is in fact
| z4 | very good for @ >1, as results
| from the fact that the two
| curves do not intersect here at
| a definite value of v, but coin-
cide over a certain range of
| densities.
| | For values of @ smaller than
1 a deviation begins to show
Fig. 2. itself; this deviation at first
increases regularly in proceeding to lower values of 9.

119

It is natural to ascribe this agreement at higher, and this deviation
at lower densities to the following’). At larger densities the rotations
of the oxygen molecules are continually disturbed by collisions, or
at least interactions with the other oxygen molecules, so that the
periods of revolution of the oxygen molecules cannot play a part
in the determination of the frequencies in the system which govern
the distribution of energy.

For those densities the frequencies are determined by the analysis
according to Jnans of the molecular rotatory motions in the system
into natural. vibrations; the relations given in Suppl. N°. 32a § 2 are
then valid as approximations.

At small densities, however, at which every molecule performs
in the mean a certain number of revolutions before its rotation is
disturbed by the collision (interaction) with another molecule, it is
the numbers of revolutions of the individual molecules in the unit
of time which govern the distribution of energy. These frecuencies
are then determined at the limit by Etnstwin’s relation *).

Uy = 4 LD (2x)?
and are independent of the density.

Between these two extremes a transition range lies.

If (for 7’ = 85) the number of collisions, which an exygen molecule
undergoes. in 1 sec. at e=1 (the molecular diameter 6 = 3.10—-8
derived from the viscosity), is compared with the number of revolutions
per sec. (distance of the oxygen atoms being assumed = 0.7.10—%,
derived from the moment of inertia calculated according to Hom‘)
from O—1, which value was assumed according to Fig. 2 for
oxygen in the gaseous state), one finds that in the mean the oxygen
molecule makes 0.4 revolution between two successive collisions. It
is, however, not necessary to assume that the number of times that
the rotatory

y motion is disturbed in a second, coincides with the
number of times that this is the case with the translatory motion.
Some room is thus left for an average number of revolutions between
two successive disturbances of the rotatory motion other than the
number just mentioned. But if we assume that the order of magnitude
will not be essentially different, the result of the calculation mentioned
above is such as to be quite consistent with the theory developed

above that at g@=1 a transitional region begins in which the

1) Cf. the note quoted p. 112 note 1.

*) Rapports conseil Solvay 1911, p. 433.

8) E. Hotm. Ann. d. Phys. (4) 42 (1913, p. 1319. The ¢ used by Houm
corresponds to / in this paper.

120

frequencies of the individual molecules begin to play a part for the
energy distribution.

This theory involves that for smaller densities «, is no longer
determined by the relations of Suppl. N°. 32a, equations (4) and
(5) of this paper. Notwithstanding that, in consequence of the relative
insensibility of the way in which w, depends on 7’ for the special
assumption about the distribution of the frequencies (cf. Suppl. N°. 31
§ 7 by Oosrprnuts), a good agreement may still be obtained by
those relations with the observations considered in this paper, but
then the values of 7,, which give such an agreement, do not have
the meaning laid down by the theory in Suppl. N°. 32a,

Meanwhile the part for the smaller densities (@ < 0.15) of the,
@, ,o-curve of Fig. 2 may be given a simple meaning by supposing

15
the curve for this region to represent — A, if 4 is determined
2

by the fact that the u,,2-curve on the side of the high temperatures
approaches asymptotically to
uy kh (T + A).

As according to the relations of Suppl. N°. 32a § 2 (ef. Suppl.
4
2)
N°. 32) § 5) 0,=—A, the curve has also this meaning for

o> 1. For a nearer interpretation of the intermediate region the
theory will have to be further developed.

On the side of the small densities the curve in Fig. 2 has been
extrapolated (indicated by dots) to a part that terminates parallel
to the c-axis, in agreement with the theory given above, that at
small densities the frequencies of rotation are no longer dependent
on the density.

In this region of densities the rotatory energy is determined as in
the simplified scheme of Estrin and Strrn or of OosTErauis, in
which to all the molecules the same velocity of rotation was ascribed,
or better in the more elaborate theory of Hotm'), in which the

1) &. Houm. Ann. d. Phys. (4) 42 (1913), p, 1311. This theory, in which in the
system of rotating molecules all frequencies occur, and for the distr:bution of the
molecules according to the frequencies, in a way analogous tc that which PLancKk
in his recent theory followed for linear oscillators, the plane in which the condition
of a molecule rotatimg about one axis is represented by the values of its azimuth
and moment of momentum, is divided into regions of constant probability limited
[aes ; 3
by energy curves 4=” ir 8 consistent with the resu’ts of ByerRum and EK.
y. BaHR concerning the discontinuous character of absorption spectra in the
infra-red of gases of not too high densities, if it is assumed that the absorption

121

distribution of the velocities of rotation over the molecules is taken
into account.

Resuming we may conclude, that the observations by PERRimR and
KAMERLINGH ONNES concerning the susceptibility of liquid mixtures
of oxygen and nitrogen, although they do not furnish an experimentum
erucis between the theory of the negative molecular field and the
application of the quantum-theory on paramagnetism, nevertheless
fit without any constraint ') into the whole scheme which can be
built up on the basis of this application.

§ 6. The results of the former § concerning the dependence of
6, on the density lead to ihe following inference regarding the
influence of the rotatory motion on the external pressure. For those
densities at which w, is determined by the equations (4) and (5),
and at which 4, — 07s, the energy u, and also the entropy s, for
the rotatory motion are represented by the same functions (only
with another value of @,) as the corresponding quantities for the
translatory motion in-an ideal gas.

In that case the rotatory motion gives a contribution to the external
pressure similar to that of the translatory motion. The ratio of this
contribution, for one degree of freedom, to that which in an ideal
gas is due to the translatory motion, approaches to 1 at increasing
temperature *).

At small densities, however, vz. in the region in which 6, does
not depend on o, the rotatory motion does not give a contribution
to the external pressure. This agrees with what has always been
of radiation energy supplied from outside only occurs when the representative point
has arrived at one of the limiting curves mentioned above (for instance in conse-
quence of the probability of emission on reaching a limiting curve, cf. PLANCK,
Theorie der Wiirmestralung, 2te Aufl., § 151, being changed by the presence of
the radiation from outside) The observations by E. v. Baur, Verh d. D. physik.
Ges. 1913, p. 1150, concerning hydrochloric acid seem to be mere favonrable to
this view than to a distribution, in which, in the plane mentioned above, only the

1 hy ? z : 5 .
energy curves | m+ >} > are covered with points, which is the assumption

alluded to in the note quoted p. 112, note 1.

1) The views advanced in this § about the coming into the foregrond of the
frequencies of rotation of the individual molécules are im fact, as will appear again
in § 6, a necessary complement for small densities to the theory of Suppl. N°. 32a.

*) I find that A. Wont, ZS. physik. Chem. 87 (1914). p. 9, by quite different
considerations was also led to the suggestion that at large densities the molecular
rotatory motion may give a contribution to the external pressure. (Note added in
the translation).

122
derived for an ideal gas, e.g. from Borrzmann’s entropy principle,
cf. Suppl. N°. 24a § 4, or from the virial theorem. Conversely it
necessarily follows from this, that in Fig. 2 the 4,, e-curve at the
small densities must change its direction to one parallel to the g-axis,
as is clearly indicated by the point e = 0.08,

In conclusion we will return for a moment to the assumption
rigidly adhered to in this paper, zzz. that the presence of the nitrogen
molecules does not exert any influence on the distribution of the
rotatory energy of the oxygen molecules. The following mechanism
would be in accordance with this supposition: the oxygen molecules
behave at a collision (at least with the nitrogen molecules) as rigid
smooth spheres, they carry a (magnetic) doublet (or have according
to Suppl. N°. 324 § 7 a magnetic moment in consequence of a
rotation about an axis of small moment of inertia with zero-point
energy in the temperature region considered); the nitrogen moleeules
have a_ structure such that they do not exert a directive force on
the oxygen molecules. The object of this suggestion is, however, no
other than to show that the assumption mentioned above is not an
impossible one.

Chemistry. — “Vhe Allotropy of Cadmium. IY’. By Prof. Ernst
Conun and. W. D. Hertpprman.

The electromotive behaviour of Cadmium.

L. The dilatometric measurements made with cadmium which had
been deposited electrolytically, had shown ') that this material is a
modification which is not stable af room temperature. This corre-
sponds with the result found by Ernst Conrn and E. GoLpscamipt *)
in their investigations on the electrolysis of solutions of tin salts.
When such a solution is electrolysed below 18° C. there is not
formed grey tin as might be expected, but the modification whieh
is metastable at this temperature is deposited.
~ In the following pages we give an abbreviated account on the
investigations we have carried out in order to identify the product
which is formed during the electrolysis of solutions of cadmium salts.

2. Some years ago Huxnrr*) deseribed “a low voltage standard
cell”, represented by the following scheme :
1) These Proc. p. 54.

2) Zeitschr. f. physik, Chemie 50, 225 (1905).
8) Trans. Americ. Electrochem. Society 7, 358 (1905).

123

| Solution of cadmium sulphate | Cd-amaleam
* | of arbitrary concentration 12.5°/, of Cd by weight

The electromotive force of this combination is 0.0505 Volt at
25°.0. The reproducibility is about 0.5 millivolt. The cadmium elec-
trode of this cell has to be electrolytically deposited, as Th. W.
RicHarps and Lrwis') have proved, that only this kind of electrodes
give a definite potential. Ernst Conn and Sinnien*), who used these
cells in their piezochemical investigations also found that they are
reproduceable.

3. Some points in the construction of such cells which play an
important role in the experiments, to be described below, may be
given here. (Fig. 1 A).

Fig. |.

The glass part is a thin walled tabe about 8—10 mm. in dia-
meter, closed at one end and provided with a platinum wire; two
ov three centimeters above the closed end is a platinum spiral, with
its end fused through the side of the tube (the wires are thoroughly
cleaned with aqua regia before filling the cell).

In filling, the spiral is pressed to one side and some 0.5 cc. of
12.5 percent cadmium amalgam is brought into the lower part and
melted (carefully avoid bringing the amalgam in contact with the

1) Zeitschr. f. physik. Chemie 28, 1 (1899).

*) Zeitschr. f. physik, Chemie 67, 1 (1909).

124

platinum spiral). The spiral is then pressed down into a horizontal
position. The tube is now filled up with a solution of cadmium
sulphate of arbitrary concentration (the E. M. F. of the cell is in-
dependent of the strength of the solution).

In order to produce the cadmium electrode a current of 1 or 2
milliamp. (1 or 2 milligrams Cd per hour) is passed from the amal-
vam to the platinum spiral. At least 18 milligrams must be depo-
sited. The cell may then be sealed off.

4. We specially call attention to the following passage in HuLEtr’s
paper: ‘‘The electromotive foree of these cells is high when the
cadmium 1s freshly deposited, and the length of time required to.
reach the normal value seems to depend on the thickness of the
deposit. Air free cells and those saturated with Cd(OH), behave like
ihe others and I have as yet no explanation of the high E. M. F.
of newly constructed cells.” Our table I shows this decrease of
potential of newly constructed cells. It amounts to about 1 millivolt.

POA BLE i:

Temperature 25°.0.
E. M. F. in Volts.

ee ——
eng | |

TO cds ee | |

5 > 2 After 1) After 2) After 3| After 4| After 5| After 7| After 8
sont ates ae

i 5 5 day days days | days days days days
= vo

= | Eo

z| £

a. | 0.05156 | 0.05105 | 0.05084 | 0.05078 | 0.05070 | 0.05065 | 0.05052 | 0.05052

| |
b. | 0.05143 0.05099 | 0.05082 | 0.05076 | 0.05068 | 0.05067 | 0.05054 0.05056
| 0.05154 | 0.05103 | 0.05084 | 0.05076 | 0.05070 | 0.05067 0.05056 | 0.05058

0.05151 | 0.05099 | 0.05082 | 0.05076 | 0.05070 | 0.05067 | 0.05056 | 0.05056

| 0.05162 | 0.05113 | 0.05090 | 0.05084 | 0.05074 | 0.05070 | 0.05058 | 0.05058

Ss
~

5. These determinations and those to be described below were carried
out by the PogecEnporrr compensation method. The resistances used
had been checked by the Physikalisch-Technische Reichsanstalt at
Charlottenburg-Berlin. The same was the case with the thermometers
used. Our two standardelements (Weston) were put into a thermostat
which was kept at 25°.0. We used as a zero instrument a Drsprez-
p ArsonvaL galvanometer. It was mounted on a vibration free sus-

125

pension (Junius). The readings were made by means of a telescope
and seale; 0.02 millivolt could easily be measured.

6. As it was:very important for us to get rid of this variation
of KE. M. F. we tried to find its cause. We thought it might be found
in the electromotive behaviour of the cadmium amalgams, which has
been studied particularly by H. C. Bur’).

Fig. 2 contains his results as far as they play a role in our in-
vestigations. The curves represent the E. M.F. (ordinates) of cells
which are constructed according to the following scheme:

Millivolts

At. °/) of cadmium.

Fig. 2.
Solution of cadmium sul-
Cd-amalgam F
ee a phate (765.4 er. Cd SO He, SO, — He
x-at. Proc. 2 pel Gas +7:
/, H,O per Litre)

The abscissae represent atom per cents of cadmium.

oy Zeitschr. f. physik. Chemie 41, 641 (1902).

126

From the drawing it can be seen that the E.M.F. of these cells
at 25°.0 is independent of the concentration of the amalgam when
its concentration lies between 9.0 and 24.4 at.percents (i.e. 5.9 and
15.4 percent by weight). As soon as the concentration decreases below
5.9°/, by weight (when we pass from the heterogeneous amalgams
to the homogeneous, (c.f. Bi1’s paper Fig. 3) the E.M.F. varies with
the amount of cadmium present in the amalgam, the potential against
pure cadmium énereasing with decrease in the percentage of cadmium.

7. In the light of these facts the high E.M.F. of freshly construeted
cells becomes intelligible.

During electrolysis the cadmium which is deposited on the spiral
is withdrawn from the upper layer of the 12.5°/, (or stronger) amal-
eam, which was originally a two phase system. It is thus possible
for this layer to become a monophase system and if this is the case
the E.M.F. will increase when electrolysis is continued. After the
formation of the cell its E.M.F. will then be too high. In the long
run cadmium will diffuse to the upper layer: this becomes again a
twophase system and the E.M.F. will decrease and finally becomes
constant.

8. In order to check this supposition we carried out the following
experiment: We put two platinum spirals into the A-shaped tube B
(Fie. 1). into the right-side tube we put some 1°/, (by weight) ead-
mium amalgam (99 parts by weight of mercury, 1 part of cadmium).
This amalgam is a fluid monophase system at ordinary temperature.
We filled the tubes with a dilute solution of cadmium sulphate (half
saturated at 15° C.). After this the cell was formed in the way
described above. (1 milliampere).

After having deposited 20 or 25 milligrams of cadmium on the
left-hand spiral, the capillary tube on the right was brought into
connection with a waterpump in order to remove the amalgam. A
number of small pieces of the 12.5°/, amalgatn were then substituted
for this.

These cells give at once an E.M.F. of 0.0503 Volt when they are
put into a thermostat at 25°-0 C. It is evident that our assumption

made above (§ 7) is correct.

9 All the cells we investigated have been produced in the way
described ; it is now possible to measure their E.M.F. at onee with-
out waiting for 8 to 14 days before their becoming constant.

10. Our dilatometric measurements with cadmium which had been

127

electrolytically deposited gave the result that this material only under-
goes transformation at temperatures below 100°, if it has been in
contact at 50° (400°) with a solution of cadmium sulphate.

The probable and obvious conclusion is that by electrolysis we
get exclusively s-cadmium, the modification which is stable at high
temperatures. If this were the case, the y-cadmium would be trans-
formed into p-cadmium at 100°, into @-cadmium at 50° in contact
with the solution of the sulphate.

If now the y-modification is really generated by electrolysis,
(analogous to what happens with solutions of tin salts) the Hunerr
cells which have been measured until now would contain this
material as the negative electrode.

If this modification happened to be transformed into the modifi-
cation which is stable at ordinary temperatures and pressures (1 atm.),
this would manifest itself by a decrease in the E.M.F.

On the one hand we are working in this case under extraordi-
narily favourable circumstances for stabilisation (change into the
a-modification) as the, material formed electrolytically is in a very
fine state of division and surrounded by an electrolyte, while the
quantity which has to undergo transformation is so very small
(20 or 30 milligrams), that the transformation, if if occurs, will be
finished in a short space of time.

On the other hand, and this is to be borne in mind in researches
of this kind, the possibility exists that the transformation which has
to take place spontaneously, may be suspended, if the metal depo-
sited by electrolysis forms only one single modification, as the germs
needed for transformation are then absent.

1i. That the stabilisation generally does not occur is shown by
our dilatometrie observations as well as by many other facts i.e. by
the experiments of W. Jancer,') Ernst Conen,*) Bun’) and Hunnrr,*)
who all found the same E.M.F. (50 millivolt at 25° C.) for cells
which were constructed according to the scheme:

How obstinately the transformation may be delayed might also

1) Wied. Ann. 65, 106 (1898).

*) Zeitschr. f. physik. Chemie 34, 612 (1900).

3) Zeitschr. f. physik. Chemie 41, 641 (1902).

4) Trans. Amer. Electrochem. Soc. 7%, 333 (1905). —

128

be inferred from Hunerr’s') words: “many of these cells are still
in good order after five years.”

This wonld be in perfect accordance with our own experiences :
Crark-cells which contain ZnSO,.6H,O as solid depolariser preser-
ved their E.M.F. for five years notwithstanding their having been
standing at room temperature, i.e. 25 degrees below the transition
point of ZnSO,.6H,O. As in the case of Hunter's cells they had
been sealed up after formation.

12. On account of these observations it might be expected that
even under circumstances favourable to a transformation (stabilisation)
of the negative electrode only a certain number of Hurerr cells
would show the transformation.

On December 11'? 1913 we prepared three H.C. (N°. 1, 2 and 5)
in the way described above (§ 3) at room temperature (80 mgr. Cd on
the spirals). We then substituted a 12.5 percent cadmiumamalgam
for the | percent. The E.M.F. was now 0.0503 Volt. After standing
for two months at room temperature the cells were measured again
on February 26% 1914. The E.M.F. of 1, 2 and 5 had deereased to
00475 Volt at 25°.0 ©. and this value remained unchanged. As
might have been expected the E.M.F. had decreased by stabilisation
of the cadmium.

13. We prepared two new cells (nos. 6 and 7) in the same way
as 1, 2, and 5. Immediately after the preparation their E.M.F. were
0.04847 and 0.04795 Volt respectively. Some days later these values
became constant: 0.04788 and 0.04778 Volt. Stabilisation had begun
already during electrolysis.

14. In order to determine whether «cadmium is formed during
electrolysis if, this modification is present on the spirals before electro-
lysis begins, we shunted the cells 6 and 7 in a current of 1 milli-
ampere. In this way we deposited upon the a-cadmium which was
present, a fresh quantity of 30 mer.

After formation we put a fresh (12.5 percent) amalgam into the
cell, while a fresh solution of cadmium sulphate was also introduced.

Subsequent to this treatment the E.M.F. at 25°.0C. was again
0.05026 Volt which proves that y-cadmium had been formed on the
old layer of «-cadmium.

15. On continuing our experiments we found that on one oceasion

1. Trans. Amer. Electrochem. Soc. 15, 435 (1909).

129

cells of O.047 Volt E.M.F, on another, cells of 0.050 Volt E.MF,
were obtained.

As our dilatometric measurements had shown that stabilisation
occurs with great velocity at 50°, we prepared cells (C and O) at
47°.9. The dilute amalgam was then taken out and an 8.5 percent
(by weight) amalgam was put in, while a fresh solution of cadmium
sulphate was used. We substituted an 8.5 per cent amalgam fora 12.5
percent as our intention was to measure these cells also at 0° C.;
At this temperature the 12.5 percent amalgam is a monophase system
and such a system must not be used.

In this way we found at 25°.0 C.

Cell C: 0.04745 Volt.
Cell O: 0.05022 __,,

The cadmium in cell © had thus been stabilised at 47°.9.

16. In order to check the results found up to this point we also
determined the E. M. F. of our stable and metastable cells at 0° C,
If the differences in E. M. F. at 25°.0 between the different cells
were really to be ascribed to the presence of «cadmium (cell C) and
y-eadmium (cell O) the difference which was at 25°.0 C. 2.8 millivolt
ought to increase at 0° C. as we are at that temperature at a greater
distance from the metastable transition point ¢-cadmium = y-cadmium.

The measurements at 0° C. gave the following results:

cell C: 0.05225 Volt.
cell O: 0.05626 __,,

While the difference was 2.8 millivolt at 25°.0 C. it has increased
as might be expected to 4.0 millivolt at O° C.

17. Several phenomena which are described by Hunerr, but which
are obscure until now may find an explanation in the light of our
experiments. HuLerr says: “A number of cells were made with addition
of Cd (OH), thinking this might make a more uniform cadmium
deposit; also the air was completely removed from three before
sealing, and in others the air was removed and the cell saturated
with nitrogen and with hydrogen. All of these gave very variable
results, but in each case only 10 milligrams of cadmium had been
deposited on the spiral, and | have lately learned this is too little
cadmium, since some cells prepared as above described, excepting that
only 10 mg. of cadmium was deposited on each spiral, showed the
same irregularities and tendency to constantly decreasing electromotive
force. These cells were recently all discharged and then reversing

Proceedings Royal Acad. Amsterdam. Vol. XVII.

130

the current about 26 mg. of cadmium was deposited on each platinum
spiral, and they seem to be all coming together nicely and to the
value indicated by the old cells”.

18. Our observations agree perfectly with those of Hunerr but
we have to add the following restrictions: A number of our cells
in whieh only LO mgrs. of cadmium were deposited indicated imme-
diately after formation an E. M.F. of 0.0502 Volt at 25°.0 which
decreased during 2 days. Then it became constant: 0.047 Voit.
Transformation into @-cadmium had consequently occurred; the faet
that only a small quantity of cadmium is present causes the KH. M. F.
fo reach very soon its definite lowest value. The phenomenon obser-
ved by HuLrrr is therefore the quick stabilisation of y-cadmium.

19. Prof. Hunterr has been kind enough to communicate to us
ihe following facts: “Twelve cells which had been sealed after
formation remained unchanged from March 18" 1905 to May 7 1914,
i.e. during 9 years. Their EK. M.F. has been during all this time
0,0505 Volt. The quantity of cadminm on the spirals varies between
3.7 and 13.7 mers. of cadmium”.

20. The decrease of E.M.F. which had been observed with cells
which contain only 10 mers. of cadmium is consequently not to be
ascribed to the minute quantity of metal’) deposited on the spirals;
this quantity is much less in the cells which have been constant
during 9 years. The reason of the decrease in E. M. F. of those cells
is the transformation of y-cadmium into «-cadmium.

21. In order to check this conclusion we prepared a number of
cells (at room temperature) whieh only contained 5 mers. of cadmium
on the spirals. Some of these remained metastable (0.050 Volt) while
others were transformed into the stable form (0.047 Volt) after some days.

22. Although the discussion of a number of questions must be
delayed until a subsequent paper, we will mention here the behaviour
of cadmium which has not been formed by electrolysis.

In our second paper we stated that a piece of cadmium chosen
at random which had been produced from the molten metal contains
three modifications: «, B and y-cadmium. If such is the case, it might

1) OpprBEcK found [Wied. Ann. 31, 337 (1887)] that a layer of metal A of
2>10-® mm. suffices to give to a metal on which it has been deposited the
potential of A. As the surface of the spirals in the H. C. was 0,28 cm? the layer
of cadmium deposited is much thicker.

131

be expected that the potential of such a material against cadmium
which has been formed by electrolysis should be zero. In erder to
test this conclusion we carried out the following experiment: We
prepared a certain quantity of electrolytic cadmium (Prep. A) (Comp.
our second paper § 8) and determined (at 40°) the potential diffe-
rence between this material in a solution of cadmium sulphate which
was half-saturated at 15° C. and:
1. Cadmium, which we received from KAnLBaum (molten) in a
finely divided state (Prep. B).
2. Cadmium which we had used in our dilatometric measurements ;
in this material the presence of y-cadmium was presumed. (Prep. C).
Making use of the small apparatus shown
in Fig. 3 we first determined the potential
difference between two samples of the same
material, subsequently that between samples
of different preparations. In this way we found:
E.M.K. of A against A = 0.000037 Volt.
a Be) eee B= 01000018) Volt:
~C ‘A C= 0.00000 — Volt.

Be MEK A 3 3 = 0.090037 Volt.
Ae) C0 0000377 Volt:
From these measurements we see that y-
cadmium is really present in our preparations,
Fig. 3. as the dilatometer had shown.
Utrecht, May 1914. van “T Horr- Laboratory.

(July 3, 1914).

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.

PROCEEDINGS OF THE MEETING
of Saturday June 27, 1914.
Vou. XVII.

DEce —

President: Prof. H. A. Lorentz.
Secretary: Prof. P. Zeman.

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Zaterdag 27 Juni 1914, DI. XXIII).

COW EE anes Se

JAN DE Vries: “A triple involution of the third class”, p. 134.

W. Kapreyn: “On the functions of Heruirs.”’ (Third part), p. 139.

M. J. van Uven: “The theory of Bravars (on errors in space) for polydimensional space,
with applications to correlation.” (Continuation). (Communicated by Prof. J. C. Kavreyy),
p- 150.

M. J. van Uven: “Combination of observations with and without conditions and determination
of the weights of the unknown quantities, derived from mechanical principles.” (Commu-
nicated by Prof. JAN DE Vrigs), p. 157.

F. A. H. Scurememaxers: “Equilibria in ternary systems.” XVI, p. 169.

A. Smits and 8. Posrma: “The system ammonia-water”. (Communicated by Prof. J. D. van
DER WAALS), p. 182.

N. G. W. H. Brercer: “On Hermire’s and Apev’s polynomia.” (Communicated by Prof.
W. Kapreyn), p. 192.

Ernst Couen: “The metastability of the metals in consequence of allotropy and its signi-
ficance for Chemistry, Physics and Technics’. II, p. 200.

Pu. Konuystamm and K. W. Warsrra: “Measurements of isotherms of hydrogen at 2C° C,
and 159.5 C.” (Communicated by Prof. J. D. van per Waats), p. 203.

K. W. Watsrra: “The hydrogen isotherms of 20° C. and of 15.5 C. between 1 and 2200 atms.”
(Communicated by Prof, J. D. van pER Waats), p. 217.

D. J. Kortewec: “The different ways of floating of an homogeneous cube”, p, 224.

A. Wicumann: “On some rocks of the island of Taliabu (Sula-Islands)”, p. 226.

F. M. Jascer and A. Simex: “Studies in the Field of Silicate-Chemistry”. II. On the Lithi-
umaluminiumsilicates whose composition corresponds to that of the Minerals Eucryptite
and Spodumene, p. 239. Ibid ILI. On the Lithiumaluminiumsilicates, whose composition
corresponds to that of the Minerals Eucryptite and Spodumene. (Continued), (Communi-
cated by Prof. P. van RompurGn) p. 251.

E. Laqueur: “On the survival of isolated mammalia: organs with automatic function”, (Com-
municated by Prof.,H. J. HampBurGEr). p. 270.

C. A, Crommetin: “Isothermals of monatomic substances and their binary mixture:. XVI.
New determination of the vapour-pressures of solid argon down to —205%.” (Communi-
cated by Prof. H. Kameriincu Onngs), p. 275.

Il. KaMErRtINGH Onnes: “Further experiments with liquid helium. J. The imitation of
an AmprRE molecular current or a permanent magnet by means of a supra-conductor”,
(Cont.) p. 278.

H. Kamertinen Onnes: “Further experiments with liquid helinm. K. Appearance of begin-
ning paramagnetic saturation’, p. 283.

10
Proceedings Royal Acad. Amsterdam. Vol. XVII.

W. Karreyn: “On some integral equations”, p. 286.

H. G. van pe Sanne Banunuyzen, N. Winpesorr and J. W. Diererinx: “Comparison of
the measuring bar used in the base-measurement at Stroe with the Dutch Metre No, 27”,
p. 300. ; ;

Hi. G. van pe Sanpe Baxuvyzen: “Comparison of the Dutch platinum-iridium Metre No. 27
with the international Metre M, as derived from the measurements by the Dutch Metre-
Commission in 1879 and 1880, and a preliminary determination of the length of the
measuring-bar of the French base-apparatus in international Metres”, p. 311.

L. K. Wotrr: “On the formation of antibodies alter injection of sensitized antigens”. 1,
(Communicated by Prof. OC. Eyxman), p. 318.

F. M. Jarcer: “The Temperature-coefticients of the free Surface-energy of Liquids at Tem-
peratures from —80° to 16500 C. 1. Methods and Apparatus. (Communicated by Prof.
P. van Romeuren). (With two plates), p. 329.

F. M. Jarcer and M. J. Suir: Ibid If. “Measurements of some Aliphatic Derivatives,” p. 365.
Ibid IIL. ‘Measurements of some Aromatic Derivatives.’ (Communicated by Prof. P. van
RomeBurcn), p. 386.

¥. M. Jarcer and Jur. Kaun: Ibid IV. “Measurements of some Aliphatic and Aromatic
\thers”. (Communicated by Prof. P. van Rompuren), p. 395. ?

F. M. Jarcrer: Ibid V. “Measurements of homologous Aromatic Hydrocarbons and some of
their Halogenderivatives”, p. 405. Ibid VI. “General Remarks”. (Communicated by Prof.
P. van Rompuren), p. 416.

H. Haca and F. M. Jarcer: “On the real Symmetry of Cordierite and Apophyllite’. (With
two plates), p. 430.

P. ZEEMAN: “FRESNEL
p. 445.

J.J. van Laan: “A new relation between the critical quantities, and on the unity of all
substances in their thermic behaviour’. (Conclusion). (Communicated by Prof. H. A,
Lorentz), p. 451.

s coefficient for light of different colowrs”. (First part). (With one plate),

Mathematics. — “A triple involution of the third class.” By
Professor JAN DE VRiks.
(Communicated in the meeting of May 30, 1914).
1. I consider the projective nets of conics represented by
Qaz? + Mag? + aMaz = 0 and Ab.* + 16,2 + 26 —
The points of intersection of corresponding conics form a quadruple
involution *).
On the straight line YZ, which we may represent by 2, = ey, +
+ 6z;, the two nets determine the pairs of points, indicated by

YA (Q’ay?+ 296a,az+o7a.2) = 0 and A (9%,? +200b,b.+-0°b.*) = 0.
3 2

These equations produce the same pair of points, as soon as the
relations

Day? = +t LAby?, LAayaz =e Zhbybz,, Dda.* = x1 > hb,’.
3 3 3 3 3 8

are satisfied.
By elimination of 4,2',4" we find from this system the relation
| Ay’ —tby", AyQz—tbybz, az’—tb* |= 0. . = 4 (2)
1) This involution is an intersection of the linear congruence of elliptic twisted

quartics, which I haye considered in my communication in vol. XIV, p. 1127 of
these Proceedings.

135

trom which it appears that YZ contains three pairs of the involution ;
the latter is consequently of the third class.

2. We shall now suppose that the two nets have a common base
point 4; they produce then a triple involution of the third class. We
choose the base point 4 for vertex QO, of a triangle of co-ordinates.

Through QO, pass o

‘ conies of the first net, which are touched

there by the corresponding conics. For we have the conditions

Ss — > ‘ Sy) = SS
Sr — 407 and 2 Na — t= be,
3 3 3 3

so that the parameters 4, 4,4” are connected by the relation

aes
aie Oued |
3 3 .
| — — [=== OL ies Voeomas cle ectperttig(())
eid a =b,,4
3 3
Now we find from (1)
| Ie Ie
|) ea Ge
iL ete.

|
|

| 12 "2

| BE ose

If we substitute these formulae 2, 4', 4" in (3), an equation of the
eighth order will arise. The locus of the pairs Y', X" of the triple
involution (Y*) associated to O,== A is therefore a curve of the
eighth order, which we shall indicate by «&; A is a singular point
of order eight.

By (3) two projective systems with index two are separated from
the two nets, which systems produce the curve «*. Their intersec-
tions with the arbitrary straight line 7, are the coincidences of the
(4,4), which the two systems determine on 7. If 7 is laid through
A, the free points of intersection are connected by a (2,2); one of
the 4 coincidences of this correspondence lies in A, because two
homologous conics touch each other and 7 in A. Hence it appears
that the s¢ngular curve a has a quintuple point in A. This corre-
sponds to the fact that (V*) must be of the third class; the three
pairs on a straight line 7 laid through A are formed by A with the
ihree points in which 7+ is moreover cut by @*. The line «c= XX"
envelops a curve of the fifth class; for of the system (x) only the
lines which touch e* in A pass through A.

3. A is not the only singular point of (X*). The homologous
conics intersecting in a point Y are determined by

Ziha,? = 0 and Pi ie
3 3

If these equations are dependent, JY becomes a singular point.
10*

136
Through Y pass then two projective pencils of conics, which deter-
mine a quartic represented by
Qy> ax? bx? Ohare cnt re. ((24)
or also by
[B52 Gat Mast ie=Oh\ (212) 5 ees
The singular points are determined by the relations
Qy? ay" ay’
by? by? By

[aoe

Now the curves a,? 6,'? =a," b,? and a,’ 6,’? = ay’ 6,’ have apart
from the point QO, (which is node on both) 12 points in common.
To them belong the three points, which a,? =O and 6,7 = 0 have ©
in common apart from O,; they do not lie, however, on the curve
ay" by"? = ay'" b,. There are therefore, besides the singular point A,
nine more singular points By; the pairs of points, which form with
ZB; groups of the involution (X*) lie on a curve {;*, so that By is
a singular point of order four.

The singular curve (;* is produced by two projective pencils with
common base points A and ;; it has therefore nodes in these two
points. From (4) and (5) it appears that this curve also passes through
the remaining singular points. The straight lines 2, which contain
the pairs X’,X’’ lying on s;', envelop a conic.

As §,* passes through A twice, there are in (X*) two groups in
which the pair A,45; occurs; so 5, belongs twice to a*. This singular
curve has therefore besides its quintuple point A, nine more nodes
Ey, is consequently of genus two and of class 18.

On each of the 8 tangents of a*, passing through A, two pairs
of the (X*) coincide; from this it ensues that the straight lines s
on which two pairs have coincided, envelop a curve of class eight,
which we indicate by (s),.

4. We can now determine the order « of the locus 4 of the
pairs of points X’, Y’’, which form groups of the (X*) with the
points Y of a straight line / As a* contains eight points of J, a
passes eight times through A; analogously it has quadruple points
in By. The w points of intersection of 2 with an other straight line
/* are vertices of triangles of involution, of which a second vertex
lies on J, so that the third vertex must be a common point of A
and 4*. As these curves, besides in two vertices of the triangle
determined by the point //* and the w points mentioned, can only
intersect moreover in the singular points, we have tor the deter-

13%

mination of 2, the relation 2? = «+ 2+ 87+9>< 4"; hence 15.

The transformation (XY, X’), which replaces each point by the two
points, which (X*) associates to it, transforms therefore a straight
line into a curve of order fifteen with an octuple point and nine
quadruple points.

As 7 contains three pairs X,X’, which supply six intersections
with 4’, the curve of coincidences Jd is of order nine. Apparently
d* has a quintuple point in A and nodes in By.

With a’, J’ has 56+ 9X 4=—66 intersections in A and B;;
the remaining szv are coincidences of the involution of pairs lying
on a@*. Analogously we find that /* has fowr coincidences on £;'.

The supports d of the coincidences envelop a curve of the éenth
class (d),,, which has a quintuple point in A.

5. The locus of the pairs X’, X’’, which are collinear with a
point /, is a curve «*, passing twice through 7 where it is touched
by the lines to the points “” and #”’, which form a triangle of
invoJution with /. It is clear that e* will pass three times through
A and twice through each point 4; it is consequently of class 30.

To the 26 tangents of «°, passing through /, belong 10 lines d;
the remaining ones are represented by 8 bitangents, which are
straight lines s.

If EF is brought in A, then «* passes into «*. For a point 2, &§
consists of ~,* and a curve ¢;‘, which passes through A and the
points 4; and has a node in 4; The two curves have 14 inter-
sections in the singular points; the remaining two are points /’ and
i’, belonging to = B;,. The 6 tangents passing through 2,
at es; are supports of coincidences; the curve (d),,, has 2, for
node.

The curve «* has with d*® 51 intersections in A and #;; of the
remaining common points 10 lie in the coincidences mentioned above,
of which the supports d pass through /. Consequently there lie on

é* 11 coincidences Y= X’, of which the supports do not pass

through /, whereas \’ and X’’ are collinear with /. These 11
points belong to the curve e,, which contains the points YX, for
which the line «= X’X’’ passes through /#. The curves ¢«* and g
also have ihe points 4” and /’’ in common, forming a triangle of
involution with ££. As Z£ is collinear with 5 pairs of the /? lying
on @* and with 2 pairs of the /* lying on Ly, &, passes five times
through A and twice through #;. Consequently ¢° and «, have in
all 3X5+9X2-+13=—64 points in common; the locus of X
is therefore a curve «,*.

138

As EF is collinear with 5 pairs’) X’, X’’ of a’, and with two
pairs of §2°, €* has a quintuple point in A and nodes in bg.

If / is brought in A, &,°

For £, &.° consisis of the curve 8,* and a curve *3,‘, which
passes three times through A and once through the 8 points Bz.

The intersections Y of «° with the straight line / determine 8
lines w= N’N’’ passing through /; we conelude from this that x
envelops a curve of the eighth class (1), when X describes the straight
line J. In confirmation of this result we observe that with the 8
intersections Y of / and «* correspond the 8 straight lines passing
through A(X’’) to the associated points X’.

As (/), must be rational, consequently possesses 21 dbitangents,.
/ contains 21 pairs Y,¥, for which the corresponding points X7,.X7’;

coincides with a’.

V’,¥” are collinear.

6. An arbitrary straight line contains three pairs (Y’, X"), (V7, 1"),
(Z’,Z") of N*’; the corresponding points X, ’, Z apparently form
a group of a new triple involution*), which we shall indicate by
(XYZ); it appears to be of class 21.

Apparently (XYZ) has singular points in A and B;. Let x be
the order of the curve «, which contains the pairs }, 7, belonging
to NA; let further y be the order of the corresponding curve
b, belonging to Bg.

Let the straight line 7 be described by a point 7, the associated
pair X}” will then describe a curve 2, the order of which we shall
indicate by z. If attention is paid to the points of intersection of 7
with @ and ~;, it will be seen that 2 must have an 2-fold point in
A, a y-fold point in By.

In order to determine the numbers a, y, 2, we may obtain three
equations.

We consider in the first place the intersections of the curves 4
and gw, which are determined by the straight lines /and m. To them
belong the two points which form a triplet with dm, further z points
Z, for which X lies on 7 and Y on m; the remaining intersections
lie in the singular points. So we have the relation

2 2) ee ae? Esa 5 eee
Let the curve «a® be described by 7, then the figure of order 82,
1) The curves g® and <-§ have 3X5+9X2X2=5!1 intersections in the
singular points; they have 3 more points in common on FA; the remaining 10
intersections form 5 points A’,X” collinear with £. From this appears anew that
the curve of involution z® is of class 5.
*) This property is characteristic of the triple involutions of the ¢hird class.

135

which is described by the pair X, Y, will be the combination of
twice a’, five times a® and twice Bx.
Hence
SSS Gas bye ste So og eS ea a 6 l(t)
If Z deseribes the curve *3,*, the corresponding figure of order 4z
consists of the curve @,*, of three times @*, and of the 8 curves

Bw (k £1). Hence :

AV EY) ote og a, Oe a Ose Gs)
Out of (6), (7), (8) we find by elimination of « and y,
2? — Viz + 882 =0;

so z is equal to 63 or 14. The second value, however, must be
rejected ; for we have proved above, that (XYZ) is of the class 21,
so that 7 has 42 points in common with 4 at the least. So we find
the values

z= 63, « = 40, i iis

For the involution (YYZ), A is a singular point of order 40,
B, a singular point of order 16.

As 7 ana 4 besides the 21 pairs already mentioned can only have
coincidences in common, the curve of coincidences (XYZ) is of
order 21, Jd*’.

Apparently a‘? has in A a 20-fold point, @,'° in Bz an eight-fold
‘point; in these points d** has the tangents in common with «* and 3;.°.

If X is placed in A and Y in By, c= X' X" envelops a curve
of the 5t class, y= Y'Y"" a conic; so there are 10 straight lines
a=y. From this it ensues that the singular curve @*° has ten-fold
points in B;. In a similar way we find that the curve (;"* has
quadruple points in /,; it passes ten times through A, eight times
through Dx.

Mathematics. — “On the junctions of Hermite.” (Third part).
By Prof. W. Kaprryn.

- (Communicated in the meeting of May 30, 1914).

12. After having written the preceding pages, we met with two
important, newly published papers, on the same subject. The first by
Mr. H. Garsrtn: “Sur un développement @une fonction a variable
réelle en série de polyndmes” (Bull. de la Soe. math. de France
T. XLI p. 24), the second by Prof. K. Runer ‘Ueber eine besondere
Art von Integralgleichungen” (Math. Ann, Bd. 75 p. 180).

140
In this section we will give their principal results though not

altogether after their methods, and make some additional remarks.

13. Mr. Garprun considers the question of the expansion of a
funetion between the limits @ and 6, in a series

fe) = AM, (a) + A, (a) +.

where
6
el Ls
A, = — —= [e—“7 (a) My (a) da.
2°n!l Vax. ;
a

He finds that this expansion is possible when /(«) satisfies the
conditions of Diricatrr between the limits a and J. This agrees
with our result in Art. 7, the only difference being that our limits
were —oo and +o. This difference however is not essential, for
considering a function which has the value zero for all values
a>a>b Art. 7 gives immediately the expansion of Mr. Garsrun.

His proof rests on two interesting relations which may be easily
deduced from the formulae in the first part of this paper.

The first relation

S Ay (#) Hp (@) ay alts Ay 43 (x) HT, (a) — H,, (x) Ay+1 (a) (29)
Fp 2p! 2r+lp/ e—a

may be establishedin this way.
According to (5) we have
2xHy 2) Sas x 2nH,—1 (x
v LT, (a) Jal +1 (%) + n 1 (x) (n> 0)
20H, (a) = Ap (a) 2nIT, - 1 (a)
Multiplying these equations by H/,(a) and //,(2) we find by sub-
tracting
2 (@ —a@) A, («) Hy (a) = Ani («) An (a) — An (#) An-1 (2)
— 2n|H, (#) Hy—i (a) — Hp—1 (x) I, (@)).
Hence, putting for m successively 0,1,2,..n, we get
1 | 2(¢-a)H,(«)H (a) = H,(x)H,(a)-A, (2), (a)

(2(e-a)H, (@)H, («)=H, (a), (@)-H, (x) 1, (@)-2 |, (a) 41, (a)-H (x) 2, (a) |

2(r-a)H, (a), («) =H, (a) H (a) -H,(a)H,(«) - 4[H,(w)H, (a)-H, (w) 1, (@)]

—— | 2a) Hy (0) H, (a) =H 4.1(0)H, (0) Hye) 4 Ce)
—2n| H,(a)H, —\(a@)-H" (2) H, (a) |.

141

in question

Multiplying these relations with the different factors written on
the left, the addition of these products immediately gives the formula

The second relation

ales Ga Vals | ¢ A

See ee OES ee co. (30)

1 27 nl
0

may be obtained by introducing (9) into the first member

Thus we get

T,(@)H,—-1(2)
1 27. nl

eon" wo

ioe} u2 eo
ial —— nm f :
—— = e 4 u®cos | vu — — J|du J e—’v —! sin
wu | Qin 2
0
where

NIT
vv — =) dv
. 2
1 wo yryr nm nx
—2 cos{ wu — — }sin{| xv — =
o 42". n! ( 2 ) ( 2 )
__ cos au sin xv eur iy sin wu COs VY %, urk+ly2k+l
Fx ; Q2k (Qh) F ] Q2R+N(2h+ 1)/
uv uv uv uv
cos au sin av (e2 +- e ® i sin xu cosav (e2—e 2
re v ( 2 ) v ( 2 )
Substituting this value, it is evident, according to the formulae of
Art. 6, that all the terms of this sum vanish except only the term
corresponding to —1.
Hence

= H,,(«) ay
=

@ =
oe COS LU SIN LV
— du dv
jl Qn nl ae v 5
and because
eb u?
Ss Ji
J e COBL DIGI —= Vor ean Ne ree Vn ence as (22)
a
0
ea vp
&, H,(a a ae 1 (coma sie
er € dv.
ae Qn, Rees v
0
If now we iply
O and w, we hav

multiply the equation (a) by dev and integrate between
e

149

&® wu?

x
7 4 Stn eu af
fe du=V ax | e-* de,

0 0

thus finally
HF

5S Hr(e) Hn— Ce) == et f ee? da.

1 22 nl

14. ° Prof. Rune gives the solution of the integral equation

TF =| K (2) p(w -- 2) de <.5,2 eee

where /(w) and A(x) are given functions and g (x) is required, by
means of Hermire’s functions.
He assumes
K (x) = e—* [a, H,(x) + a,H,(x) + a,H,(2) + ...]
gp («) = e—** [b,H,(2) ++ b,H,(a) + b,H,(@) + J

which gives

a
J) = Gn be fe Hf, (x) e"t+2? HH, (u + «) dz
or, after some reductions
: 4 u
Wm oo “(Ve
(a) — = (— 1)"anbn : — =e
i ) VAR th ( ) ; (V2 yntn

If now, the given function f(w) is expanded in this form

| u u

"(u) = = ats cs (v2) ar : (v2) sie
u) = —e Cy C, — Cy a

i V2 V2 (V2)

we have from (31)

c) =a bn 3 16; = 0,000), 4) Cy =, 0s 10 Ge Oraienere
and it is evident that from these relations the coefficients 4 may be

determined. If /(w) and g(x) were the given functions, the same
relations would be sufficient to determine the function A (7).

15. The preceding reduction rests on the formula

ie 1
ET +) = —— [A,(2) + C."A-a(a)7,(y) + Cy" Ap—0(w) H,(y)4+. .
wer
+ C,,(y)) (32)

143

where C’ are the binomial coefficients. This relation may be obtained
in the following way.
According to Art. 8 Il we have

. h? h®
eens Th H, @) =le Dye (2) a 37 H, (<) ety ein ts) (p)
and, expanding by Taytor’s theorem
F(« +h, y + &)

TA (a) ea ad

l d
e— (tk? —(y-+k)? et? +9? —er"-+7" | ev aey | e—y* al =) +e? ao ) |
ai Y

i ie Pads o 5 d is d ae et a e
eye (eat ae [eee ey et :
rary da? ‘ uF da \ dy ‘ By da? rs | -

which may be written

k?
e— 2h 2h 1 AH (0) + Hy) +5 [A (0) 42110) (+H (0)

where

Putting now ¢ Seen (p) and k= no in.(g) we get
V2 V2
e-(a+yhve—l? — 1 —h H, (=) as = IT, (=) ect
. h
easy i218 — | Va [| H, (x) + A, (y)] +
jE EG) Roe Gy 4 Fy ee
(V2)72/ :

hn
Comparing the coefficients of — im the second members we obtain
nh.

the required relation (31).
Proceeding to the reduction of the integral

M ee] EH, (w) e~2? IT, (u +a) da

we put, according to (2)

qn
Lith (wv) —— (— 1)m ev oe (e-2")

dam
then
xD
>in
, M= ip) ron OM) whe? Hh, (u +2) de.
dat

Now, integrating by parts we have generally

i44

in jin U
fe a da=(— 1m firs dw +
< ¢ Lym Lym

+ | oS V dU dm—2V qm—1 U |

Seo iy

da dx dxm—* dam—1

thus, assuming
OG 6 =n)

and introducing the limits —o and o

= dm
M =/e"= [e—utt? A, (uta)] da
ain

= (1)"fe-2 dutn —u+r)?) d
— ) é damtn (e . ) v
— (<1 fe —x2—(u-+xr)? et (u+-2) dz
or, adopting
—v
uv V2 t= ——
V2
See -
N= ames ap ad Antn (ee) dg.
V2 V2

Applying now the relation (32), it is evident that the integral
reduces to the first term, thus

(_D* pat An+n (v)
V2 (VY Q)mn

Uu
Ue Tn, a7
(-1)" ~2 (ys)
= -—— e = :
VY 2 (Vv g)mtn
16. We will now compare the preceding solution of the integral-
equation (81) with the formal solution given by Prof. K. ScHwarzscHILp
Astr. Nachr. Bd. 185 N°. 4422).
Putting

or finally

Cer ey 18 Cae
the equation

fe (t.s) F'(s) ds = B(t)
0
takes the form

145

fA (e— (u+®)) F (e—*) e-* dx = B (e—*)

or, assuming

e—* F (e+) = K (a)

A (e— (4) = o (uta)

Ble) =f)
{xe gp (u -+ «) dx = f(u).
Now Scawarzscaitp multiplies this equation by e-’“ du and inte-

grates between the limits —o and + o, thus

[reo e—4u du =f ¢ (x) ae fy (uta) e—%u du

= | K (ec) e* de fo (v) e—2” dv

and puts

2 i ,2 .
Tw = fro eudu thus F (4) = 5— fren e— Pu du
aT

—o

5 ier
K (x) =z (a) e da x (2) = x I* (zie dx
ast

—D

~ Pye ‘
@p (v) = Paedy , Bo()= ml @p (v) e—?” dv
therefore
F(A) = 2aL (—-A) ® (A)
or
Ky) :

2x b(—1)

LQ)=

Multiplying again by e’*da and integrating between —o and
+ o this relation, he obtains
ei a)
K («) = — ——_—— et dj.
22.) b(—2)

—o

If now we compare this result with the preceding, we have

146

ee
F(a)= xf eu du

or
u
ar. 2 Ripe |e 5 a Wee
F(a) 1 Ve ( — F NS (va) :
b=— - CA Cy —— CF ae 5 du.
on V2. ‘V2 (ar

The general term in the series of the second member being

Se } . Pay) ‘eo
Jens = fe 2 IT, Ga e—44 du = V 2 fe 0? FT, (v) e742 dy
V2

—o —on

it is obvious that for 2 = 24 the imaginary part and forn—=2k+1
the real part of this integral vanishes. Thus for m= 2h

i v2 | e—* Ao}. (v) cos (A v V2) dv,

where according to Art. 8 IL

2
= Tops 2p
os (AvV2)—e ~ S(--1)P ——— Ae, (v
cos (Av ) é =i ) 2302p)! 2) (v)
thus
2k+1 2

a ea
Pop — (=a) 2 Vaaric mmaate
In the same way, we get

22
Poppy = — i(— 1k 241 Ve 7 ARH
and therefore
32
Y eT s% eee
iC) = DS Po}. SS Ps

\ ) 2V 27 Ok 2k u 2k+1 2k-+1

2 2
Biers s |
= 58 [2 (— Mk ow Ei S (1h conga PE].

In the same manner we find

® (2) = * [3S (1) bop 22!# — 2 S (—1)* borg BAH]

Va
and finally

147

LC a Shoot iS (—1) hoop 12H

ar : ex dx.
rf S(—1)bad* piste ee

If now the conditions
SUNS C100 a0) c, =a,b, —a,b, + a,),,
are satisfied, A(z) must be reducible to
e— [a HH, (x) + a, H, (v) + a, A, (x) +...)
It is easy to show, that this is the case; for if the conditions are
satisfied we have
D(—1)Fenp2 + iS (—1 hong 22k 41

S(— yo! iS (— 1) EH a,?-+-a,2* ... —i(a,A—a,A*-+ ...)

——n Ob

thus
NY ey
iKe(2)\— BV= Oe [> —1) ao, 2-1 (-1)F aon) A2AF1] (cos Ax + isinaa)da
“Va
2 2
1 aoe.
= ——_ | e * [cos Av XS (—1)' ap 2k + sind x S (—1)F agp 4 2k+1] da.
Va

or, introducing (9)

=} =
Hoy, (x) e-? = Gade € 4 yok cos Aw da
Vae

ae apes
Hox.43 (x) e—? = -—— e A2K+1 sin Ax da
Vw

K(#)=e = [a, ‘Hi, («),+ «, A, (#).+.2, Hf, (z) +...
17. From the relation (32) another important result may be

deduced. For multiplying by e—” dy and integrating between — o
and o, this relation gives

yH (224) 4 Va
fe Jab (Se) a = (van

ae+-y= aV 2
eS
(V2 )rh

or, putting
fave H,(a)da = H,(z).

—o@

Therefore, assuming

148

1 =
@;(a) = a 2 H,(w)
22Y/nl x
we obtain
Q)rFl ( — —(Y—= ay?2 +23
Cs (G)) = Vv = | e a 3 ein
Va

thus, in the same way as in Art. 9
3

= 1 gee 24
By — — (a2—-—ary2+a3
A= (V2), K(z,c) = Va Boe ( 3 i

m
Here the value of the function A’ (@.«) is finite for wand @ + o.
In the same manner as in Art. 9, therefore
es L)Ppn)a
K(«,e) == nl“) Pn)@)
0 an
or
e—(a2—2xa) 2+ Ce > H,(«) Hy(@)
1 3n+1
22 ni

which may be verified by (9).

18. Now, according to the theory of the integral equations the
determinant D(a) of the kernel A(v,¢) must vanish for the values
4=V2y41MmM=0,1,2..)).

To examine this, we write D(a) in the form which is given by
PLEMELJ ')

Oe Pappa 3
Se = (sea a GaP SE on:
D(a) 1 2 as
where
a, = | K(a,2)dz2, af K (eae, a,—|\K,(@ x)da,..-:
K,(a,@) = [Kew Ky—1(y,@) dy (n =1,2.3...)
and

K,(v.a) = K (a.a)
From K (vy), which may be written
K (ay) — Agha 2kay—ly*

1) Monatshefte f. Math. und Phys. 1904 p 121.

149

the functions A,,(7y) which have the same form

Ki, (xy) = Ane —hnax* + 2k, xy—lny’ ,

may be easily deduced, for
ace

K,(w.a) = AAy—1 fe (C+ hn) y? + 2(he + ky a@)y— (he? +1, 10° ) dy

-@
and
2) 7 oa)
5 G2 fh gq \?
: == =i j= =
fe Sy 2gy—h dy ——/ On | é ( ) dy
=o —o
g—fh —
ara
=: ————
Vif
Hence
—h,v2+-2h,va—l,a@?
A, é —
ke? kkn—1 Re
A —— == a? +2 : ca—| l4— ae a
ee! = ( I+-hyn—1 Lt hy—1 i l+hy—1

= V; e
Vit hn ‘
which gives
APA = ke k kn— 1
u— —_— Vas hy=h— a a — ieee l,=l,-1— me : -
Vhthy-1 la-hn—1 I+hy—-1 bt hy

Now, we know

4 : h i k=/y 2,1 8
Jal SS oF OOS => ay — —
Va Biv, 2
thus
i. 5 2 5
A, == , kh ES — Se LS =
V32 6 3 6
1 9 2V2,
A, =——= », 4, S — , 4 = - z neers
Via 14 7 14
1 17 4 17

: “ Wiba 3
and
nH
ee LA Bet A Eas ae Re ee
Cn oon et Sk,
This gives
11

Proceedings Royal Acad. Amsterdam. Vol. XVII.

n+1
2S
~ as r?
oy n+l i
: Pp Penal ay ls
QnA = fa (ez) dz = Veronad e af Cc =Ep
9 2a

Constructing now, according to Wee an integral funetion
7(a), with the assigned zeros
a= V2, 2=(V2)", 2 = (V2)...

we obtain

F@) = eG) (1 —— ,)
F(9) n=0 (V2)n+1
or, assuming 7(0)=1, G@a=0, a= r
f (a) = IT (1—AorH),
Thus ic
Tita aes PO AR sk he

70) Aa TS Ss
and expanding the fractions of the second member

Sep Se 2 =) OF
7@ eae ry +4 ee ete An eas
Comparing this with
D(A)
Giese At+a,vo+.
we see that /(4)= D(A), tor (0) = DO) =1 and
a Srp — i's = : :
p= aa ppt np
22
Mathematics. — “The theory of Bravais (on errors in space)

for polydimensional space, with applications to correlation.”
(Continuation). By Prof. M. J. van Uven. (Communicated by
Prof. J. C. Kaprryn.) 1)

(Communicated in the meeting of April 24, 1914).

In the theory of correiation the mean values of the products aja%
are to be considered; denoting these by 77, we have

1) The list of authors who have treated upon the same subject, may be supple-
mented with: Cu. Mi. Scuots. Theorie des erreurs dans le plan et l’espace. Annales
de |’Ecole Polytechnique de Delft, t IL (1886) p, 128.

+n +o
TT ae E : : —(b,.%"+ @it..+b ) :
Vik = = =a UU € da, ..da
n RP.)
j= OX =—H

To integrate in the first place over all the variables x except
xv; and 2, comes to the same thing as to drop the g—2 linear

relations x= Da; v;(/==7,4). Thus we start, as it were, only from
1
the two equations

Bj = aziz + ajgve +... + ayers,
Le = agiyvi + apgove +... + ager.
and find therefore

oo 2 ee
pup +2 bi Ke jep + bpp’ eh?) |
Yjik = LIL dajday ,
— oO U
where
E' == ES “ byy'; bik
=p" Dik's Dick

D’ yepresenting a determinant of the matrix

Qj1y Aj2y +++ Aj

|
IE | |
| cet 5 Qp2s +++ Akz |
Besides
i Ae Gia sss « Ofens
Dy = aj, Aj2y 2 0 6 Ajay
hence
Day?
pees TIS es
bj; Sse = ES ap; ;
oe = — EH Dajiapi;
in. = E'S a5;7.

By performing the integration we obtain for 1;%

t =a
ater bite = Aj Uk
lik == ) 7! 9

Sy? . 5
z =v; Ma, — (bj j'aj? 4 2b ja jap ben’ 247) rire = Aji
a vj dz ;* = — —.
\n _
—@ —@

Now the correlation-coefficient 7;; of v; and a, is defined by the
expression
A hn

152

—

V nj ;%Kk
This correlation-coefficient can therefore also be written in the
following form

> ajl al
i —— —
> aj". > axl”
or
By
Vik

V Bj; Bre
Introducing the coefficients «;;, we find

> €/? aj] Akl

rik = —————————————— et)
VS ef ae ae

We now will imagine the variable w to be connected with some
cause Q;. To express our meaning more clearly: we suppose the
quantity 2 to be built up of some variables w, viz. as the sum
of these variables, in such a way, that in this sum the term wy 1s
lacking if ; is not subject to the influence of the cause Q.

So in the relation

Vj = aj, U1 + ajzue +... + aju +... + Qjz Us
we have
aji=1, when Q does act upon aj,
aji= 0, when Qi does not act upon 2j.

Thus in 2 e? aj? only those terms &,*s &*)++-&,? occur which

(—
correspond to the variables u,,, u,,,...Ur,, due to the causes
Oe GOR Weise Qn, actually influencing «;; on the other hand those

terms are lacking, which owe their existence to the causes not con-
tributing to 2;.

In the sum 2 €/?aj;@% Only those terms &’ occur, for which both
il

aji=1 and az=1, that is to say: the terms, which derive from

the causes (Q), acting both upon a; and zx.

The expression 1j;, = > &aj,a,, therefore may be called the
i-1

square of the mean value of those elements of «j and xk, which are
due to the common causes.

z,;, We may define the correlation-coefficient of the quantities 7; and

av, in the following manner, proposed by Prof. J. C. Kaprnyn *).

The correlation-coefficient rj. of x; and xp is that part of the
square of the mean error common to «vj and aj, which is due to the
common causes.

Supposing every quantity w; to have the same mean error, or

€; = €9 == ...=>=6& ,
we find for rz
= aj) Ay)

Hg Ni SS eT
V Sa;)’. = ap?
Now + a;,* apparently equals the number A; of the causes acting

upon 2j, ay? the number NV; of the causes influencing x, and

2 aj, ax, the number N,;;, of the causes contributing both tov; and x,.
Jt Ek J 5 ‘ k
Thus, in the case of equal mean errors, we have

in other words: for ¢,=6#,—=...=e«, the correlation-coefficient
equals the quotient of the number of common causes, divided by
the geometrical mean of the numbers of the causes, which act upon
xv; and 2, resp.

If both xz; and zz are subjected to an equal number (V; = V;,—.V)
of causes, Vj, of which act both upon 2; and a, then
Nyx
No
in other words: the correlation-coefficient is that part of the causes
of x; (resp. 2%) which also contributes to zz (resp. 2;).

The expressions for the correlation-coefficients admit of a very simple
geometrical illustration.

Calling spherical simplex S, a (g-dimensional) 9-gon lyeg on a
g-dimensional hypersphere (extension of the spherical triangle in
3-dimensional space) we may state that a spherical simplex |S. has

9 (e—1) as
—— edges pj, = Pj Pr.

Gsavertices) 2 er. =... 3P, and

Opposite to the vertex P; we find, in the (@—1)-dimensional linear
space a;, the (curved) (¢—2)-dimensional face of S,, which contains
the remaining e—1 vertices P; (j=|=2).

Further we denote by 2a), the angle between the linear spaces
x; and a; [consequently also between the (@—2)-dimensional faces

1) J. CG. Kapreyn. Definition of the correlation-coefficient; Monthly Notices of

R. A. §., vol. 72 (1912), p. 518.

154

(Pi; Pa. se Pia Pha. PA and te Res en e ee

Building the positive-definite determinant

| 1 1 .€08)19) oh RCOSYPiS wy a= mismieenCOS OH om
|
| |
cos P12; ] Te COSV0D3) uated i COSiDDD.
r=
cos Pig, COS P23 1 spn) eet SBCOS IS
COS Pip , COSP2ap , COSPgo 3 - = - 1 |

and representing by Cj, the minor of cos pyr, we have by the theory
of the spherical simplexes
:
Ujk
V Cy; Con

cos Hj, = —

Substituting
big =H" bj = Gy Me C08 zk

the quadratic form H in the expression for the probability W trans-
forms to

H = Bb 5; 0; + 2 Vd jK w; wp = ZV (qy aj)” + 2 > cos pju (95 %7) (Gk ee)-

This form is positive-definitive, when

r>0,

or, in other words: when the arcs pj, are the edges of a o-dimensional
spherical simplex.

Furthermore
P o ~
i —— GL
1
and
i °
I V-
1 Y
Bip = ——_~ XK Cite
qj Qk
whence
Byy. Cir
i — Z g - == — cos IT;x,.

VBij Bex V Cjy Crt
So, putting H in the form
H = XJ (qj 2;)? + 2 = cos pjx (qj 7) (ge 2k);
the ares pj; must be the edges of a 9-dimensional simplex and
moreover: the correlation-coefficients are, but for the sign, equal to
the cosines of the “opposite angles” IT;,.
In the case of “errors in a plane” only a circle-biangle P,P, is
to be considered. Then the are P,P, =p,, equals the angle J,

11515)

included by the opposite spaces (straight lines, radii of the cirele)
a, = OP, and x,=OP,, O being the centre of the circle.

So, in the case of two variables x, and x, with the quadratic form

JE Oe tie PAO Cy Ol a= Opt re
we have to put
bi, =" 3 b,, = 49; ’ bb. =H G2 COS Py 5s
whence
E = q,’ 9," sin* p,,-

The correlation-coefficient 7, now takes the value

i —— 1 COS ——|——1C08, Da — —.

DVGe

Considering the errors in 3-dimensional space, the spherical simplex

13
2

is a spherical triangle P,P, 7.
The quadratic form //, after being transformed, reads
HH Gy? 749g %y +9 q © y $29.93 2g COSPy y $29,912 gi, COSP y +24, Jo iV COP,

The opposite angle J/,, of the edge (or side) p,, now merely is
the angle P, of the triangle. Denoting, for the present, the edges
(or sides) by p,, Py, Ps» So that

(eg 0 Tee 9 WS

we have
COR = —— COS Ti == —IC0Se
and
cos P, + cos P, cos P, ee ;
COS Py, = C08 Py = = = =—- els,
SUPE Spas V(1—r, ,?)(1—",,”)

I= 1 — cos’ p,, — cos" p,, — cos” p,, + 2 cos p,, COS p,, COS P,,
= 1 — cos’ p, — cos? p, — cos* p, + 2 cos p, cos p, COs ps.
Putting further
Pitptp=2s , P+P,+P,=28,
we may reduce T to
T= 4 sins . sin (s—p,) . sin (s—p,) . sin (s —p,)
= 4 cos S. cos (S—P,) . cos (S—P,) . cos (S— =|

0 TEA JER Gp Lee
The relation
ajay Biz
= — = —_ a

2 2H

here involves

Ons Of
Be | by 5, Oss Jz Qs Sin® Pp,
— = = Sao Sete :
In = 97 2B QE:
Now
a — 4 cos 8. cos (S—P,) . cos (S—P,) . cos (S—P,)
e — . . . 4
; GOs 1 i Tee
hence
sin? P 1
i —e : x ’
13 2[—4cos S . cos(S—P,) . cos(S—P,) . cos (S—P,) ~~ q,?
Putting
— 4cos 8. cos (S—P,) . cos (S—P,) . cos (S—P,) = Q,
we obtain
ae ae
io = 2 2 ’
whence
sin P,

ho
u V2Qn,,

Further we find, after reduction,
Q = 1 — cos’ P, — cos? P, — cos? P, — 2 cos P, vos P, cos P,,

consequently
rae i Pa + 2 Toa Tig Ties

Finally
(RS one oe Oba qa" Osa Q° =
= etek Pain? Phen Plein 873,N1s%ssQ

Introducing the mean errors 7,, 9, and 9, of 2, 7, and a,, Which

satisfy the equations
& —— Pt een
Ub 4h 9 Ye = hee

yy = han ’

we find
sin P; ; :
ee ee)

ni V2Q

Psa e Ie

and
Tes Tis Tie

1 betel feat ih 9 723 ae
=— ee — evel Je
Geos. i eae

ds, .05,.08,.

Ps
—
(22)"2 1, 4,%,VQ

157

Mathematics. — “Combination of observations with and without
conditions and determination of the weights of the unknown
quantities, derived from mechanical principles. By Prof. M. J.
van Uven. (Communicated by Prof. JAN pr Vaiss).

(Communicated in the meeting of May 30, 1914).

The theory of the combination of observations by the method oc
Jeast squares has already been the object of numerous geometrical
and mechanical illustrations. In the geometrical representations the
leading part is usually played by vectors (L. von Scururka '), C.
Ropricurz*)); the mechanical ones are taken partly from the theory
of the ‘pedal barycentre” (Y. Vinuarceau *), M. p’Ocaene *) ), partly
from the theory of elasticity (S. Finsrerwanper®) R. b’EmILIo‘),
S. WeELnmIscH, PANTOFLICEK ’), F. J. W. Warrier’), M: WrsterGaarD *),
G. ALBENGA ")).

In the following paper we will try to develop a mechanical
analogy of the solution of the equations furnished by observation,
supposing that no conditions are added, as well as for the case
that besides the approavimate equations of condition (called by us:

1) L. von Scururka. Eine vectoranalytische Interpretation der Formeln der Aus-
gleichungsrechnung nach der Methode der kleinsten Quadrate. Archiv der Math. u.
Physik, 3. Reihe Bd. 21 (1913), p. 293.

2) (C. Ropricurz. La compensacion de los Errores desde el punto de vista geo-
metrico. Mexico, Soc. Cientif. “Antonio Alzate’, vol. 33 (1913—1914), p. 57.

3) Y. Vimrarceau. Transformations de |’astronomie nautique. Comptes Rendus,
1876 I, 531.

4) M. p’Ocaene. Sur la détermination géométrique du point le plus probable donné
par un systéme de droites non convergentes. Comptes Rendus, 1892 1, p. 1415. Journal
de l’Ecole Polytechn Cah. 63 (1893), p. 1.

5) S. Finsterwatper. Bemerkungen zur Analogie zwischen Aufgaben der Aus-
eleichungsrechnung und solchen der Statik. Sitzungsber. der K. B. Akad. d. Wissensch.
zu Miinchen, Bd. 33 (1903), p. 683.

6) R. p’Emito. Illustrazioni geometriche e meccaniche del principio det minimi
quadrati. Atti d. R. Instituto Veneto di scienze, lettre ed arti, T. 62 (1902—1903),
p. 363,

7) S. Wettscu. Fehlerausgleichung nach der Theorie des Gleichgewichts elasti-
scher Systeme. Panroruicex. Fehlerausgleichung nach dem Prinzipe der kleinsten
Deformationsarbeit. Oesterr. Wochenschrift f. d. 6ff. Baudienst, 1908, p. 425.

8) F. J. W. Wutepte. Prof. Bryan’s mean rate of increase. A mechanical illustration.
The mathematical Gazette, vol. 3 (1905), p. 173.

%) M. WesterGaarp. Statisk Fejludjaevning. Nyt Tidsskrift for Matematik, B, T. 21
(1910), pp. 1 and 25.

10) G. Atpenca. Compensazione grafica con la figura di errore (Punti determinati
per intersezione). Atti d. R. Acead. d. Se. di Torino, T. 47 (1912), p. 377.

158

“equations of observation”) also rgorous equations of condition
are given.

Moreover, in either of these cases also the weights of the unknown
quantities will be derived from mechanical considerations.

The method here developed is founded on the staties of a point
acted upon by elastic forces and is in principle closely related to
the procedure of the last-mentioned mathematicians.

To obtain general results, we will operate with an arbitrary
number CV) of unknown quantities or variables, which are consi-
dered as coordinates in -dimensional space. In order to render the
results more palpable, we shall, at the end, recapitulate them for
the case of two variables.

I. To determine the V unknown quantities

ii iy. Zoe: ou « (UND)
the » (approximate) equations of condition or equations of observation
aja -+ by + o2+...4-m=0 (CS Oa)
are given, with the weights g; resp.

In the sums, frequently occurring in the sequel, we will denote
by > a summation over the coordinates 2, Up poor OY Over the
corresponding quantities (for inst. their coefficients @;,b;,¢;,...) and
by | | a summation over the m equations of observation, thus over
2 from 1) fom:

Putting accordingly

aj? + 6? +o? ... = Bia?
and introducing

aj bj Ci mM;
oS VSae = Sat = Sas ANS bi see A
we may write the equations of observation in the following form
Vi=aet By tyet...+u=—0 G=1e 2)
or
V;=Zaje¢+ w= 0 (CSS thpo so):

These equations have resp. the weights
Pi=H > ai’.

The equations V;=0 represent (V —1)-dimensional linear spaces;
their normals have the direction cosines (aj, 3;, yi,-.-) resp.

In consequence of the errors of observation, the approximate
equations |; =O are incompatible; in other words: the n linear
spaces 7;=0 do not meet in the same point. By substituting the
coordinates w,y,z,... of an arbitrary point P in the expressions

V;, the latter obtain the values v;, representing the distances of the
point P to the spaces V;= 0.

The distance from V;—=0O to P is to be considered as a vector
»; with tensor v; and direction cosines a, Bi, yi,..-

We now imagine a foree ¥; acting upon P (in V-dimensional
space) in the direction of the normal »; (from P to V;=0) and the
magnitude of which is proportional to the distance v; and a factor
pi characteristic of the space V;. (The space V;=0, for instance,
may be considered as the position of equilibrium of a space V;=7;
passing through P by elastic flexion.)

So the space V; acts upon P with the force

$= — pity.

All the spaces V;(¢=1,...n) combined consequently exert on P

a resultant force, amounting to
5 = [oi — [pal

This resultant force depends on the position of the point P.
Hence we have in .V-dimensional space a vector-field 5. determined
by the above equation.

Now the question to be answercd, is: at which point Pare these
forces §; in equilibrium? For this point P we have

=A")
or
lp pasi|i—20

The “components” of this vector-equation in the directions of the

axes are

pore | 07 lor 87 0) perry 07s.
Substituting for v; the expression V;= Sa;c-+- ui, we obtain
[piai?] a + [piaiBi) y + [piaiyi] 2 +.-.-+ [pia cal === (l),
[piGiai] « + [piBitly + [piBivile +--+ ipibiuil =.
[piviei] « + [piyiBily + [piv le +--+ [piviu] = 9,

or by
aj b; A Cj mj ; esas
== ———_ , pi = = YS 8 SS SS EH HL MG =»
VA OO V ai’ ar (ea

[giai?] a + [giaibily + [giaic. ] 2 +--- + [gaimi]=0,
[gibacle + [gibi*)y + [gible +.-- + [aibimiJ =O,
[giccac |e + [gicrbily + [gia*]2 +--- + [giami] = 9,

In this way the ‘normal equations” are found,

160 .

The force §;= — piti has the potential
Ui= piv? =tpiVirs
for
: OU; OV;
(Fi)x = — —— = — pi Vi —— = — pivia; ete.
Ow Oa

The whole potential therefore amounts to
U=[Uil= 3 [pivi').
As the equation V;= Sa2-+4=0 has the weight p;, the
mean error of weight 1 is determined by

hence

At the point P satisfying the normal equations the potential and
consequently also €° isa minimum. The “weight” of the distance v; was
pi- This weight may be determined a posteriori, if we know the
influence of the space V; alone acting upon any point. We then
have but to divide the amount /; of the force §; by x.

II. In order to find the weights of the unknown quantities, we
now remove the origin by translation to the point P, which satisfies
the normal equations.

Calling the minimum potential U/,, denoting the new coordinates
by w',y',2',... and introducing

V;'=aye' t+ Biy + ye +... aie’,
we obtain
lp? Va) 2 (Ey 20

So U’ is the difference of potential existing between a point
(v', y',2',...) and the minimum point P.

The equation [p; V;"]=2U’ represents a quadratic (N — 1)-
dimensiunal space &, closed (ellipsoidal) and having P as centre.
This space is an equipotential space and at the same time the locus
of the points of equal ¢. We shall call these spaces 2 briefly hyper-
ellipsoids. The hyperellipsoids $2 are homothetic round P as centre
of similitude.

Introducing the principal axes as axes of the coordinates _X, Y, Z, ...,
we obtain for £2 an equation of the form

AX? BY? 2072 4... = 2107

The components of § in the directions of the principal axes are

found to be

au" ? aU’ E du! a
eS — dX =—_— AX, Fy =>— Pia —— Deh 7 — ry; === UC
We may therefore attribute these components to attractive forces
of the spaces ¥ = 0, Y=0, Z=—0,... (principal diametral spaces),

which are perpendicular to these spaces and proportional to the
“principal weights’ A, B,C,...
For a point on the principal axis of X holds
xe —— AX 1, oH yi — Ol 7 108 rete:

Consequently the principal weight A may be determined by dividing
the force at a point of the principal axis of X by the distance Y
of that point to the principal diametral space Y = 0. To determine
the weight of another direction !, only those points are required, at
which the direction of the force coincides with the direction |, i.e.
the points the normals of which to the hyperellipsoids $2 have the
direction 1. When dividing the amount of the force existing at such
a point Q by the distance of the tangent space of Q to the centre
P, the quotient found is equal to the weight of the given direction.

So, in order to determine the weight g, of the direction of the
original z’-axis (or of the w-axis), we only have to turn back to the
coordinate system w,y7/',2',..., relatively to which the equipotential
spaces have the equation

WA 40

For a point Q(a’,y’,z',...) at which the normal to the equipotential
space, passing through Q, is parallel to the w'-axis (or to the x-axis),
we have

Ffys—g0' , Fy=0 , Fy=0, ete

or
so pe our Ou!
apr = 9 , eae : ape ete,
hence
[pia Vi] == gee! , [pir Vi'}=0 , [piyiVi'] =, ete,
or
Lpiai*] a + [piaisil y' + [piaivi] 2! +... = goa’,
[piBia:]e' + [piBi7ly + lpi Bivile' +-...=0,
[piy.ai |e’ + [piviBily' + (piyZ)]e' +... 9,
or

y!
Dpa

: 1 : eH
[pia |— + [piaibi] — + [piaiys] —-+...—1=0,
Ju 4 Jat

; | i zZ ’
[pi Bias] — + [pi Bi") if + [piBiye]—t+.-..+90=9,
Ja Jad Jat

It ea
[piyees] — -[piviBi]— + [pivi*] — +--- -0=9,

Ix Jar Ja

or
] y! 2!
Jgiai?] 7 all le [gia; b; | ——1 |= laiaic | es +...— 1 == (0)
Ix Jar Jak
1 < Of Zz
lgbier] + [9 8i*] — +. [gi bit] — 2 =-F 0 = 0;
Ox et Dyk
1 y' ber 2 :
[gicia;| == [eieib; = =— [gier=]) —— + - - = 0;
Ix Jat Jat
Yo aes 4 ag ble
So — is apparently found as the first unknown quantity in the
De

“modified” normal equations, modified in this way, that the constant
terms are replaced by — 1,0,0,... resp.

Considering U (e.q. U;) as an (N + 1)" coordinate perpendicular
to the N-dimensional space (v7, v, z,...), the equation

Vii 20;
represents a quadratic space of NV dimensions, built up of 0 (N—1)-
dimensional linear generator-spaces, all parallel to (V;=0, U=0),
the intersections of which with the planes perpendicular to (V;=0,
U7=0) are congruent parabolae. The parameter of these congruent
parabolae is —.
pi
The quadratic space pi Vi? =2U; will briefly be called a parabolic

eee ; il
cylindric space with parameter —.
su Di
The equation

| pi V2) 2 U
represents a quadratic space W of N dimensions, the centre of which
is at (7 =o, and the intersections of which with the V-dimensional
spaces U = const. are hyperellipsoids 2. Thus YW is the extension
of the elliptic paraboloid.

The point 7 of WY with minimum JU (U,), and hence closest to
(7=0, which is called the swmmit of ¥% is projected on U=O
in the point P, satisfying the normal equations.

By displacing the system of coordinate axes (w, y, 2,...,U) (by
translation) from O to 7, ¥ obtains the equation

[pi V;"] = 2 U'=2(U—D)).

By constructing the enveloping cylindric space, the vertex of which

163

coincides with the set of points of the space «—O at infinity, thus
the tangent cylindric space, the generator-spaces of which are parallel
to the z-axis, we find for this cylindric space the equation

Onatha ——ay life

Ree :
Its parameter is —, or the reciprocal value of the weight of the
Gx
direction «.

Ill. We now suppose, that the variables w, y,2,... must at the
same time satisfy the following » rigorous equations of condition
Day ee) 0 (Gisaa5, 2)
Then the point P is constrained to the common (V—»)-dimensional
space ® of intersection of the »(N—1)-dimensional spaces ®;.
Now the point P, subjected to the elastic forces §;, is in equi-
librium, when the resultant 4 = [6;| is perpendicular to ®.
Let the normal at P to #; have the direction cosines
O®; OP; 0’;
Ow Oy Oz

a! J

eae a Se tc
(98 ee 0@;\? ca (0D; \; ie
SS >
v>(5') a CG) v3(%)

The normals at P to the spaces #; form a linear v-dimensional
space. In this space % must lie, which means: § can be resolved
in the directions of these normals, the wnit-vectors of which will be
denoted by w

So we have

a
—

5 = [9 wy]
where | ]' signifies the summation over j from 14 to ».
The components of this vector-equation are
Lpivias |] + [99 as’! =0, [pe riBi] + Lay B=, [piri ye] + [qi vi']'=09, ete.
or
[piai*] x + [piarBily + {pieivi] = +--+. + [piaiui] + [gj ey] = 0
[piBiec] @ + [pibi*] y + [peBivi] 2 4- ©. - + [piBiwi] + lay 8;'T = 9,
[piyi ag] @ +- pees Ny Yet Piva lee seer ‘ [piyier] + [aj v5) =,

Putine
a ee? ie ae a,
G=UVV= » (y=1,..>)

Ow ,
we may write the above equations in the form
, OD;
Ow

=20)

[giai*) @ + [giaidi]-y + [aiaic le 4+... + [giaimi] + [qi

164

0D; ,
[qi bai) @ + [oi bi*] y + [oi dici] 2 4-6 <. =E [ai bimi | + lay >, l=05
y
0; _,
[meres ]@ + [oerbi]y + [oe] 2 +... + oem) + [y' 7 Y=0,

These N equations serve, together with the » conditions ®; =0, to
determine the NV variables 2, y, 2,... and the vy auxiliary quantities q;’-

Now the solution of the problem is not represented by the centre
of the hyperellipsoids £2, but by the point, in which the intersection
space ® (space of conditions) is touched by an individual of the set
of the hyperellipsoids 2.

The analytieal treatment of the problem is simplified by taking
the coordinates so small, that in the expressions ®; homogeneous
linear forms suffice. The geometrical meaning of this is that a new
origin O' (vy, Yo, Zo, --) IS Chosen in the space of conditions ® near
the probable position of the required point. So the spaces ®; are
replaced by their tangent spaces /;, and the space of conditions by
its tangent space R&R of N—vr dimensions, intersection of the tangent
spaces Lj.

Denoting the coordinates obtained by translation to O’ by §, 9, §, «.,
so that e—.w2,+6,... and putting
ae, + Biy, + Yiz%) + aah , axe, + by, + cz, +... + mj = mi;
we find
2U =[pilaiw + iy + yi» + wi] = [pais + Bin + iS + + HH)

putting
aE + Bin + iS 4-... gi Vi,
20i= [pi Vi).
The equations #; (x,y,z...) = 0 may now be written:

(Pbjn Odd) (Day
Ds (a5) Yurzo.- - | —— 5 ' ) ae C+...)/+..S0

Ow
or, since O” is assumed in ®; =O, and higher powers of §, 7, &...
are to be neglected,

OD; OD; OD; io :
Eee be 02 (y= ee)
Ow Oy

02
or
W,=a;§+86;n+y7/S$4+...=2a;5=0. (j=1,..-»).

So the normal equations appear in the following form

[viae?) § + [eae br] + (yeaie |S +.» + [gcaimi] + [ar oy!) = 9,
[yi bias | § + [gobi] my + [ue bier]$ + -- + [ge dime] + Lay 2s! =%

165

lgccraz] § + [gecebs] y 4 Lore?) $+. + [oiceme] + ony lk 05

IV. To determine the weights of the directions a, y, z,..., we
again begin by shifting the origin (by translation) from QO’ to the
point P, satisfying the normal equations and |W’; = 0.

a : . 7

Calling U,
potential relatively to P, &’,9)’,6’,... the coordinates with respect
to P, and putting finally

the potential in P, (7—U,=U" the difference of

as + Big py Se. vil, a St Bin! + yi G+... = Wy

we find
20) lp Va 2h; Wei

This equation represents the set of equipotential spaces 2. U/’=0
furnishes the byperellipsoid 2, touching ® (or 7?) in P.

Now those points must be found at which the force can only be
resolved into an (inactive) component perpendicular to FR and a
component parallel to the «-axis.

For such a point we have

aU ‘i
carts Feta [yee] — ges),
al OU! r nr
EE — a on et 0,
U/
eu! :
ee aie Cee Stare
or
Lpi Vir ac) -— [qpe3') = — [rye;']' + oe8',
[pi Vi Bil — (q98;') = — [585],

[pi Vi! vil — lays) = — Ura,

or putting
i) = == 8
[pias Vi'] + Lsjery''=a8', [pi 8! Vi'] + [553;'=0, [prvi Vi'l+1s;7;'I'= 0, ete.
whence =
Lpiai* |S + [pias Bil a! + [pieivi] § + ~~~ + [sjey'|’ = ge8',
[pieiai]s’ + Lpeei*) a! + [reir 1S + -.- + [s78;']' = 9,
[piy es + pivibi)a + [pixels 4 T=9,

oo ae ey
or

Proceedings Royal Acad. Amsterdam. Vol. XVIL

166

Is 9s

Ube 7 q eee
[aiai?] - + [giajb; | - i + [gja; a See es)
dé =

1 , | oS) $j
[9% ba; }— + [9: b; 7] = + a be; | SS Roo oS | [tj + 0 == (i).
gz Grs zs q |

Js JSS

1 / 2 S 7) "
lo:ciai |] — + [oie b; | oad + lai c*] Sqn 050 Sr 6 9A 10 ==10"
5 :

the conditions

' 1 ' 7] ! o .
aj +f 85) = ee ae (Gj = 5 5.0.9))s
gs ges 98

also being satisfied.
From the above NV -+ » equations with the V unknown quantities

1 9 C sos wy 1
.—=,——,... and the rv unknown quantities — , — can be solved.
ge 98) eS 9:5 9

The method of solution of Hansen is found again by introducing

SSS an <7
Gs $j !
es SS)
S a] et)
i) JES
<! 1 ! '
s qj
= — A == iB ; 3 = G& ;
9S GE JES ges
whence
k; Sajé'
=-= — = Taj A (G1 n)
gi JES

Then the modified normal equations furnish
[9ia;?] A + [giaibi] B+ [gait] C + ...+ [kj'a,;'|’ =1,
[ai bia: | A + [oibi? |] B+ lai bie] C+... 4+ [k;'8;'] == (()):
[9iccai] A + [obi] B+ [gic?|] C 4-..-+ Tew) =9,

or
[g:ai(2a; A)] + [egal als lig: b;{ 2a; A)| + [4;'3; ]=9,
[gi ¢i (a; A)] + [é;'y;'T =) eiGe
or

[kia;] + [ej'o,'! = 1, [eib:] + [4,'8,'|' =, [hier] 4 [4)'7;'' =O, ete.,
and the (rigorous) equations of condition run

= a; A— 0 (Gi eee)
From the set of equations
: Bi wae ee
=q, A= — (ee)
Ch
>), A —— 10) (== ono),

[cag Ay ey" |'=1 , [he bs 4 [4y'8;''=0 5 [Ai ci JH-14;'y;']=0 , ete. (NV in number)
the .V variables A,B, C,..., the m unknown quantities %; and the

yr auxiliary quantities /;' can now be solved.

167

The weight of x is thus defined by
1
Ia — 9 =S =

It may also be found by the following ealeulation
ke?
a = [hia A] = ZA [hia;] = A [hia;] + B [kbs] + C [hier | 4
=A— A [ka — B[AB;] — C [h'7;J —...
ll
= Al = Gea) = Se

95
so that g, is also determined by

By considering the quantity U as (V + 1)" coordinate perpendi-
cular to the N-dimensional space (7, y,z,...), the equation

[p: Vi'?] — 2 [g; W;') = 20"
represents the quadratic space ”. The origin of the coordinates
§',7/,0,..U' now lies at the point S, the projection of which on
U'=— U,(U=D) is the required point. Now this point S is not
the summit of ¥.

The linear space of conditions R of NM —» dimensions is now
joined to the point U” = @ by an (NV —v- 1)-dimensional space R,,
which passes through S and intersects the quadratic space ¥ in a

1
also has its centre in U’ =o, but is of fewer dimensions, viz.
N + (N—-++1) — (N-++-1) = N —v. The quadratic space ¥, has
its summit in S.
We now have to determine the points Q in ¥,, at which the

quadratic space ”, having the same character as Y, in that it

((v-+-1)-dimensional) spaces of normals are parallel to the a-axis. In
such a point Q ¥, is also enveloped by a parabolic cylindrie space,
the generator-spaces of which are parallel to the a-axis, and which
therefore has an equation of the form

gx §? = 2. U'.

Its parameter is

ao
In other words: — is the parameter of the parabolie cylindric
Ya

space, which has its generator-spaces parallel to the a-axis and
envelops the quadratic space ¥, .

V. We conclude this paper with a short summary of the results
for the ease of two variables w and y.
12*

168

The equations of observation are represented by the straight lines
Vi;=aje + By + w=O (weight pi) @=1,...n).
The point P(, y) is subjected to the force
6 = [di] = — [piri]
in which », represents, in amount and direction, the distance of the
line V;=0 to the point P.
The point P remains at rest, if its coordinates satisfy the equations
[pias] @ + [piaiBily + Lriecui] = 0,
[piBiai]@ + [piBitly + [piBier] = 0.
Denoting here the potential U7 by 2, we obtain
[pi(ace + Biy + wi)?] = 22.
This equation represents an elliptic paraboloid ¥, being the sum-
surface of the parabolic cylinders
pilare + Bry + fy)? = 2z;,
which have the plan z—O as summit-tangent-plane along the gene-
rator ae + By --+ wi 0, z= 0, and which are obtained by trans-
lating the parabola

lying in the normal plane of Vi= «je + 3:y 4+- a= 9, perpendicularly
to V;=0. The parameter of this parabola is ok
i

The summit 7’ of the elliptic paraboloid ¥ ({p; V,*] = 22) is pro-
jected on z—0O into the point P, satisfying the normal equations.

By constructing the tangent cylinder, the vertex of which lies
upon the «-axis at infinity, we obtain a parabolic cylinder, the
perpendicular transverse section of which has a parameter equal to
the reciprocal value of the weight g, of the variable a.

There being only two variables, only one (rigorous) equation of
condition &(v,y)—=0O may be added; (x,y) =O represents the
curve to which the point ? is constrained.

We now have to determine that particular ellipse of the homothetic
set [p; Vi?]=const., which touches the curve @. The point of
contact is the point P required.

In #, near the probable position of P, the new origin O% is
taken. We have thus only to operate with linear functions of the
coordinates. So we really replace ® by its tangent R at P.

The elliptic paraboloid 7 is cut by the vertical of P in the
point S. The vertical plane &,, which intersects z=0O along R,
pierces the paraboloid 4 along the parabola ’,, having Sas summit.

We now construct the cylinder having its vertex at the point

169

at infinity of the «z-axis and having the parabola ¥, as directrix
(ie.: enveloping the parabola ,). The parameter (of the perpen-
dicular transverse section) of this cylinder is the reciprocal value
of the weight g, of the variable z.

The equipotential lines in 2=0O are the homothetic ellipses
[pi Vi? | =const. Such an ellipse is the locus of the points of equal «.

When the (rigorous) equation of condition is: «= ceonst.. the
parabola , is parallel to the plane «=O. The tangent cylinder is
then infinitely narrow ; its parameter is 0, the weight of « is infinite.

Chemistry. — “Kquilibria in ternary systems. XVI. By Prof. F.
A. H. ScHREINEMAKERS.

(Communicated in the meeting of May 30, 1914).

Now we shall consider the case that the vapour contains two
components.

We assume that of the components 4, 6, and C only the com-
ponent 6 is exceedingly little volatile, so that practically we may
say that the vapour consists only of A and C. This is for instance
the case when B is a salt, which is not volatile, and when 4 and
C are solvents, as water, alcohol, ete.

Theoretically the vapour consists only of A+ £-+ C; herein the
quantity of B is however exceedingly small in comparison with the
quantity of A and C, so that the vapour consists practically totally
of A and C.

When, however, we consider complexes in the immediate vicinity
of the point 5, the relations become otherwise. The solid or liquid
substance has viz. always a vapour-pressure, although this is some-
times immeasurably small; therefore, a vapour exists however,
When we now take a

which consists only of 4, without A and C.
liquid or a complex in the immediate vicinity of point B, the
quantity of 4 in the vapour is, then still also large and is not to be
neglected in comparison with that of A and C.

Consequently, when we consider equilibria, not situated in the
vicinity of point 4, then we may assume that the vapour consists
only of A and C; when these equilibria are situated, however, in
the immediate vicinity of point 4, we must also take into consider-
ation the volatility of 45 and we must consider the vapour as ternary.

When we consider only the occurrence of liquid and gas, then,
as we have formerly seen, three regions may occur, viz. the gas-
region, the liquid-region and the region L—G. This last region is

170

separated by the liquid-curve from the liquid-region and by the
vapourcurve from the vapour-region. As long as the liquideurve is
not situated in the vicinity of point 6, the corresponding vapour-
curve will be situated in the immediate vicinity of the side AC.
Consequently the vapour-region is exceedingly small and is reduced
just as the vapourcurve, practically to a part of — or to the whole
side AC. Therefore we shall call this vapoureurve the straight
vapourline of the region £— G in the following. Consequently we
distinguish within the triangle practically only two regions, which
are separated by the liquideurve, viz. the liquidregion and the region
L—G:; the first reaches to the point B, the latter to the side AC.
The conjugation-lines liquid-gas end, therefore, all practically on the
side AC.

When the liquideurve comes, however, in the immediate vicinity
of point B, so that there are liquids, which contain only exceedingly
little A and C, then the quantity of 46 in the corresponding vapours
will no more be negligible with respect to A and C. The vapour-
curve will then also be situated further from the side AC, so that
also the vapour-region becomes larger. At sufficient decrease of
pressure or increase of temperature the vapour-region will cover
even the entire component-triangle. In that case we must, therefore,
certainly distinguish between the three regions, of which the movement,
occurrence and disappearance have been treated already previously.

In order to deduce the equilibrium #'+ L+G, we may act now
in the same way as we did before for a ternary vapour. We dis-
tinguish the following cases.

1. The solid substance is a ternary compound.

2. The solid substance is a binary compound of two volatile
components.

3. The solid substance is a binary compound of one volatile and
one non-volatile component.

4. The solid substance is one of the components.

1. We consider firstly the case sub 1, viz. that the solid substance
is a ternary compound; this is for instance the case with the
compound Fe,Cl, . 2HCl.12H,0.

Now we imagine for instance in fig. 7, 11, 12, or 13 (I) the
component-triangle ABC to be drawn in such a way that the point
F is situated within this triangle. Curve Mm can then again
represent the saturationcurve under its own vapourpressure of F,

val

the corresponding vapourcurve J/,;m, is then, however, no more a
curve situated within the triangle 46C, but it becomes a straight
line, which is situated on one of the sides of the triangle. We shall
call this line the straight vapourline of the compound /. When A
and C' are the two volatile components, then this straight vapourline
is situated on the side AC. As not a single liquid of curve J/m can
be in equilibrium with a vapour, which consists of pure A or of
pure (C, the points A and C’' can never be situated on the straight
vapourline. From this foilows: the straight vapourline of the ternary
compound /#’ covers only partly the side AC and in such a way
that it covers neither A nor Bb.

2. The solid substance is a binary compound, of two volatile
components. We take a binary compound F' of B and C (tig. 1)
so that 5 and C' now represent the two volatile components and A
the non-volatile component.

In order to deduce the saturationeurve under its own vapour-
pressure we may act again in the same way as we did before
for the general case. For this we take a definite temperature 7’ and
a pressure ? in such a way that no vapour can be formed and the
isotherm consists only of the saturationcurve of /°. This is represented
in fig. 1 by pq.

At decrease of P the region L—G occurs; such a region is
represented in fig. 1 by Cdee, with the liquid-curve de and the
straight vapourline Ce,. The liquid’ e is in equilibrium with the
vapour é,, the liquid @ with the vapour C and with each liquid of
eurve ed a definite vapour of the straight vapourline Ce, is in
equilibrium.

We may distinguish three cases with respect to the occurrence
of this region L—G.

a. In the equilibrium L—G of the binary system BC a point of
maximum-pressure occurs. The heterogeneous region L—G arises in
a point of the side BC.

b. In the equilibrium L—G of the binary system BC a point of
minimum-pressure occurs; one heterogeneous region arises in 2 and
one in C, which come together at decrease of P in a point of BC.

ce. In the equilibrium L—G of the binary system SC’ neither a
point of maximum- nor a point of minimumpressure occurs; the
heterogeneous region arises in / or in C.

Here we consider only the last case and we assume in this case
that Cis more volatile than B; after this the reader can easily

deduce the two other cases. At
decrease of P the heterogeneous
region arises, therefore, in the angu-
lav point C’ (fig. 1) and it expands,
while curve pg changes of course
its form and position, over the
triangle. Under a definite pressure
the terminatingpoint e of the liquid-
curve coincides with the termina-
tingpoint p of the saturationcurve,
under a definite other pressure e
coincides with ¢.

When e coincides with g, we
may imagine in fig. 1 that the
liquideurve is represented by qq’,
d or by gqq',; in the latter case it
intersects the curve qp, in the first

case it is situated outside this curve. When e coincides with p, we
may imagine that the liquideurve is represented either by p/ (fig. 1)
or by a curve, not drawn in the figure, which intersects pq. Now
we shall examine which of these cases may occur.

To the equilibrium between a ternary liquid w, y, 1—a—y, and
a binary vapour y,, 1—y, the conditions are true:

ee 5 fans, :
et! an Tin (y—y,) Ox = 4, anc Oy Oy, So te eS eee )

Let us firstly consider the region L—G in the immediate vicinity
of the point C. As x,y, and y, are then infinitely small, we put:

Z=U+RT2rlogx+ RT y logy and Z,= U,+ RT y, log y,

The two conditions (1) pass then into:

OU OU OU
U—#«# — —y— — U, +4, SSR (@ + y—y,)=0 . (2)
av Oy Oy,
OU we OU, ; ’
— + RY logy=—+ RT logy, . . . . . (8)
Oy Oy,

Under a pressure Pe the region Z-G in fig. 1 consists only of
the point C, and, therefore, «=0, y=O and y,=0O; then the
unary equilibriam: liquid C+ vapour C oceurs. This is fixed by
LZ=fZ, 011 U= U,, wherein: 2 = 057 = 0sande7y)— 10:

Let in fig. 1 the region Cdee, make its appearance under a pres-
sure Po + dP; the points e,, e, and d are then situated in the imme-

Lio

diate vicinity of C; now we equate «= §, y = and y, = 1. From
(3) follows:

1 = ae cee a et Ae fe (4)
wherein AK is a constant fixed by (8). When we assume, as
in fig. 1, that Cis more volatile than 6, the point ¢, is situated
between C and e and “J is, therefore, smaller than 1.

Nowe we equates ()) == Po = dP vai ey — 7) andy, = 7. :
as in the point C U= U, is satisfied, it follows, that:
—RT[E+ y= y,) +[V—V,|dP=0
or

E41 (—K) —— dPighs Seema) am (5)

In the immediate vicinity of the angular point C (fig. 1) curve ed is,
therefore, a straight small line. We find from (5) for the length of
the parts Cd and Ce:

V,--V : Via
——— dP and Ce= — —————dP. . . . (6)

RI Ri (ea)

As V,—V >0 and 1—K > 0, it follows from (6) that Cd and Ce
are positive, when dP is negative. At decrease of pressure curve ed
shifts therefore, within the triangle. From (6) follows :Cd: Ce=(1—A);:
imoreeas: 1 — 7 — Coan Ce: we. find: Cd = eex

In order to examine the lquideurves going through the points
p and q (fig. 1) in the vicinity of these points, we put in (1):

C= —

Mie) ( UB Bed RI LRRD oa tc RB Stace oun WL)
we then find:
U—a ee —(y—y ee —RT«e—Z, =0 wae eaeies . (8)
Ow Matar : Oy Oy:

For the liquideurve of the region L-G we find from this:
[er + (y—y,)s + RT] de + [as + (y—y,)t]dy=0 . . (9)
For the direction of this liquideurve in its end on the side BC

(therefore «= 0) we find:
dy y—y_) s-— RI
oh a Uae (10)
da (y—y,) t
When we call g the angle, which this tangent forms with the
side BC (taken in the direction from 4 towards C), we have, when
we imagine the componenttriangle rectangular in C:
(y-—y,) ¢
Ch. ———— =5
(y—y,)8 + RI

(11)

174

For the saturationcurve under a constant pressure of /’, consequently
for curve pq, we find:
OZ 0Z

Z—x - (8—y = (Ge R age 0 (file
Z—a— + (8 Day oa (12)

or after substitution of the value of Z from (7):
[er + (y—B)s + RT] dx + [xs + (y—p)t]dy=0 . . (183)

When we call wy the angle which forms the tangent in p or q
with the side BC (taken in the direction from 8B towards C,
we tind;

gs EE
(y—B) s+ RI

Let us now consider these two tangents in the point p of fig. 1.
In this point y—3< 0 and y—y, > 0.

The denominators of (11) and (14) bave, therefore, either opposite
sign or they are both positive, so that we may distinguish three
cases. In each of these cases we find y < w; the liquidcurve of the
region /.-G and the saturationcurve of / under a constant pressure
are, therefore, situated in the vicinity of point p with respect to
one another in the same way as the curves pf and pq in fig. 1.

Curve pf can also no more intersect curve pg in its further
course; we may see this also in the following way.

At decrease of P the two curves must touch one another under
a definite pressure P;, somewhere in a point / within the component-
triangle; therefore imagining the liquideurve of this pressure P,
to be represented by ed (fig. 1), we must imagine ed to be drawn

2 z ; : dy
in such a Way that it touches pg in h. For this point nh trom (9)
ax

dy
must be equal to ;_ from (13); then holds:
aw

ar + (y—y)s + RT ar + (y—3)s + RT 15
ast(y—y)t ws + (y—pa)e . 20a

or
a) veiw oo sg (1G)

As y, indicates the vapour conjugated with liquid 4, (16) means:
the liquid-curve of the region L—G and the saturationcurve under
a constant pressure of /# touch one another in a point 4, when the
vapour belonging to this liquid / is represented by the point /.

As all vapours belonging to curve ed (fig. 1) are represented by

175

Ce,, and consequently no vapour exists of the composition /’, the
curves ed and PY therefore, cannot touch one another.

Let us now consider the tangents to the liquid-eurve and to the
saturationcurve under a constant pressure in the point q (fig. 1);
as the vapour, belonging to this liquid, may be represented either
by a point q, situated between gq and F or by a point qg, between
F and C, we must distinguish two cases.

When the vapour is represented by g,, then we have y— 7 >0
and y— y, >0. As y—/??>y-— y,, the denominators of (11)
and (14) have either the same sign or the denominator of (11) is
positive, while that of (14) is negative. In each of these three cases
we find g<ywy; the liquid-curve of the region L—G and _ the
saturationcurve under a constant pressure of /’are, therefore, situated
in the vicinity of point g with respect to one another as the curves
gp and qq',.

When the vapour corresponding with lquid g is represented by
q,, then y— /? <0 and y —y, > 0; in absolute value (y—/?)s is
always smaller than (7 — y,)s. The denominators of (11) and (14)
have, therefore, either the same sign or the denominator of (11) is
negative, while that of (14) is positive. In each of these three cases
we find ~ >y; the liquid-curve of the region L—G and the
saturationcurve under a constant pressure of /’ are, therefore, situated
in the vicinity of point q with respect to one another as the curves
gp and qq’,-

With the aid of the preceding considerations we may easily deduce
now the saturationcurves under their own vapour-pressure of /’;
for this we shall assume that the solid substance melts with increase
of volume. We distinguish three cases.

1. The temperature is lower than the point of maximum-subli-
mation 7x of the binary substance /.

In a similar way as we have deduced the general case fig. 11 (I)
we now find with the aid of fig. 1 for the saturationcurve under
its Own vapourpressure a diagram as is drawn in fig. 2; in this
figure a part only of the componenttriangle is drawn. Curve
hacmbn is the saturationcurve under its own vapourpressure,
h,a,¢c, FP, b,n, is the corresponding straight vapourline. In_ this
figure are indicated the equilibria: #74 Ln + Gy,, M+ La + Ga;
FLEL+ Ga, P+ In+ Ge F+ y+ Gy, and F+ L, +Gn,; Ln
and £, ave binary liquids. As we have assumed that the temperature

is lower than the point of maximum-sublimation 7%, of the solid

176

substance #’, the vapour m, must be situated
between #’ and x. Consequently we have
here the case that the vapour, corresponding
in fig. 1 with the liquid g, is represented
by q,; the liquid-curve of the region L—G
going through the point qg can, therefore,
be represented by qq,’ (fig. 1). It follows
from this position of gq,’ that on further
decrease of pressure the liquideurve of the
region L—G must touch curve pg ina
point m (fig. 1); in fig. 2 this point of
contact is also represented by m. Previously
we have seen that the vapour corresponding
with such a point of contact has the com-
position #’; in fig. 2 m and F are joined
for this reason by a conjugation-line.

Fig. 2. It follows from this deduction that the

pressure is a minimum in the point m of fig. 2 and increases from
m in the direction of the arrows, consequently towards n and h.
Further it is evident that the vapourpressure in / is higher than in 7.

2. The temperature is higher than the point of maximum subli-
mation 7’~ and lower than the minimum-meltingpoint 7p of the
substanee F.

In a similar way as we have deduced the general case fig. 7 (I),
we now tind with the aid of fig. 1 a diagram as fig. 3. Curve
hachun is the saturationcurve under its
own vapour-pressure, /, a,c, 6,1, 1s the
corresponding straight vapour-line. As
we have assumed that the temperature
is higher than 7’_ but lower than 7'p,
F must, as in fig. 3, be situated between
n and n,. Therefore, here we have the
case that the vapour, corresponding in
fig. 1 with the liquid g, is represented
by qg,; the liquid-curve of the region
IL—G going through the point g may,
therefore, be represented by qq‘. (tig. 1).
It follows from this position of qq, that
on further decrease of pressure the liquid-
curve of the region L—G no more

intersects curve PY:

177

From this deduction it follows that the pressure increases along
curve /im in the direction of the arrows, therefore, from 2 towards
h and that on this curve im neither a point of maximum- nor a
point of minimumpressure occurs.

3. The temperature is higher than the minimum-meltingpoint 7’
and lower than the point of maximum-temperature 777 of the binary
equilibrium #’+ 1 -+ G.

In a similar way as we have
deduced the general case fig. 12 (1)
we now find for the saturationcurve
nnder its Own vapour-pressure an
exphased curve, in fig. 4 a similar
curve is represented by the curve
hn indicated by 5; the pressure in-
creases in the direction of the arrow,
consequently from n towards h.

In fig. 4 the saturationcurves
under their own vapour-pressure of
F are drawn for several tempera-
tures (7,—T,). When we take 7,
and 7, lower than 7x, then a
point of minimum-pressure must
occur on the curves, indicated by
1 and 2. When we take 7’, between
Tx and Ty and 7, between 7'x
and 7’'y7, then the saturationcurves Fig. 4.

under their own vapourpressure have a position as the curves /2
indicated by 4 and 5, on which no point of minimumpressure
occurs. At 77 the saturationcurve disappears in a point A and
the corresponding straight vapourline im a point //, (not drawn
in the figure).

On the saturationcurve of the temperatures 7’, and 7’, we find
a point of minimum-pressure m, this pomt has disappeared on the
saturationcurve of the temperature 7’, ; between these two temperatures
we consequently find a temperature 7’, at which the point m coin-
cides with the terminating point 2 of the saturationcurve under its
own vapourpressure. As the vapour belonging to a point of minimum-
pressure has always the composition /’, this case occurs when the
liquid 2 can be in equilibrium with a vapour /” As then the binary
equilibrium /’-+ £-++ vapour /# can occur this temperature 7%,

: 178

consequently is the maximumtemperature of sublimation 7x of the
substanee /’.

Now we will deduce in another way the saturationcurves under
their own vapour pressure of /. The conditions of equilibrium are:

WA OZ OZ 07 07
a -— == fi - == 5 i =p} ah —C eS eres é iy;
ae (y—/?) hoo: .—(y,—/?) Sg ae ae (17)

These conditions follow also from the equations 1 (II) when we
equate herein @ =O and «, =O and when we consider 7, as inde-
pendent of «,. We put

Z—= U- RT ailogm 0.) ee

The three conditions (17) pass then into:

U—a« ae — (y—/?) gu = tala 5 =O cee (19)
Ow : Oy i
Z,—(y 7) Oe eee Sock) Ls her
a eae OD
nA

From this follows:

far + (y—/?)s + RT| da + [as + (y—)¢#] i —

ay av
— | V—e on = (y—/?) rm =< ie. ers as ee (22)
x Yy
F hes , OV, ‘ :
(y,—/*) t, dy, =| Vi\—(y.—") a =—wl|dP . . 7 4(23)
; i

av. av.
sdx + tdy—t, dy, = a ea en P . - ae (24)
dy, dy

With the aid of (23) we may also write tor (24,:

ee OV
(y,— 7) sdx + (y,—)tdy = i ; (y,—,;9) a oar (25)
dy

so that for the relation between da, dy, dy,, and dP we shall consider
the equations (22), 23), and (25).

In order to examine if a point of maximum- or of minimum-
pressure is possible on the saturationcurve under its Own vapour-
pressure, we take (23). From this follows ¢? =O when

Gia 0 ss on Ae

In order to examine if the pressure for this point is a maximum
or a minimum, we develop (20) further into a series: when we
equate herein y, = /7, we find:

Wes)

1
(V,—2) Oe == = t dy,’ 5h FA nee ach Sere ne (27)

As V,—v and ¢, are both positive, it is apparent that the pressure
is a minimum. In accordance with our previous considerations (see
fig. 2) we find therefore: on the saturationcurve under its own
vapourpressure of the solid substance /’ the pressure is a minimum
in a point m, when the vapour corresponding with this liquid has
the composition

In order to examine the change of pressure along the saturation-
curve in the vicinity of its extreme ends / and 7 (fig. 2, 3, and 4)
we equate «=O; from (22) and (25) we then obtain:

oy
[(y—-/?)s + RT] du + (y —B) t dy = [V—-(y—/?) ai —ydP . . (28)

Oy
(y,—/?) sdx + (y,—B) t dy = [V,—(y.—,*) ar vyjdP. . (29)

From this follows :
(y, —/?) RTdx = [(y,—/?) V + (@—y) V, + Y¥—y,) ey] dP. (80)
When AJ, is the change of volume, which occurs when between
the three phases of the binary equilibrium #’'+ 4+ G a reaction
oceurs, in which one quantity of vapour arises, then we may write
for (30):

py, RT
Sa glean Silig ela wile tae ele (31)

Now AJ, is always positive in the binary system / + ZL -+ G,
except between the minimum-melting point 7 and the point of
maximumtemperature 7'7, where AJ, is negative. In fig. 4 AV,
is consequently negative for liquids between /’ and H, positive for
all other liquids on the side BC.

—y is positive, when the liquid is situated between # and C,
negative when the liquid is situated between / and B (figs. 2—4).

—y, is positive, when the vapour is situated between /’ and C,
negative when the vapour is situated between /’ and B (figs 2—4).

In the points A of figs. 2—4 is AV,>0, /’—y>0and /?—y,>0;
from (31) follows therefore dP <0. From each of the points /
the pressure must, therefore, decrease along the saturationcurves, we
see that this is in accordance with the direction of the arrows in
the vicinity of the points / (figs. 2 -4).

In the point » of fig. 2 is AV, >0, 7—y <0 and (?—y, <0;
from (81) follows, therefore dP <0. Consequently we find that

180

the pressure in fig. 2. must decrease from n along the saturations
curve, which is in accordance with fig. 2.

In the point 2 of figure 3 is AV, >0, P—y<Oand ?—y, >0;
from (31) follows, therefore dP > 0. Consequently the pressure
must increase from the point 2 in fig. 3 along the saturationcurve.
which is in accordance with fig. 3.

In the point 2 of curve 5 in fig. 4 is OV, <0, ;“—y > 0 and
8— 7, >0; from (31) follows, therefore dP>0. Consequently
the pressure must increase from n along curve 5, which is in
accordance with the direction of the arrows.

We may summarise the above-mentioned results also in the
following way: when to the binary equilibrium + 2-+-G (in which
F’ is a compound of two volatile components) at a constant tempera-
inre we add a substance, which is not volatile, then the pressure
increases when the binary equilibrium is between the point of
maximum-sablimation 7Z'~ and the point of maximum temperature
7; in all other cases the pressure decreases.

In the consideration of the general case, that the vapour contains
the three components (XI and XII) we have deduced that the
saturationcurves under their own vapourpressure can disappear in
two ways at increase of pressure.

1. The saturationcurve of the temperature 7’7 disappears in the
point #7 on the side BC |fig. 5 (XD)].

2. The saturationeurve of the temperature 77 touches the side BC
in the point 7 and is further situated within the triangle ; at further
increase of 7’ it forms a closed curve situated within the triangle,
which disappears at 7’z in a point within the triangle | fig. 6 (XJ)].

In the case now under consideration, that the vapour consists only
of B and C, only the case 1 oceurs; this has already been discussed
above and is represented in fig. 4. It follows already immediately
from the following that the case 2 cannot occur. On a closed
saturationcurve under its Own vapourpressure a point of maximum-
and a point of minimumpressure occurs. On the curves now under
consideration only, as we saw before, a point of minimumpressure
can occur, so that closed saturationcurves are impossible.

We may deduce this also in the following way and we may
prove at the same time these curves, just as in the general case, to
be parabolas in the vicinity of 77.

When we consider the binary equilibrium #’+ liquid AH +
vapour, then «=O; we equate y=y,, y,=~y,., and the pressure
= Py. To this equilibrium applies:

Be NG) ee Ze We |
(Of = (Y,—i?) = — G60 Z, - (fon ) - 50)
Oy OY, (32)
dU . OZ,
dy e on,
further we have:
(Y:-0—/?) a =F (F—y,) V, =r [%o— Yao] v= 0 as (33)
which condition we may also write:
Wee U Va == V, = V
= a (34)

y—0 = Yr — [2 ee
For a ternary equilibrium /’+ 4 + G, the liquid of which is
situated in the vicinity of point //, the pressure is equal to
Ba «, f= Ss, 7, 4 and 7, 7. 7,-
The three equations (17) pass then, when we use the conditions
(22) into:

Ss RSI. Hy AYL=0 (85)

RTE+[v-V] a+ 4r&? + 4tn?+-4 (5
dv oOoV

[p—V,] a ate $e, LF =e 2 Gan a) Sd <5 5 OG: 4 (y,—/?) L, =? (36)

iS ee va ae th sap kes os ot * (S18)
Herein is:
2 OV Os Ot 0?V
Ts EAR fey foo toe ES hE Wee yth

Oy Ow ~ OY dyOP

(38)
4 Os 3 0?V 07V
a! Sam oe

TE. Ov, ne ot, 0°V, OPA as 6
—=i fey a un —_— enc 3¢
fig Malka hag apt og eS (89)

In (35) and o6 Y, and y)9 are replaced by y and y,; we shall
do the same in the following equations. When we multiply (385)
by y,— and (86) by y—@, then it follows with the aid of (37) that:

(y,—B) RTS + 2 (y,—B) 7 & + § (y—B) ty’ —3 (y—B) t, 1,"

mitre dV ( 2) OV. Ov are UTES
AF 2 (( UP) dP ts y ey) =e = i= ap +(y, —B)sSy—= ( )

From (36), (87), and (40) it follows that this can be satisfied by:
7, Of the order -, 4 of the order a and § of the order 2°.
From (35), (86) and (37) then follows:

OV OV,
i —— |o and t.y, =(|u— a. . . (41)
Oy Oy,

Proceedings Royal Acad. Amsterdam. Vol. XVII.

182

Substituting these values in (40) we find:
2): (4. —=B) RLS ears. al A ose oe emer es)
wherein a has the same value as in (21) (XII).
From this it follows with the aid of the first relation (41) that:

2 (y,— 8) RT § = —_.__7?. ... . (43)

In the same way as in (XII) we find that we may write for this:

j2
t® (y—B) (y,—y) —
Sa (y—B) (1 —9) ao
PRT ==

WW. és)

d*l
LP?
curve going in fig. 4 through the point H is parabolically curved
in this point and touches the side LC in this point.

d?l
As in this point y—-8<0, y,—y <0, y,—8< 0 and TP >;
a

§ is always negative. From this it follows that this parabola has
only the point 47 in common with the triangle and is further
situated completely outside the triangle. Consequently only the point
H vepresents a liquid; its other points have no meaning.

wherein is fixed by (24) (XID. From this it follows that the

(To be continued).

Chemistry. — “The system Ammonia-water’. By Prof. A. Smits
and S$. Postma. (Communicated by Prof. J. D. vy. p. Waats).

(Communicated in the meeting of May 30, 1914).

After the preliminary communication’) on this subject the inves-
tigation of the system NH,-H,O has been continued in different
directions, and it has now been completed.

The continued research was directed in the first place to the
accurate determination of the meltingpoint lines, corresponding
with the pressure of one atmosphere. These determinations, which
were now carried out by means of a gauged resistance thermo-

1) These Proc. XII, p. 186.

183
.
meter’), as is in use in this laboratory *), gave the following result.
} . <9
) (Method of procedure : supercooling a little and then seeding).
[initia eee
Concentration point of par peut
mixture solidifica- | ti
tion cauon
100 mol. 9%) NH; | — 77.6°.
94.7 = 80.9" |
90.4 — 83.7 |
86.5 — 87.2
— 92.4
81.55
— 92.6 | — 92.5°
78.45 = 68 Tee 92.5:
73.5 — 82.2 | — 92.6
71.1 — 80.3
69.9 = TOT |
66.7 — 718.8
65.8 —— 18.9)
64.6 — 719.2
62.0 — 81.0
61.3 — 81.7 | — 86.0
60.7 — 82.3 iors 86.0
60.3 — 82.9 — 86.0
59.0 = 85,2) |= 8548
51.0 — 84.1 | — 8.8
53.0 — 80.2
50.2 — 79.1
50.1 — 79.0 |
49.3 == 719.0) |
43.9 | — 83.0 |
42.2 — 86.0 |
1) Gauging points were: melting ice 0°, melting mercury — 38.85°. Boiling
CO, + alcohol — 78.34° + 0.20 (B—76). Boiling point of oxygen — 182.8° 4- 0.56
(B — 76).
2) Cf. pe Leeuw. Z.f. phys. Chem. 77, 603 (1911).
: 13*

184

jneulritia| al = eee
Concen- : Final point
tration Point. oF of solidifi-
mixture on cation
40.6 — 88.2)
39.8 = O07 |
39.1 == Ol7
35.75 =5 Ohi
34.5 — 100.3
34.0 — 96.7 |
32.6 == 789.24)
29.7 1492 |
28.7 = (F353:|
27.6 | 163i
26.55 | — 50.4
|
23.0 | — 43.5
20.2 | = 3440
17.9 | — 28.6 |
|
4.46 | — 4.8
0:0) 9 0.0
|

This result is expressed in Fig. 1.
From this 7-X fig. follows :
for the point of solidification of the compound 2 NH,.H,O0—78°.9.
ra) ie a 5g - NH,.H,O—79°.0
Further the eutectic point of NH, + 2 NH,.H,O + IL appears to lie
at 81.4°/, NH, and — 92.5°.
a ss yf , of 2NH,.H,O-+-NH,.H,O-+ L appears to
lie at 58.5 °/, NH, and — 86.0°.
3 . or ,» of NH,.H,O + H,O +L appears to le
at 34.7 NH, and — 100.3°.
Great difficulties were experienced in the case of the mixtures
with less than 50°/, NH,, in consequence of the great viscosity of
these mixtures at low temperature.
Shortly after our just mentioned preliminary communication a
treatise on the same subject by Rupert’) appeared in Journ. Am,
Chem. Soc. 81 866 (Aug. 1909).

1) Buriher Goinammenien Journ. Am. Chem. Soc. 82. 748 (1910).

30)

~b0}

~100+

ee oe — re = =
Ny 10 50 YW kD 60 Wiha 40 30 20 10 0
X

Fig. 1.

As point of solidification Ruprrt determines the point at which
the crystals brought into the liquid no longer grow or disappear.
He measures the temperature accurate down to 0°.5 with a verified

toluol-thermometer. Below —- 100° he uses a thermo-element, tested
by comparison with the toluol thermometer and with the boiling

point of liquid air. He himself considers the determinations with
this thermo-element insufficient, which tallies with our results, as by
extrapolation about —125° may be derived from Rupurv’s investigation
for the temperature of the eutectic point NH,.H,O + H,O + L,
whereas this point lies certainly 24° higher according to Fig. 1.

Leaving the region of concentration 80—40°/, out of account, the
agreement between Ruprrt’s results and ours is fairly satisfactory.
If we compare the principal points, we get what follows:

186

REET Oe

Observer NH; 2NH3.H_O | NH,.H:0
RUPERT. = 16220 se eo nO sale 28
2 | | |
Smits, Postma | — 77.°6 | — 78.°8 79.°0
|
Observer Eutecticum | Concentration Temperature
RUPERT. NH; -+ 2NH3.H20 + L 81.2 mol. 9/9 NH3 — 94.°0
S. P. | F fe , VSIRS Leena — 92.50
|
RUPERT. 2NH3.H,0 + NH3.H,0+L /|57.9 _, il — 87.0
|
See 5 = Sholay ‘ — 85.9°
NH; .H,O0 + H,0 + L not determined by RUPERT
. ee . r 34.7mol.%)NH3|} — 100.3°

It is at onee apparent from the determination of the melting-point
diagram that the two chemical compounds, one with 2 mol. of
NH, to 1 mol. of H,O, and the other with 1 mol. of NH, to 1 mol.
of H,O are already considerably dissociated in liquid state at the
temperature of solidification.

Boiling-point lines.

After centainty had been obtained in the way described here
about the existence of two solid compounds between NH, and H,O,
it was of importance to examine whether the existence of these
compounds in the liquid state would also follow from the boiling-
pomt lines observed at different pressures. These determinations,
which were carried out with an apparatus as was used by
Dr. pe Leruw’), yielded the result that there was no indication to
be perceived that could point to the existence of compounds in the
liquid. Hence it followed from this that at the observed boiling
temperature the dissociation was already too strong, and that the
investigation has therefore to be continued at still lower pressures.

As the dynamic method is attended with all kinds of difficulties
at low pressire, it was desirable to apply the statistic and not the
dynamic method in the continuation of this investigation, and deter-
mine the vapour pressure line of different mixtures of definite
concentration, from which the boiling-point lines and the p-a-lines

1) ZA. phys. Chem. 77, 284 (1911).

187

might then be derived. This investigation, in which also the mixtures
which had previously been investigated dynamically were verified,
yielded the followimg result.

The following mixtures were examined.

88,0 mol. °/, NH, 54,7 mol. °/, NH,
Sng Se a Sib) eee oo
Oe ek hi = 39:7" ae
TA Cie ee A. 35.97) een
695 ee, 39:7. ae
cn ee O35. Gi as, ae

62,7 ”? ” ”

the results of which are expressed in fig. 2.

These vapour pressure lines enable us to read the corresponding
boiling temperature for a definite pressure (see table I), hence to
indicate the boiling-pomt lines, and that with an accuracy down to
tenths of degrees, and it is also possible to indicate the vapour
tension of different mixtures for a definite temperature (see table II),
hence to find the (pz)y-lines with an-accuracy of + 0,5 m.m. Hg.

Fig. 3 contains the boiling-point curves, from which it appears

100

80 x Sstatisch

Geng dynanr sch
70
Le
60
50
40
30

-30

-40

-00

Ty AV Bri E:T

T-X- or boiling-point lines for different pressures.

mol. % NH3 | fp = 50mm. | p= 100 mm. DAMEN SET p=380 mm. | P/=760 mm.
100 SE AIGEGN lk == 6122: || ==! 6liz4y pe 3.35 | ==, 4653) plik = =03a04
88.0 Seioe ale = Goro. ler S0tise | eesti 249.6)” N= °30.4
84.1 — 741 Geo ates en — 400g |=729)3
77.8 = 7.0) | = 6215) ||. = 563 i aI | == 40.5). | = 26-8
74.6 = 170.85 | = Gl! =054,0\5 | = derae ele ergant — 25.4
69.5 =ycs.6- 88 — 587 | 52.4 | = 438 | 2eae.gt || @= ong
66.3 — 66.4 — 56.4 = 50.20 | 4 — 34.0 = 199
62.7 63.6) |= 536 |} = 47.25 || — 48.6 | 230.9): = Sit
54.7 2G! earns ee © eens eas | poe
51.5 Seo 42.1 SES | Ewa. al KG a
39.7 mar SSeORn tee COLI Oye 19: G2m | 10-20 = Ike a
35.9 — 32.7 | —21.3 | —140 | — 44 | + 44 =
32.7 wey 8c g5|| =e 1G iG wel le me OF 250 =Peco.6510|| 15,914 a
25.6 aS eo Or ese fl) eee ode el ce ipe7s a Ps

TABLE IL
p-X-lines for different temperatures.
; Le
t=—10° | t= — 65° | t= — 55° | t = — 45° | r= — 35° | t = — 30° | t= — 250

mol. °/) NH3 | pincm.Hg. Pp 7) 7) P p p

—
100 8.25 11.75 22.6 | 40.95 | 69.95 pe eae
88.0 7.2 10.2 19.6 | 35.5 60.6 71.4 aa
84.1 6.7 9.6 18.5 | 33.4 57.3 73.6 =
71.8 5.8 46«| «8.4 1652) |). 12955 BO}pieleG5r0y a
TAG) 15:3 (4a 14.9 | 27.4 47.2 61.0 | 77.4
69.5 | 4.58 6.5 12TH esos ee 40] 52.5 | 66.8
66.3 5 Sra ye os5) pale Waite Ona 20.5 | 36.0 46.9 | 59.7
eS fees (eel Asse page 922 17.25 | 30.55 39.9) | =
Sg ee Disie lee 5h 10.6 19.4 25.1 | 33.55
Bie S eel see ane oil 1cGs 4.2 | 8.3 he abs 20.7 27.15
39.7 | = | 0.85 1.41 3.08 | 6.1 8.3 | 11.0
35.9 | = | oe + 1.1 2.15 4,35 | 5.9 | 7.95
Sie 8) Wee i OL Ie) Oi8 16 | 3.15 be ate | 6.45
Dotemie ese othe ye = 0.9 1.65 2.3 | 3.1

190
that even that corresponding to a pressure of 50 m.m. He. does not
reveal anything about the existence ef compounds in the liquid

phase; there is nothing to be detected here of a constriction at the
place of the compounds, as was found by Dr. ArEn’) in his investiga-

110)

gop CM Ha.

Suse

ith +.

NH; qa

Fig. 4.

tion of the system sulphur-chlorine, and by Dr. pr Lrruw’) in the
system aldehyde-alcohol.

Still more interesting is the consideration of the liquid lines of
the (px)7-sections, which are represented in fig. 4 for the tempera-

mes ——= PH = SS a Re — die. 55°, —65°, and — 70°. *)
1) Z. f. phys. Chem. 54, 55, (1906).
2) loe. cit.

8) The vapour phases of the mixtures need not be investigated, as it appeared
from a preliminary investigation that they practically consisted only of NH at
the examined temperatures, as was indeed to be expected a priori.

era

eS? i &

191

We sce that at all the temperatures mentioned here these liquid

lines exhibit the type of negative liquid lines’), as was met with
by Konxstamm and van Daursen’) for the system ether-cnloroform,
and by Grrtacn*) for water and glycerin, while as Baknuis RoozeBoom
remarked, such a line may also be derived from the investigation
carried out by ScHREmNEMAKERS*) for the system acetone-phenol.

Nor do liquid lines of the (px)7-sections give the least indication
of the existence of compounds in the liquid phase, and it is most
remarkable that this even applies to the liquid lines corresponding
to a temperature of — 70°, so only 9° above the temperature at
which the compounds separate out of the liquid; an indubitable
proof therefore that the compounds found undergo a dissociation in
the liquid, much greater than would have been expected.

To complete the investigation the most important lines of the P7-
projection of the spacial figure were also determined, the result of
which is expressed in fig. 5, in which the three-phase lines of the

two compounds are very apparent. The difference in triple point
pressure of the two compounds.amounts to +17 m.m. Hg.

Finally also the. plaitpoint curve was partially. determined; as was
to be expected this curve does not present any particularity either.

Anorg. Chem. Laboratory of the University.

Amsterdam, May, 1914.

1) Baxuuts Roozesoom. Die Heter. Gleichzew. Il 40 (1904).
*) Verslagen d. Kon. Akad. v. Wet. 1901, 156.

3) Z. f. anal. Chem. 24, 106 (1885).

4) Z. f. phys. Chem. 39, 500 (1902),

192

Mathematics. — “On Hermite’s and Apri’s polynomia.” By
N. G. W. H. Beverr. (Communicated by Prof. W. Kaprryy).

(Communicated in the meeting of May 30, 1914).

Prof. Kaprryn has deduced the following expansion ‘) :
(a—b6x)?

1 spe =a Or H,( oe)

ee > —_— ep

Vy (1—6’) 0 2n on! (1)
in which #, (2) represent the polynomia of Hermite. Let in this
expansion «=O, then we find:

(2)

2x2
1 ie _ 2, 6H,(2)H,(0)
VO—é6’) R erie anal
Now it holds good for the polynomia of Hermite that:
i ue
Hon+1 (0) = 0 Hz, (0) = (— 1)" x > ae)
On account of which the above relation passes into:
6272
os ix eo == \(= 1p , Hen() (4)
V(1—6’) 0 22n. nl
For the polynomia ¢, (7) of ABEL we know the expansion:
x9
1 i= oo
aay = San ety / > 6 ope
If we replace in (4) 6? by 6 we find:
62:2
eae 18 eS (—1)" Hor(2)
Vy (1—d) 0 222. mJ
1
If we multiply the first member of this relation by t——— and
vy (1—6@)
(2n)!

the second member by
. Q2n (p!y2

04 a (n!)

to the first member of (5). By equalizing the coefficient of 4” in the
two second members, we find the following relation between the
polynomia of ABeL and those of Hermite:

6”, the first member becomes equal

yp (a= > | 1)jr-k (24)! — Ho, 9%(z) - (6)
Q2n pe (k@—hE _.

If we multiply both members o7 (6) by
Hyp, —i (3) e—™ dx

y These Proceedings. Vol. XVI, p. 1198 (22

193

and integrate between —o and + o, then we find by application
of the well-known integrals :

+a
[eo (a) Ey, (a)\e—* dz == 0 moe n

+a
de (2) e—? da = 2" .m!i Yn:
—on

ae Qn—2i)M(2i!
| in () Hon si(e) db = (=I) en

Ss)

~]
—

Prof. Kaprayn deduces the following representation by means of
an integral for HeRmirr’s polynomia ') :

Cae eae wn
e — 7
let @) = e *u cos { vu — — )du.
n Va 9
J
0

If we substitute this expression in (6):

; ~=— 2h)!
P(x’ )= : fe ae (S128 — y2n—2k eos (wu—(n—k) x) du
22a k—=0 (k!)?(n—hk)!

or, if we work out the cosine

ao u?
ex? —— n (2k)! p :
Gila") = — e 4 cosaudu + ~ ) urxn—k) , . (8)
221V/ ar, k=0 (k/)?(n—h)!
0
Now is
8
(2h)! = fe-wyhay
0
consequently

f+ 2)
7 Db)! n 2(n—k) <
Ss ess y2(n—k) — S ee : “ yy dy a
> (k(n —h)! 0 (k/)?(n—b)! ves

v » (9)

7° NOGA cant OE A ok

ne 1 y 2k — y2n ul fn yi \2
= yen e—vdy = ae : —— e—Ydy 2S = ==
i 0 (kL)? (n—h)I \u mi o KILE u

For AseL’s polynomia we have:

: ens al n\ (y \2*
a ue een, k u

1) lie. p. 1194 (9).

so that we can write for (9)

, oa
yen y"
€Yapn | ——, | du
ni, w
0

Substituted in (8) we get the double integral

io 2) 2 i 3)
u 4

ex? as
D(a?) = EL fe 42"+1 cos wud | e—ul ep, (—t?) dt
0 0
if we introduce y = wt.

By substitution of «= 2y it passes into

im i] a) .

e—¥ yn) cos Danydy | ee Pri—t*)dt . . (10)

0 0

Now we make use of the relation *) also deduced by Prof. Kaprnyn

Pilz?) = nl 70

i t yo Prt)
Bat = ea (11)
(SED a) es

vu 0

In (10) we substitute «= ¢ and then. multiply both members by

1
e—t dt
140

and integrate between O and o, then we get by making use of (11):

ive}

+e) a) D
3 tn 4 : ‘ 2yVt
r ef : for y2n-l dy {e—20 Gn(—wu*) du ae gv" dt.
A (1+¢t)"11 niV x, ‘ : : 1+t
0

0 0

0
According to a well-known integral in the theory of the integral-
logarithm, 1s *)

oo RD

“cos 2ypt _ ( # cos 2yHa : ;
| — dt==2 | SS hi, (e2)—ey li (e—2Y)
: l+e

consequently

2) Lo)
Ae = us = dt= oi ey" y2n+ie—2u]7 (e21/) or Uli(e —2y)'dy
i (1+) nlm, : : : :
0 0 (12)
5 fens) du.\-
0 |
By summation from 7 =O to n= we find:

1) lc. XV, p. 1250 (14).
2) See for instance “Theorie des Integrallogarithmus Dr. Nietsen page 24.

195

ng ~
4 BREA a icy tees : Sryelrve
ears e—#" e—24lt, (e7Y) + e2yli(e—2Y) dy | e—2y"'du >’: : Gf i(-u’*)
a QO 7!

0 10)

Now is’):
s

Pm (a) = e*J (2 az)
m!

>
—_—
)

in which J, represents the function of BesskL of order zero. From
this it ensues consequently that :

4 i
— Va, yie—2li, (é 27) + yli(e »—2y) iy fe e—2yu J. y(2iuy) lu.

As is known,
oa) y2ny2n

Jy (Quy)

u=0 (n We
so
« ) yen Jie] roa) if 7
—2uy J, (Qiuy) du = + +— {- 2uyy2ndu= = ——— J e—% 22n dz —
ot ive ~ aaa y(n!) 292n-+1
0 0 v
ee eee
ay y(n 3 22n1 *
Introducing this we have
en (eee & 2n)!
1 = — —— | [e—2v i, (ev) 4+. e2y li (e—2)] dy . 5
Vn no (n/)?220+1
0
or
l oD
af — | [e—2y li, (29) + ey li (e—2y)] dy . (03)
2n Me
as 271 1
Meciine to an integral used before, is
ao D
7 . DQ,
fleom (e27) + e2yli(e—29) | dy=— :f tcostdt cen til 108 taretg =" dt .
« Yas
) 0
Formula (18) may also be written as follows:
1 4 ij AR 2y F ;
= — lim costarctg—dt . . (14
a (2n 1 Vz y=00 “¢ !
E = rest 0
n=0\ 2 J 2241
. . . an . .
By multiplying formula (11) by ar and by summation from 2 = 0
ni

fo n =oo we find:

1) These Proceedings XV, p 1246 (9).

196

et ey t n * e—! oOo at
if OD) = 4) = J, (2V ct
| Ie Ga 070 “lre) = ieee: 0 gs (0) Nike eres (2V at)

0 0

meat +(«—1)t
‘| aS nae fr nevend

(15)

In order to deduce some more relations from formula (11) we set
to work as follows. In Dr. Nianp’s dissertation’) the following

relation is deduced for ABen’s polynomia:
n—1
=
Gn (v=) = — = gx(e)-
k=0

By summation of formula (11) from 2=0 to n—1:

on n—1 tn ie n—l
,—t > = = n (t) dt
Jere at a lee eae
0
or
alae 1! ae ay lt
FE A eu
foams re Ok
0 0
or

s t .
aya | Ge 1 (t) dt
fe py” al te ee

We integrate the second member partially :
-
| (l+¢+1

et et
ei pet ces a Ore Fe) Tey

0 0

ety, (t) dt =

(16)

aya! oe =
——— +f Ta Gn (t) dt 4 (to Gn (t) dt .
0 0

Formula (16) passes into:

Ae pr
n n \d
See =f Oe ee bias

or by application of (11):

1) Over een bijzondere soort van geheele functién. Utrecht. 1896 p, 19.

197

&
t

tn n a eH
e—t___ dt= | e—'—____dt -++- | ——_—_q, (#) dt.
fi (Ite 4 (ah Say ay
0 0 0

The first integral of the second member we convey to the first
member, and we find:

fe ae dt = we t) dt ae
“(pay =farp el Se aa
0

0
If we apply the same process to this, and again to the result,
ete., we find at last after m-fold appliance:

na oO
[ : tim : { et 5
e— ana —————(pal(t) dt ee 8)
7 (1 +4) J +o" ie (
0 0
We can render this formula still more general by summation
from 2 —0O to n= o after division by (—1)" m/; we get:
iv 2) a
fo fr Guat
e—2t r= (|= ((a\@iig 6 6 6 6 (ale)
| (i441 pg m)
0 0

We apply the process explained above to this again and by
summation again after division by (—1)" m/ ete. we finally find:

on trp Pn (¢)
—kt ey, | aoe / a eee ; : ; )
Je (1+¢°+1 a [i (t+ kyr at (20)

in which % and m represent positive integers.
Of course a formula analogous to (12) may be deduced from this

53 un

a
J Gay
0

\ (21)
«2 ®
4 ie 2 > 0 da] > * > Fi 2

— ey yar Je—2ykli, (224!) + e2ykli(e 2k) dy fe- 24 Pn (—#*) dt.

mY a _ ;

0 0

By summation, formula (18) is, however, found again.

The formulae (4) and (5) may also be used in order to express
the polynomia 2, in g’s. For this purpose we multiply the two
members of (5) by

1 fire tetas 1 10:5
eee ii ec OT Las saat ap ae

By equalizing the coefficient of G' in the second member of the

Proceedings Royal Acad. Amsterdam. Vol. XVIL.

198

equation, thus obtained, to the coefficient of 7’ in the second member
of (4) we find:
. eal n 1 1.8.5...(2k-8) :

Hp,,(#)=(-1)" 22"! } pp(z?)- Se a Ts ORT aan Pn—K x") } (22)

By means of this expression an integral may be deduced.

For if we multiply both members by

e— “ip (x) da

after replacing 2? by « and if we then integrate between O and o,
we find, using the following well-known formulae ') :

fe m (x) Pn (vz) da = 0 m == x
0
a
foro (cdo!
- 0
° l 1.5.5.. .(2n—2m— 3)
=a ») Ho a) da = (-—1)"4+! 22n , SS, ——
| é Pn (a) Foy (Y v) da ( 1) al nt (n m)! Dn—m
7
or after some reduction:
: ni
e— Pn (@?) Hon (x) ede —(— 1)"+12"-+-m—1 _____ 13.5... (2n —2m—8) (28)
ys (n—m)!
0

maon—l.
In the same way we find

D
.

fe —2* Qn (&") Ho, (@) veda == (—1). 228-1 nr, 2a)

vu
0
and
—_
| e— @n—i- (a?) Hon (a) cde = (—1)s" 229 eee)
0

If we write formula (22) in this form:
1 £m)
Ph Ve —2 kd

Fo,, (x) — (—1)" 22n mI

Y nv") 4 pn—1 (27) Pi (v7)

we know that)

fo 2)

ox? ¥
Ci oh (Ge) == mae —40 KT (2e)//a)da.
0

!) Dr. Nistann’s Dissertation page 11.
*) These Proceedings XV. p. 1247.

199

This we substitute:

io 3)

il! a
Hp,(a) = (—1)”. 22" Indep, (w?)—3nlg,—1(@’)— — @t fe*F,2e/ee
Dae
0
Ls n! Aha -
iin
We further introduce:
& 3
(=) Sit 2 dt
0
and
ta! @r—(2’) = ava is i) (2aVa)da . na” 1 fetentae
0
We find then:
FF LIE [o-“Neavejtafet 23 ” ok tk
0 0
or ea, some reduction
(—1)—! — Han (a) + 1! gy (0°) =
Ee >. (26)

= eee (2a a) da fe tt Weta ma | dt
2Y/ x : :
0 0

For «=0, the following identities arise from the formulae (6)

U
and (22):

mi \>
x, (24I(2n—2k) )! ni? n\k
a) se ——— or — 22n — > ——— (27)
a kP(n—h)!? (2n)/ ro ( 2n
2k
and
9, n 9 F 5)
(Caren Sealer aes aieel Claeee
n! 2 p= k! ok
or
St Stee | ay
nf? ve 2 ke=2 KI Qk
(2n)!

14*

200

Chemistry. — “The metastability of the metals in consequence of
allotropy and its significance for Chemistry, Physics, and
Technics”. Il. By Prof. Ernst Conen.

The specific heat of the metals 1.

1. In my first paper ') on this subject I called attention to the
fact that the physical constants of the metals hitherto known, are
to be considered as entirely fortuitous values which depend on the
previous thermal history of the material used.

In that paper I wrote with regard to the specific heat of the
metals: Considering, for instance, the important part whieb the
specific heats of the metals have played in chemistry and physics
during the last few years, it is evident that a revision of these
constants is wanted.

2. Reviewing the earlier literature dealing with this constant, I
found that it contains already a number of data which prove unequi-
vocally that the specific heat of the metals does indeed depend on
their previous thermal history.

Le Verrmr published in the year 1892 a paper *) “sur la
chaleur spécifique des métaux”, in which he describes his measure-
ments with copper, zine, lead, aluminium, and silver. The calorimetric
determinations were carried out between O° and 1000° by the method
of mixtures. The temperature of the metal at the moment at which
it was brought into the calorimeter was determined by means of
a Ln CHareLigr pyrometer.

3. Le Verrier stated that the mean specific heat remains as a
rule constant till 200—3800°, after which it changes abruptly, as
Pioncuon *) also found in the case of iron, nickel and cobalt.

The variation of the total heat (i.e. the quantity of heat required
to raise the temperature of 1 gr. of the substance from 0° to # C.)
with the temperature is consequently to be represented by a curve
with breaks and not by a continuous one.

In the neighbourhood of these breaks the condition of the metals
is not only a function of the temperature, but also of their previous
thermal history.

‘) These Proc. 16, 632 (1912).

2) CG. R. 114, 907 (1892).

3) CG. R. 102, 675, 1454 (1886); 108, 1122 (1886). In full: Ann. de Chim.
et de Phys. (6) 11, 33 (1887).

201

As a consequence of the retardations in the structural change
(changements d’état) of the metal, a different value of the total heat
is found on cooling from that on heating.

If a certain piece of metal is cooled or heated repeatedly, differ-
ent values for the total heat are found. If we start from a lower
temperature and return to it after having overpassed the break
in the curve of total heat, a closed and not a single curve is obtained.

4. This result is in complete harmony with the dilatometric and
electromotive force measurements carried out by myself in collabor-
ation with messrs. He_berMAN and MoksveLp, on copper, cadmium,
zine and bismuth, measurements which led to the conelusion men-
tioned above.

5. Le Verripr’s paper contains some interesting data which we
shall now consider in connection with our dilatometrie and eleetro-
motive force measurements.

The curve representing the variation of the total heat of copper
as a function of the temperature, consists of four parts. At 850° an
absorption of 2 Cal. occurs; at 550° an absorption of 2 Cal.; while
at 750°, 3.5 Cal. are absorbed.

Thus, while our dilatometric measurements proved that there exist
more than two modifications of copper, the same fact was noted a
long time before by Lu Verripr, using a different method.

The measurements of Le Verrigr which are summarized in table I,
have, however, been quite overlooked hitherto.

It may be pointed out here that the transition temperatures which
can be deduced from Le Verrier’s determinations will generally be
too high. This is a consequence of the retardation of the molecular
changes, which were also observed by him. Fresh experiments with
the pure modifications of the different metals will throw light upon
this point.

6. From the determinations of Lu Verrier there follows also, that
there exists a transition point for lead which has so far been unknown.
Experiments in this direction are in progress in my laboratory.

7. The same may be said with regard to silver.
8. Aluminium shows, according to Ly Verripr, an absorption of

10 Cal. at 535°. It may be pointed out that Dirrensercer (Phys.
Techn. Reichsanstalt at Charlottenburg—Berlin) proved ten years

Temperature.

0—230°
220—250

250—300

O—110°
100—140 very variable

110—390

300—400

0—300°
300—530

202

DABBLE

Mean spec. heat.

Pb.

0.038
Almost nil.
0.0465

0.096

Total heat.

0.038 X t
Almost constant.
8.15 + 0.0465 (#250)

0.096 « ¢

absorption of 0.8 Cal. in
the neighbourhood of 110°

11.36 + 0.105 (¢ -110) .

0.105
31.4 + 0.122 (¢t- 300)
0.122 \ increases rapidly above 400° and
ra amounts to 46 Cal. in the neigh-
bourhood of 410° immediately
before melting.
Al.
0.22 0.22¢
0.30

Te crystallization of the silicium

| occurs at + 500° and the break

530—560 ? lies with Al which contains Si in
the neighbourhood of this tempe-

rature

65 + 0.30 (t-300)

Absorption of 10 Cal. in the
neighbourhood of 535°

139 ++ 0.46 (t-530)

540—S00 0.46 170 Cal. at + 600°; increases
rapidly and exceeds 200 before
melting (620°).
Ag.
O—260° 0.0565 0.0565 ¢
260—660 0.075 14.7 + 0.075 (f—260)
44.7 + 0.066 (t-660)
: : 62 Cal. at + 930, imme-
660 —900 0.066 diately below the melt-
ing point.
Cu.
0—360° 0.104 0.104 ¢
320—380 0.104 Absorption of 2 Cal. at + 350°
360—580 0.125 37.2 + 0.125 (#360)
560—690 0.125 Absorption of 2 Cal. at + 580°
580—780 0.09 37 + 0.09 (¢—580)
740—800 0.09 Absorption of 3.5 Cal. at + 780°
780 —1000 0.118 eM N a aed

117 Cal. at + 1020°.

208

after Le Verrier that this metal is capable of existing in more than
one allotropic modification and he found a transition temperature
between 500 and 600°. I hope shortly to report on this point, in
connexion also with a question which is important from a technical
standpoint i.e. the disintegration of aluminium objects at room tem-
perature, a disease which is the cause of a good many complaints in
industrial circles as well as in daily life.

9. That others had never observed the phenomena described by
Ly Verrier may be explained by the fact that they had not heated their
preparations repeatedly to high temperatures, as he did. We have
also observed during our dilatometric researches that such a transition
point can be overpassed several hundreds of degrees without any effect.
If on the contrary the metal is repeatedly cooled and heated the
transition is “set going”. As the means of overcoming these retard-
ations are now known we are able to avoid them. A systematic
research in this direction is now possible and I hope to report
shortly on it.

Utrecht, June 1914. van “t Horr- Laboratory.

Physics. — “Jleasurements of isotherms of hydragen at 20° C. and
15°.5 C.” By Prof. Pa. Konystamm and Dr. K. W. Watsrra.
Van per Waats fund researches N°. 7. (Communicated by

Prof. J. D. vaAN DER Waats).
(Communicated in the meeting of April 24, 1914).

§ 1. Choice of the substance and the temperature.

With the apparatus described in N’. 5 and 6 of this series we
have made measurements of hydrogen isotherms at 20° C. and
15°.5 C. This choice was led by the following considerations. As
we already set forth in the beginning of Communication N°. 5, one
of the motives of our research was the desire to be able to make
an accurate comparison with the results obtained by AmaGat. Our
first intention was to determine anew AMAGAT’s air isotherms; then
we were, however, checked by peculiar difficulties. Every time,
namely, when a measuring tube was filled with air in the way
described in the previous Communication, and was then left for

204

some hours at high pressure, (above 1500 atm.), it appeared to be
unfit for accurate measurements after that time. When the apparatus
was opened, the mercury appeared to be quite contaminated, the
glass tube and the platinum contacts being also covered by a black
substance.

Though in view of AmaGat’s experiments it could hardly be
supposed that this substance was mercury oxide, formed by the
action of the oxygen on the mercury, experiments of various kinds
made it impossible to assume another cause. The supposition that at
high pressure amalgamation of the platinum took place, proved
erroneous, for in the black substance no trace of another metal than
mercury could be demonstrated. Also the humidity of the air proved
to be entirely without influence. When it finally appeared that neither
filling with hydrogen nor with nitrogen yielded any trace, we
could not but conclude that we had really to do here with the
same phenomenon that Kurnen and Rosson‘) and Kurrsom*) had
observed when using closed air-manometers, namely that oxygen and
mereury act on each other at pressures of about 100 atm. KiEsom,
however, describes a slow action, which only after the lapse of
months manifests itself clearly; whereas we could demonstrate the
formation of mercury oxide with certainty already after a few hours
on account of the so much higher pressures.

How it is that neither in his determination of air-isotherms nor
in that of oxygen AmaGaT was troubled by this action, we cannot
explain. After we had once ascertained it, the use of oxygen and
oxygen mixtures was of course excluded. We therefore resolved to
begin with measurements of hydrogen, which is most easily obtained
in very pure state. The choice of the temperature of our measure-
ments was directed by the desire to obtain a direct comparison with
AMAGAT’s Measurements on oue side, and a supplement to SCHALKWIJK’S
very accurate measurements at low pressures on the other side.

§ 2. Filling of the apparatus with pure hydrogen.

Most of our determinations have been made with hydrogen from
the factory ‘Electro” at Amsterdam, which sells cylinders of com-
pressed electrolytically prepared hydrogen. For the further purifi-
cation and the filling of the apparatus with purified gas the arran-
gement was used of which fig. 12 gives a schematic representation.
It fits on to the most lefthand part of fig. 6 at /.

1) Phil. Mag. Jan. 1902, p. 150.
*) Diss. p. 50—53. Thesis III.

205

A horizontal glass tibe «@ passes on the lefthand side into a
vertical tube c via an emergency reservoir 4. The tube c ean be
fastened to the Gaedepump by means of a glass spring and a ground

joint piece. In the middle of the tube @ is a three-way-cock <A,
which gives access to a vertical tube d. A tube e is fused on to
d, the former being provided with a cathode and an anode, which
are connected with the secondary wire of a Ruhmkorff bobbin. The
primary wire is simply connected with the electric light bebind an
incandescent lamp. The purpose of this tube will be mentioned
presently. Attached to @ is a branch tube 7, bent downward, which
may be considered as one of the limbs of a siphon barometer. The
other leg yg of the barometer is fastened to the righthand part of
the tube a. In this there is another three way-cock 6 with a branch
tube 4. To suck the mereury easily into the barometer tubes, resp.
to expel it from them, a vertical tube with cock C is adjusted into
the transition from / to g. On the tubes / and g, which are filled
halfway with mereury, millimeter divisions have been etched to a
height of 1 m. To make the mercury mirrors visible at a great
distance care has been taken that a lamp can be slid up and down
behind these tubes, a strip of ground glass between the lamp and
the tubes intercepting the heat and making the light more diffuse.
To the right of the place where the tube g opens into a, the latter
is bent downward, and passes into a wider tube 4, This tube is

206

provided with four branch tubes, which can all be shut off by cocks
secured by mercury. For the filling with a single gas the presence
of two of these branch tubes is sufficient, namely / and m, resp.
with the cocks D and /. Tube / leads, as appears from the fig.,
to the mixing vessel, in which the normal volume at 1 atmosphere
can be determined. The tube m leads to the gas reservoir via the
purification apparatus. This gas reservoir is in casu a cylinder of
hydrogen as said above. The rubber tube, which is connected with
the pressure regulator, is fastened on the other side with solution to
a horizontal glass tube 7. This tube 7 has a vertical side tube s,
+ 1 m. long and ending at the bottom into a vessel with mercury.
Further 7 is connected by means of a rubber tube to a tube of infusible
class g, Which is filled with platinum asbestos. The latter tube is
connected again by means of a rubber tube to an ordinary drying tube
p, with phosphorpentoxide, and the latter tube is again in connection by
means of rubber with the above mentioned tube m. All the closures
of rubber to glass are secured with solution. >

In order to fill the measuring tube with pure hydrogen, the cocks
BE, D, and F’ are opened after the already mentioned operations
(Comm. N°. 6, p. 828). The position of three-way-cock A is such
that both sides of @ are in communication with d. The three-way-
cock B shuts off the tube g at the top. Position I.

The airjet or oil-pump is made to serve in the beginning, the
Gaede-pump completing the evacuation. When the air is sufficiently
rarefied, the cock /’ is closed, and the empty tubes m, p,q, and r
are filled with hydrogen from the cylinder. The mercury, which in
the tube s has risen to barometer height in the meantime, will
deseend; the mereury difference in the tubes / and g still indicating
the barometric height.’) Then the hardglass tube g is heated, till
the platinum asbestos begins to glow. The cock # is slowly opened.
And while the gas is flowing into the empty space & and further,
the hydrogen tube is again opened, so that the pressure in the tubes
in, pg, and + always remains + 1 atm. This is desirable because
in case of too great rarefaction the glowing hardglass tube g indents,
and soon gives way. The gas that flows through mm to the different
tubes, is almost pure, for the oxygen, for so far as it is present in
ihe electrolytic-factory hydrogen, is quite combined with hydrogen
to water throngh the catalytic action of glowing platinum asbestos,

1) On account of an eventually too high pressure the tubes m, p, q, and r
might burst now, if the open tube s with mercury safety valve had not been

added.

207

and the water formed is entirely retained in the phosphorus pentoxide
tube p. When the mercury in f and g is again at the same level,
it may be assumed that everything is filled with hydrogen of one
atmosphere. Now the cock / is again closed; / and the other tubes
are again evacuated. An idea about the purity of the gas which
was found in the tubes after the first filling, is now given by the
discharges in the cathode ray tube e. As long as traces of oxygen

still contaminate the hydrogen (i.e. with air — and the presence
of the latter appears at the same time — the only possible con-

tamination) the tube will be filled with red light. When pure hydrogen
has filled the tubes, the light will exhibit the well-known rice-colour.
An opinion may then be formed at the same time about the degree
of rarefaction attained, and also about the closure of different cocks
and couplings.

The tubes are then again filled with purified hydrogen, and after
another evacuation and filling the purity of the gas in all the tubes
may be safely assumed to be sufficient. Then the cock VD is closed,
the mereury bulb (see Comm. N°. 6 p. 828) is raised, and the pure
hydrogen is in the first “pressure stage” \see p. 823). Now for a control
the cock # was always closed once more, and the part of the tubes
k, a, gy, d, f, and e was exhausted, to ascertain the purity of the
gas with which we are going to work by means of the colour of
the discharge light.

If, what need not yet be done, (p. 830) it is desired first to
determine the normal volume of the gas at + 1 atm., before it is
brought into the first “pressure stage’, /’ must be closed before the
last filling. The difference in height between the mercury levels in
Z and ¢, and also the temperature of the thermostat must be deter-
mined. The barometric height can be read with the siphon baro-
meter /, g.*) But now the tube / must be in communication with
the outer air. This may be effected by turning the cocks uf and B
90° in positive resp. negative direction (Position ID). Then the tube /
gets into communication with the outer air via / and /. This remains
the case with g. But to prevent the tubes d and 7 to get commu-
nication with the outer air also the cock A must be turned, but in
opposite direction. The determination of the normal volume in JV’ has,
however, as said before, only sense when we wish to convey a
quantity of gas quantitatively to the measuring tube, which has not
yet been done.

To ascertain whether sufficiently pure hydrogen was obtained in

1) By means of a cathetometer and the scalar divisions etched on the tubes.

208

this way, we made also a series of experiments with distilled hydrogen
from the Leyden laboratory. The quantity of admixtures had been

estimated at at the most by Prof. Kamuriinga Onnes. We

5000
oladly avail ourselves of this opportunity to express our indebtedness
to Prof. Kamertincu Onnes for his kindness. In the filling with this
gas the purification apparatus could safely be omitted ; the cylinder
was therefore immediately connected with the tube m. The results
of the measurements with this agreed within the limits of the errors
of observation with the results obtained with the gas purified by
us in the way described above.

§ 3. The measurements.

How through the different “pressure stages” the gas is conveyed
io the measuring tube, has already been described above. Also how
the temperature is then kept constant. This is seen by the deviation
of the galvanometer, inserted into the Wuratstonr bridge. To get
a first idea the pressure at which the galvanometer needle deviates
is read on the manometer, and a corresponding number of weights
is placed on the rotating pressure gauge, after it has been brought
in communication with the tubes. If the number of rotating weights
is too great, some are taken off till the galvanometer needle has
returned to its original zero position. At last a final condition is
reached, in which the putting on of 50 grams on the rotating weights
makes the needle deviate, while the needle returns to its position
of equilibrium when this weight is removed.

The accuracy with which the pressures are thus measured on the
small and the large pressure balance generally amounts to this 25
erams up to 900 atmospheres. When the measurement is made with
the small pressure balance, which goes up to 250 kg. per em*. the
galvanometer needle may be made to deviate and return by putting
on or taking away 10 grams, and even when the contacts are very
clean with less. As, however, 25 gr. implies already an accuracy
of 1 to 10.000, whieh is not reached on account of other sources
of error, there is no sense in going so far in the determination of
the pressure. We only mention the fact as a proof of the very great
accuracy of the pressure balance for relative pressure measurements.

When one pressure measurement has thus been made, the pressure
is increased. The galvanometer needle, which now would continue
to deviate, must again be brought back to zero, because now another
resistance of the volume wire is measured,

209

Thus for every platinum contact in the measuring tube the pressure
at the corresponding volume is determined. Then the pressure is
diminished, so that two series of observations of the same results
must be obtained, but one passed through at increasing, the other
at decreasing pressure. The pressure differences at two corresponding
observations of two such series rarely amounted to more than 50
grams. It must of course be continualiy verified whether the tem-
perature differences inside and outside the measuring tube have
disappeared. This has taken place when the resistance of the tem-
perature wire (ef. Comm. 6 p. 833) has become constant.

In the measurement of the highest pressures, so when the large
“head” of the pressure balance is used, i.e. between 1200—2400
atinospheres, the accuracy of the pressure measurement becomes less,
especially on aceount of the increasing viscosity of the mineral oil
used as transmission liquid. Yet the error will certainly remain
below '/J00-

§ 4. Determinations between 2 and 200 atms.

As was already mentioned in Comm. 6 (p. 830) unforeseen diffi-
culties prevented us from determining the normal volume of the
quantity used in the apparatus itself. For the determination of the
isotherm of 20° C. we could make use for the calculation of the
normal volume of ScHALKWIJK’s measurements, as will become clear
from the discussion of our results. Such data were wanting for 15°.5 ©,
And in order to be able to carry out al! the same an accurate
comparison with AMAGAT’s measurements, we have executed measure-
ments at lower pressures at that very temperature. In this way a
control was obtained whether the equation for low pressures derived
from the measurements may be extrapolated.

We shall return to these points when our results are discussed,
and first give a description here of these measurements too. As we
again wished to use a large quantity of gas, the iron vessel D used
in the large apparatus was used as a pressure cylinder. We then
could fill the piezometer with a quantity of gas of the order of
magnitude of 1 liter at 1 atmosphere.

The piezometer originally consists of two pieces. The upper part
was as the upper reservoir of our ordinary measuring tubes. At the top
at a (fig. 13) there are 4 etched lines to be used after the cleaning
of the tube. Lower down there is a widening 4; under this a sealed
in platinum wire c, and at last an etched scalar division d. This
tube was connected with a capillary, and bent round. A_ platinum
wire is sealed into the bent part. Here a current can enter, and

210

leave through the mereury at the wire sealed in higher. When we
provide the side-tube with a scale, and fill everything with mereury,
and place it in a waterbath, a very accurate gauging is again
possible as described in Comm. 5 p. 766. We first gauge the dis-
iances of the etehed lines, then the volume from these lines to the
sealed in wire, and then from there to the etehed scalar division,
and this division itself.

a G

Fig 13. Fig. 14.

The large reservoir, which is to be sealed to this top piece is
calibrated after this sealing, by tiling with mereury the volume
from the scalar division on the top piece to the sealar division at
the bottom on the bottom piece.

We now know sufficiently accurately the volume from the etched
lines to the sealed in wire, and from here to the sealar division
under the large reservoir. The tube is now fused to at the upmost

211

line, and at the bottom a bent tube is added. The brass flanged tube
i of the pressure cylinder had been previously cemented at ¢, and
after a few drops of mereury have been brought into the large
reservoir, the tube is evacuated and filled in a horizontal position.
When the tube has been filled with pure hydrogen, it is put erect,
and the drops of mercury shut off the gas from the outer air. Then
the whole thing is placed in a waterbath of 15°.5, while the differ-
ence in height of the mercury in the tubes / and g is read. As
the volume up to the scalar divison, and the division itself too, has
been gauged, we now know the volume of a definite quantity of
hydrogen at about 1 atm. and the desired temperature. In order to
determine the pressure accurately, the pressure of the outer air
must of course also be determined, for which purpose the siphon
barometer is again used (p. 205).

We can further dispense with the side tube, for it only served
to protect the mercury at the bottom of the tubes against the water.
It is knocked off at g, and after the still remaining tube has been
entirely filled with mercury, the whole arrangement is put in the
pressure cylinder filled with mereury. The pressure cylinder is
closed, and connected with the hydrostatic press, which connection
is also in communication with the pressure balance. By means of a
rubber stopper a glass cylinder provided with a side tube at the
bottom and at the top is put round the projecting part, so that
water of 15°.5 from a thermostat keeps the gas at the desired
temperature. The current was closed on the iron pressure cylinder ;
then it passed through the mercury, and. when the required height
had been reached it passed further through the platinum wire. By
means of the pressure balance the pressure at which the platinum
wire is reached, hence the pressure at which the gas volume is
diminished to the upper part, could be very accurately determined.

§ 5. Corrections.

Some corrections should be applied to the experimental results
obtained in the above described way. First of all in the gauging
the volume is obtained in gr. of mercury of a definite temperature.
To reduce these values to the accurate volume in em‘. two reduct-
ions must be applied. A reduction should take place to em*. by
dividing the value in gr. of mereury by the specific gravity of
mercury at the temperatures of the gauging. The specific gravity of
mereury according to the Tables of Lanponr and Bérnsrein was
used for this- reduction. Further the compressibility of the glass of

212

the measuring tube should be takea into account. The gauging takes
place at J atm.; during the measurement the tube is subjected to
a pressure on all sides, in consequence of which the volume decreases.
As the correction in question is only a small one, we have thought
that for our first calculations it would suffice if we took the com-
pressibility of our glass equal to the valne determined by AmaGat.
We have therefore put the factor of compressibility at 22 x 10-7
and assumed this quantity to be constant between 1 and 2500 atms.
Also to the values of the pressure read directly some corrections
should be applied. The weights in kg. read on the pressure balance
should first be reduced to ke. per em*. by taking the value of the
effective area into account. In anticipation of the comparison of the
small pressure balance with an open manometer of sufficient capa-
city discussed in Comm. N°. 5 p. 759, we have assumed that the
effective area of the small balance, the piston of which is as
accurately as possible ground in at 1 em?*., really amounts to 1 em’.
Since we wrote our first communication we have been greatly
strengthened in the conviction that we cannot make great errors in
this way, by the result of Grora Kuein’s research '). According to
his investigations*) the error in consequence of the neglect of the
difference between piston and cylinder sections for ScHArFER and
BUDENBERG’s balance amounts to at most O.1°/,,, and the deviation of
the indicated and the directly measured value of the difference of
the two piston sections is 0.4°/,, in the case examined by him.
Now the large pressure balance could be compared with the small
pressure balance by méasuring the same point of the isotherm in
the neighbourhood of 250 atms. first with the one, and then with
the other. So the measuring tube with the galvanometer in connection
with it ete. serves simply as a manoscope, to judge when in the
use of the two balances the pressure is exactly equal. It then appeared
from some observations carried out in this way that when the section
of the small balance is put at = 1 em*., the section of the small
head of the large balance must also be put at 1 em*. within the
limits of the errors of observation. As at these pressures the errors
of observation are very small as we saw above, and will certainly
remain below 0,2°/,,, this result is a new confirmation of the great
accuracy of the Scuirrer and BupeNnserG pressure balances, and it
gives therefore a new support to the validity of the made supposition.
In the same way a comparison was made between the small and

1) Untersuchung und Kritik von Hochdruckmessern. Berlin 1909.
2) sO! (Clty peel

213

the large head of the large pressure balance in the neighbourhood
of 1200 atms. Instead of the theoretical numerical ratio +4, three
measurements gave resp. the values 4,012, 4,015, 4,016, average
4,014. The weights when the large head is used, must therefore be
multiplied by this value.

The thus obtained value for the pressure in the head must now
still be corrected for the excess of pressure of one atmosphere, and
for the hydrostatic pressure difference between the head of the
pressure balance and the measuring tube on account of the mercury
and oi! columns. ‘These liquid columns were roughly measured, in
which 1 em. of mercury more or less need not be considered ; nor
need the oscillations of the barometer be taken into account.

Finally the thus obtained pressure had to be reduced to atmospheres
of 1,0336 kg. per cm*.

In table T.

The column under v, indicates the weighed volume in er. of mercury.
g g 4;

- 3 » Pkg the number of kg. on the pressure balance.

Dy oe - pe the pressure, corrected for hydrostatic pressure
difference in kg. per em’.

33 5 », p the corrected pressure in atmospheres.

rn % » § the ratio of the volume at 1 atm. and at the

measured pressure in consequence of the com-
pressibility of the glass.
Bv, the product of 8 and »,.

” > ”
E *. , » the corrected volume in em*.
5) 3 » pv the product of p and v.
TWIN NSS MG TE, IU
5), November 1912.
E— 2025
CE —— ——————
vg Pre Po p | > pug v Pr

67.1491 195.850 194,750 188.419 | 0.99959 | 67.1216 | 4.95473 | 933.57
55.0632 | 245.400 | 244.300 | 236.358 0.99948 | 55.0346 | 4.06250 960.26

45.4959 | 306.575 | 206.175 | 296.222 | 0.99935 | 45.4663 | 3.35620 994.18
|

37.3710 | 390.200 | 389.800 | 377.128 0.99917 37.3400 | 2.75633 | 1039.49
31.0962 | 494.550 | 494.150 | 478.086 0.99895 | 31.0636 | 2.29302 1096.26

27.4110 | 587.000 | 586.600 | 567.531 099875 | 27.3756 | 2.02087 1146.91
22.7296 | 769.500 | 769.100 744.098 | 0.99836 | 22.6923 1.67508 1246.42
19.3102 | 992.625 | 992.225 | 959.970 | 0.99789 19.2695 1.42242 1365.48

Proceedings Royal Acad. Amsterdam, Vol. XVII.

214

TABLE I. (Continued).
November 21, 1912.
t—20%
Ys Pre | Pe p B Be, v | pv
|
90.3267 130.200 129.100 124,903 0.99973 | 90.3019 | 6.66580 832.58
87.5019 134.700 133.600 129.257 0.99972 87.4774 | 6.45734 834.66
85.4277 138.250 137.150 132.692 0.99971 85.4029 | 6.30420 | 836.52
43.7526 | 292.925 | 292.525 | 283.016 | 0.99938 43.7255 | 3.22769 | 913.49
34.5011 391.600 391.200 | 378.483 | 0.99917 | 34.4725 | 2.54466 | 963.11
25.0070 | 599.600 | 599.200 | 579.721 | 0.99872 | 24.9750 | 1.84358 | 1068.76
December !!/;5, 1912.
6209)
60.4928 222.500 221.400 214.203 | 0.99953 | 60.4644 | 4.46331 956.05
58.0°61 233.000 231.900 | 224.361 0.99951 58.0676 4.28639 961.70
55.9451 243.350 242.250 234.375 0.99948 | 55.9160 | 4.12756 967.40
53.7822 254.700 253.600 245.356 0.99946 | 53.7532 | 3.96791 973.55
48.5533 286.400 | 286.000 276.703 | 0.99939 | 48.5237 | 3.58188 991.07
45.9361 306.000 305.600 295.665 | 0.99935 45.9062 | 3.38867 | 1001.91
42.9934 331.450 | 331.050 | 320.288 | 0.99929 | 42.9629 | 3.17140 1015.72
39.4220 | 368.750 368.350 | 356.376 | 0.99922 | 39.3913 | 2.90775 | 1036.25
35.8492 | 415.575 | 415.175 | 401.679 | 0.99912 | 35.8177 | 2.64396 | 1061.99
22.0889 | 814.000 | 813.600 | 787.152 | 0.99827 22.0507 1.62772 1281.24
February 10, 1913.
120%
65.7937 225.050 = 223.950 += 216.670 +=: 0.99952 —s«65.7621 = 4.85437 ~—- 1051.80
34.9813 485.200 484.800 469040 0.99897 34.9453 2.57956 1209.92
27.9749 660,000 659.600 638.158 0.99860 27.9357 | 2.06214 1315.97
21.3124 995.000 | 994.600 952268 0.99788 21.3470 1.57578 | 1516.32

20S
Ug Pre Po. p p Ug
65.7937 | 220.200 219.100 | 211.929 | 099953 | 65.7628 |
34.9813 472.950 472.550 | 457.188 0.99899 | 34.9460
27.9749 | 641.825 641.425 | 620.574 | 0.99863 27.9366
21.3924 | 964.100 963.700 | 932.372 | 0.99795 | 21.3486
14.4836 487.750 1960.3 1896 6 0.99583 14.4232
February 13, 1913.
C=20'
65.7937 196.850 195.750 | 189.391 | 0.99958 | 65.7661
34.9813 416.300 415.900 | 402.382 0.99911 34.9502
27.9149 558.800 558.400 | 540.251 | 0.99881 | 27.9416 |
14.4836 , 400.250 1609.1 | 1556.8 0.99658 | 14.4341
April 22/54, 1913.
G— 7202.
36.1414 351.450 351.050 339.643 0.99925 —-10.7858
32.4244 402.700 402.300 389.221 0.99914 13.7748
21.1098 | 720.400 720.000 696.590 | 0.99847 17.2937
17.3297 | 980.000 | 979,600 | 947.755 0.99792 21,0775
13.8172 , 361.000 1451.5, 1404.3 0.99692 | 32.3965
10.8401 | 587.750 | 2361.7 | 2284.9 0.99497 36.1143
April 22/94, 1913,
E— Nde.08
36.1414 345.900 | 345.500 | 334.272 | 0.99926 | 10.7864
32.4244 395.950 395.550 | 382.691 | 0.99916 | 12.0677
21.1098 708.200 | 707.800 684.791 | 0.99849 | 13.7753
17.3297 | 964.100 | 963.700 932.374 | 0.99795 | 17.2942
13.8172 | 355.750 | 1430.4 1383.9 0.99695 | 21.0779
121097 457.000 | 1836.9 1777.2 0.99609 | 32.3972
10.8401 580,250 2255.8 0.99504 36.1150

215

TABLE I. (Continued).

2331.6
|

February !\/;2, 1913.

4.85443 |
2.57962 |
2.06220 |

1.57589
1.06468

4.85467
2.57993
2.06257
1.06548

2.6559
2.3914
1.5559
1.2765
1.0168
0.7962

2.6659
2.3914
1.5559
1.2766
1.0168
0.8904

0.7962

Pov

1029.03
1179.37
1279.75
1469.32

2019.27

919.42
1038.14
1114.30
1658.74

905.45
930.79
1083.89
1209.81
1427.89

1819.24

891.16
915.20
1065.47
1190.26
1407.15
1582.42

1796.07

15*

TABLE I. (Continued).
June 4, 1913,

= ee
he sae |
Vg. Pre Po Pp p | pug | vb Pu
a ee EEE eee eee ee

64.3346 | 141.800 140.700 156.13 | 0.99970 | 64.315 4.7476 646.28

| | | |
59.8154 153.475 152.375 147.42 0.99968 | 59.796 | 4.4140 | 650.71
27.1963 | 370.500 370.100 358.07 0.99921 | 27.714 2.0502 | 734.12

21.2326 | 524.750 | 524.350 507.30 | 0.99888 21.209 1.5656 | 794.23

16.2658 766.100 | 765.700 740.81 0.99837 16.239 1.1987 | 888.01
|
| | |
12.1023 | 1236.000 | 1235.600 | 1195.4 0.99737 12.070 0.89097 | 1065.07
|

In conclusion we give the two observations at 15°.5 for the deter-
mination of the compressibility between 100 atmospheres and atmos-
pheric pressure. The first column gives the pressure in atm., the
second the volume in em*. the third the product pe.

ABE we
November 1913.
[5 == Va\ea),
1.0384 | 484.6 503.19
97.91 5.4474 | 533.35

December 1913.

as NSD
|
1.0004 | 536.07 | 536:28

104.82 | 5.4474 570.99

Amsterdam. Physical Lab. of the University.

PACE

Physics. — ‘The hydrogen isotherms of 20° C. and of 15°.5 C. between
1 and 2200 atms.” By Dr. K. W. Watstra. Van per Waats’
fund researches N°. 8. (Communicated by Prof. J. D. van
pER WAALS).

(Communicated in the meeting of May 30, 1914).
Tete er

§ 1. Agreement of the observations below 1000 atms. with
SCHALKWUK’S csotherms.

For each of the series of observations given in the preceding
Communication we have determined an empiric equation of the form ;
PV=a+6D+cD+d.

As only series of observations below 1000 atms. can be represented
by this equation with 4 virial coefficients, only these series come
into consideration for the present. The obtained observation material
above 1000 atms. will have to be considerably extended to enable
us to calculate the following virial coefficients with the same
certainty.

If of the above equation we wish to determine a, }, c, and d,
we get a number of equations equal to the number of obser-
vations, and consequently then with 4 unknown quantities. To
solve these equations according to the method of least squares
is not feasible, as then the normal equations become practically identical,
which may already be seen beforehand. We have been able to apply
Prof. E. v. pb. SANDE Bakunuizen’s method successfully, which was also

ie— 202: 5), November 1912. T=20°. 21 November 1912.
P | PH(O) | PYO) (AC) P| PY(O)| PY (0) | (O¥(C)
| |
959.97 1365.48 1365.48 0.00 579.72 1068.76 1068.76 0.00
744.10 | 1246.42 1246.43 | —0.01 378.48 963.11 963.11, 0.00
567.53 | 1146.91 1146.81 | +0.10 283.02 913.49 913.49 0.00
478.09 | 1096.26 | 1096.42 —0.16 132.69 | 836.52) 936.49| 0.03
371.13 1039.49 | 1039.49 0.00 129.26 | 834.66 834.66/ 0.00
296.22 | 994 18, 993.95| + 0.23 124.90 | 832.58 | 832.55] +0.03
236.36 | 960.26] 960.42] —0.16 PV =710.50 4311.45 D +
188.42 | 933.57] 933.56) +0.01 Bie OE inte 02D

PV = 829.71 + 445.08 D +
+ 353.40 D2 + 197.28 D4.

787.15 | 1281.24 | 1281.25) —0.01 962.27 | 1516.32 | 1516.32 0.00
401.68 | 1061.99; 1062.00 —0.01 638.16 | 1315.97 | 1315.97, 0.00
256.38 | 1036.25 1036.21 0.04 469.04 1209.92 1209.92. 0.00
320.29 1015.72) 1015.76 —0.04 216.67 1051 80 | 1051.80. 0.00

295.67 | 1001.91 1001.81 +0.10 PV = 923.03 + 508.75 D +

+ 552.10 D2 + 296.55 D4.
276.70 | 991.07; 991.12; —0.05

245.36 | 973.55) 973.51) +0.04
234.38 | 967.40) 967.35) +0.05
224.36 | 961.70) 961.75) —0.05
214.20 956.05 956.11 —0.06

PV = 842.61 + 409.64 D +
+ 423.18 D2+ 191.36 D4.

used at Leyden for the calculation of Amacat’s values at the time.
(See Comm. 71). In how far we have succeeded in determining
the empiric equations may appear from the following tables. We
have placed there side by side P, ’V(O) — observed pressure and
pressure <X volume —, and PV((C) — caleulated with the known
volume from the empiric equation ; (V0) —(C) the difference between
the product PV following from the observaticn and that following
from the formula.

i202: 11,5 February 1913. i200: 22/5, April 1913.
Jee IEMA (OD) | 1ZAUA(G)) | (0)-(C) Ie PV (0) | PV(C) | (O)-(C)

932.37 | 1469.32 | 1469.32} 0.00 947.76 1209.81} 1209.81; 0.00

620.57 | 1279.75 | 1279.75) 0.00 698.53 | 1086.84 1086.84 0.00
|

457.19 | 1179.37 | Bee 0.00 389.22 | 930.78 ae 0.00

211.93 1029.03) 1209.03) 0.00 339.64 905.45) 905.45 0.00
| | | |

PY = 904.53 + 499.85 D + PV = 732.67 + 358.69 D+

++ 494.67 D2 + 298.61 D4. + 257.51 D2+- 101.20 D4.

219

T =-20°. + June 1913.

P PV (0) | PV(C) | (0)-(C)

——

740.81 | 888.01 888.01 | + 0.00
507.30 | 794.23 | 794.22 | + 0.01
358.07 | 734.12 | 734.12 | + 0.00
147.42 | 650.71 | 650.68 | + 0.03
136.13 | 646.28 | 646.30 | — 0.02

PV = 596.07 + 207.24 D+
+ 147.31 D2-+ 34.13 D4.

To find out whether these series of observations are in harmony
with each other, they can be brought in correspondence directly.
We did so before, and found only a slight deviation between them.
Besides it is also possible to try and make all the series of obser-
vations agree with ScHALKWIUk’s isotherm, and then compare them
also inter se. But then there must first be a reason to suppose that
it was possible to make these observations agree with SCHALKWIJK’s,
and this had soon appeared. When in December 1912 only three
series of observations had been found, we caleulated from that
which contained the greatest number of observations (Dec. ''/,, 1912)
an empiric equation from four of the observations, viz. at 787.15,
401,68, 320,29, 276,70 atms.

The other observations of this series appeared to be in good
agreement with the found equation :

PV = 841.70 + 415.09 D + 414.10 D®? + 198.16 D*.

Also the two series of observations of Nov. 1912 appeared to be
in harmony with this. Then a comparison with ScHaLKwisk’s obser-
vations was attempted by reduction of the above equation to one
with the same virial coefficient: @ as SCHALKWIJK, viz. @ = 1.07258.
This reduced equation then becomes:

PV = 1.07258 + 0.0,6740 D + 0.0,8569 D? + 0.0,,6659 D*,
SCHALKWIJK giving:

PV = 1.07258 + 0.0,6671 D + 0.0,993 D?.

This equation holds from 8 to 60 atms., ours from 200 to S00
atms., but we are now going to try to extrapolate with respect to
the region of the lower pressures in order to compare these extra-
polations with SCHALKWIJK’s.

The differences are most apparent when the product PV’ is deter-

220

mined from the two equations for different values for D, and the
products are joined in the following tables. PJ (GS) is then calculated

from ScHALKWIK’s equation with 3 virial coefficients; PV (P) from

our provisional equation,
D PY (S) | PVP) | (PS) D | PV(S)| PV(P) | (PS)
| | 1.0733 | 1.0733 | 0.0000 100 | 1.1492 | 1.1486 | —0.0006
10 | 1.0794 | 1.0794 | 0.0000 200 | 1.2457 | 1. 2427) —0.0030
20 | 1.0863 | 1.0864 | +0.0001 300 |. 1.3621 | 1.3573 | — 0.0048
30 | 1.0935 | 1.0936 | +0.0001 400 | 1.4983 | 1.4963 | —0.0020
40 1.1009 | 1.1009 0.0000 500 | 1.6544 | 1.6654 | +0.0110
50 | 1.1085 | 1.1084 | —0.0001 600 | 1.8303 | 1.8718 | 40.0415
60 | 1.1162 | 1.1161 | —0.0001 700 | 2.0261 | 2.1241 | +0.0980
70 | 1.1242 | 1.1240 | —0.0002 800 | 2.2418 | 2.4330 | +0.1912
80 1.1324 | 1.1320 | —0.0004 900 | 2.4773 | 2.8102 | +0.3329

90 1.1406 | 1.1402 | —0.0004

The deviations found in this way from what follows from SCHALKWIJK’s
equation with the extrapolations from our provisional equation
appeared to be surprisingly small. Only at a density 100 or P= + 115
atmosphere pressure the difference is greater than 1 per 2000, but this
is far outside the region of ScHaLKWisk’s observations. At D = 200
or P= + 250 atms. the difference becomes 1 per 400. Later on it
diminishes again, and takes opposite sign, but D = 500 or P= + 890
atms. lies again outside the region of our series of observations.

In connection with the mutual correspondence of the series of
observations, the possibility of an agreement with ScHALKwiJK has
appeared from this.

In order to be able to compare the 7 series of observations inter
se, and judge at the same time about the agreement with ScHALKWIJK,
we have reduced the 7 empiric equations in such a way that they
give PV = 1.3573 for D=300. This is then in agreement with
the above table. Then the equations become:

1 PV =1.06625 + 0.0373496 D +.0.0375009 D2 + 0.0,,69144 D4. 5, Nov. 1912.
Il PV =1.06917 +-0.0371540 D + 0.0;72697 D2 +. 0.0;299111 D4. 21 Nov. 1912.
Ill PV = 1.07375 + 0.0,66523 D + 0.087561 D2 +0.0;,64295 D4, 1/49 Dec. 1912.
IV PV = 1.06920 + 0.068353 D + 0.(1g85981 D2 + 0.0;262047 D4. 10 Febr. 1913.
V PV = 1.06893 + 0.0362806 D + 0.081640 D2 + 0.0;:68826 D4. —'11/, Febr 1913.

VI PV = 1.05753 + 0.0374726 D + 0.077437 D2 + 0.0}263400 D4. —22/g4 April 1913.
Vil PV = 1.07341 +. 0.0;67205 D+ 0.086024 D2 +- 0.0,264632 D', 4 June 1913,

221

At 407.19 atms. (800 > 1.8573) the series of observations have
now been reduced in agreement with each other.

From these equations we calculate first the product PV for the
densities 100, 200, 300, 400, and 500 for so far as the corresponding
pressures lie in the region of observation of the series, and hence
agreement may be expected. We then find :

D100 | 200° | 300 | 400 +] 500

I | 1.1491 | 1.2429 | 1.3573 | 1.4961 —_

I | 1.1491 | 1.2428 | 1.3573 1.4963 | ‘1.6654
Il | = "1.2426 | 1.3573 “1.4959 | 1.6641
Wil is | 1.2423 | 1.3573 - 1.4963 1.6650
V | — | 1.2419 | 1.3573 | 1.4967 1.6653
VI | = | oe | 1.3573 | 1.4966 | 1.6644
Vit | a | 1.2430 | 1.3573 ae a
~j—.. = eae ee

Mean 1.1491.) 1.2427 | 1.3573 | 1.4963 1.6648

Besides with the mutual agreement, we are struck here with the
agreement of the mean values PV with those determined provisionally.

We reproduce therefore this part of the table and place the mean
values PV(M) by the side.

D | PV(S) PVC) PV(M)
|
100 | 1.1492 1.1486 i.1491

200 1.2457 (12427 | 1.2427
300 | 1.3621 | 1.3573 | 1.3573
400 1.4983 1.4963 1.4963
500 1.6544 1.6654 1.6648

It remained to draw up an equation which satisfies the last table
of the mean values with a=1.07258 in accordance with SCHALKWIIk’s
isotherm. This final equation drawn up for convenience with five
virial coefficients, becomes:

(). PV = 1.07258 + 0.0,6763D -+- 0.0,88215.D? 4
+ 0.0,,66954.D* — 0.0, 151 D",

222

This equation not only represents all our observations as well as
possible; but the agreement with ScHALKWIJK’s results appears to be
even better than for the provisional calculation, which is seen from
the following table.

|
|

D | PV(S)| PV(F)| (F)-(S) D | PV(S)| PV(F)| (F)-(S)

1 1.0733 1.0733 0.0000 60 1.1162 | 1.1163 0.0001
| | | |

101.0794 1.0794 | 0.0000 70 | 1.1242 | 1.1242 | 0.0000
| | |

20. 1.0863 1.0864 +0.0001 80 1.1324 1.1324 0.0000

30 1,0935 | 1.0936 40.0001 90 1.1406 1.1406 0.000

40 1.1009 1.1010 | +0.0001 100 1.1492 1.1491 | — 0.0001
50 | 1.1085 | 1.1086 | +0.0001

The tinal equation may therefore be considered to represent the
whole region of the isotherm below 1000 atms. The agreement with
ScHaLkWik is perfect up to = 100, which corresponds with a
pressure of 115 atms. Reversely it appears therefore that we may
extrapolate up to +120 atms. from the equation at which ScHALKWIJK
arrived from his observations from 8 to 60 atms., viz.

PV =1.07258 + 0.0,6671 D + 0.06993 D?,

At D= 200 or P=250 atms. the error which would
then be made, becomes already 3 per 1000. For greater densities
up to 2500 the number of virial coefficients 3 is too small. It
must then be 4 at least. It will not do simply to add a 4" coeffi-
cient to SCHALKWIJK’s equation, which appears from the deviations,
which (see table) are now positive, now negative.

§ 2. Comparison of the observations at J5°.5 with Amagat’s.

We have one series of observations with 4 data below 1000 atms.
and three above it at our disposal. (See p. 215).

An equation has been calculated from the 4 data below 1000 as
a control of the observations at + 100 atms. (See preceding com-
munication). To compare our data with those of AmagaT at 15°.4
we have calculated an empiric equation with 6 virial coefficients
from 6 observations. In the seventh observation at 383 atms. we
have then a control.

P |PV (0)| PV(C)\ (OO

2255.8 | 1796.07) 1796.07 0.00
1777.2 | 1582.42) 1582.42; 0.00
1383.9 | 1407.15 1407.15 0.00
932.37 | 1190.26 | 1190.26 0.00
684.79 1065.47 1065.47 0.00
383.29 | 916.64) 916.66 —0.02
334.27 891.16 891.16 0.60
PV = 637.965 + 892.46 D = 735.72 D® + 1215.49 Dt —
— 787.959 D® + 204.470 D*.

With the value of PV at 700 atms. this equation is then reduced to:
PV = 0.92967 + 0.0,18953 D — 0.0,22767 D? + 0.0,,79888 Dt —
— 0.0,,10996 D® + 0.0,,60639 D*.

The easiest way for the calculation is now to compare the pressures

for the same volumes as Amacat. We then find:

V | P(Am.) P(C) (C)-(Am )
0.002234 | 700 700 0
0.002046 800 800.5 0.5
0.001895 | 900 904.7 4.7
0.001778 | 1000 | 1005.3 5.3
0.001685 | 1100 | 1101.8 1.8
0.001604 | 1200 | 1200.7 0.7
0.001533 | 1300 1301.6 1.6
0.001472 | 1400 | 1401.0 1.0
0.001418 | 1500 | 1500.9 | 0.9
0.001370 | 16c0 | 1601.1 | 1.1
0.001326 | 1700 | 1704.2 4.2
0.001288 | 1800 1804.2 4.2
0.0012545 1900 | 1902.6 2.6
0 0012225 2000 2008.0 8.0
0.001194 | 2100 | 2113.6 | 13.6
; |

.0011685 | 2200 2220025) 20 ee

These deviations and especially the progressive ones above 2000
atms. cannot be explained from the temperature difference of 0°.1,
among others on account of their irregularity. This would give a
pressure difference of no more than 0.6 atm. at 2000 atms. For the
rest the deviations are too large and too systematical to be con-
sidered as accidental errors of observation. The most obvious explana-
tion, a systematic error in the absolute pressure measurement made
by Amagar or by us, cannot be accepted either, as it would yield
a deviation proportional for large and for small pressures. Probably
the same causes come into play, which also prevented agreement
between AMaGaT and SCHALKWIJK’s observations.

Amsterdam. Physical Laboratory of the Cuiversity

Hydrostatics. — “The different ways of floating of an homogeneous
cube.” By Prof. D. J. Korrewee.

(Communicated in the meeting of May 30, 1914).

This problem, whose treatment, however simple it may seem,
offers considerable difficulties, was lately brought to a complete
solution by Dr. P. Branpsen.

If we limit ourselves to the cases in which the specific weight of
the cube amounts to less than half of that of the liquid (which is
allowed, because the other cases may be derived from it by inter-
changing the floating and immersed parts) stable floating appears to
be possible in four different possitions.

In the jirst position four of the edges are vertical. It may be
acquired for specific weights, expressed in that of the liquid, smaller

1 1 : L 1
than a Re Y 3= 0,211... For those smaller than e == (GG
it is the only one possible.

In the second position two of the faces are vertical, but the edges
belonging to them are sloping. The surface section is consequently
a rectangle. This manner of floating is possible between the specific
weights 0,211 .... and O,25

In the third position the space-diagonal of the cube is vertical
and the surface section a hexagon. It is possible between the limits
: and : of the specific weight. For the limits themselves the cube
) a)
is lifted or immersed just so far that the surface section, perpendi-
cular to the space-diagonal, has passed into a triangle. Those limiting
positions themselves are already unstable; consequently the stability

225

of this position disappears exactly there where for specific weights
< — a hexagonal section becomes impossible on account of ARcHI-
6 2

MEDES’ Law.

This third manner of floating was, probably for the first time,
referred to in the ‘Mathematical Gazette” of Dee. 1908, Vol. 4,
p. 338, Math. note N’. 285, in which note, however, the second
one and the case now following was not referred to at all.

In the fourth position one of the planes passing through two
opposite parallel edges assumes the vertical direction. In this posi-
tion one of these edges is partially immersed, the other one quite
outside the liquid. In consequence of this the surface section is a
pentagon for which the intersection of the liquid surface with the
plane just mentioned is an axis of symmetry.

Such ‘pentagonal’ floating can only exist, however, between
narrow limits of density, viz. between the densities 0,226... and
O,24...

It should be observed that only the first and the second position
gradually pass into each other; further that a completely unsymme-
trical way of floating, in which neither one of the faces, nor one
of the diagonal planes, nor a space-diagonal assumes the vertical
position, cannot arise.

One of the greatest difficulties connected with the problem consisted
in the formal exclusion of such cases.

It further appears that between definite limits of density, several
positions, amounting at mosf to three, are possible for the same
cube, viz.,

Below 0,166... the first position is the only possible.

From 03166)... to. 0,211... the first and the third.

From 0,211... to 0,226... the second and the third,

From 0,226... to 0,24 ... (the limits of pentagonal floating)

the second, the third and the fourth.

From 0,24... to 0,25 the second and the third.

Between 0,25 and 0,5 only the third.

Strictly speaking one case in which one of the diagonal planes
coincides with the liquid-level and the specific weight therefore
anounts to exactly 0,5 ought to have been added to those mentioned
above. Dr. Branpsen has indeed proved that stability exists in this
case. Yet at the slightest alteration of the specific weight the adjacent
positions of equilibrium become unstable, ei. those which arise by

226

lifting the eube a little or by immersing it in such a way that the
diagonal plane mentioned remains parallel with the liquid-level.

A paper by Dr. Branpsen in which the results described above
are set forth and proved is going to appear in the “Nieuw Archief
voor Wiskunde’ .

Petrography. — “On some rocks of the Island of Taliabu (Sula
Islands.) By Prof. Dr. A. WicHMANN.

(Communicated in the meeting of May 30, 1914).

After G. E. Rumpnivs had deseribed. towards the end of the 17th
century, some jurassic fossils, originating from the east coast of
Taliabu') it was not before the year 1899 that new geological inves-
tigations were made again in the island mentioned above. It was
R. D. M. Verseek who collected some rocks in some places of the
north coast on the 4? and 5 of August and afterwards described
them’). In November of the same year G. Bornm followed his
example, and chose as point of departure of his investigations the
findingplace mentioned by G. Rumpnivs, and afterwards continued
his work over part of the south coast*). In December 1902, in
January and especially during the months of October and November
1904 an extensive part of the southern part of Taliabu was surveyed
by J. W. van Novunuys*). The large collection gathered by him
was described by G. Born‘), in so far as regards the fossils. In
the following lines the communication of an investigation of the
rocks may find a place.

1) D’'Amboinsche Rariteitkamer. Amsterdam 1705, p.p. 253—255.

2) Voorloopig Verslag over eene geologische reis door het Oostelijk gedeelte
van den Indischen Archipel in 1899. Batavia 1900, p.p. 9, 10, 46, 47. — Molukken-
Verslag. Jaarboek van het Mijnwezen van Ned. Indié. 37. 1908. Wetensch. ged.
Batavia 1908, p.p. 20—21, 107108, 221223.

3) Aus den Molukken. Zeitschr. d. D. geol. Ges. 54. 1902. p. 76. — Geologische
Mitteilungen aus dem Indo-Australischen Archipel. N. Jahrb. f. Min. Beil. Bd. 27
1906, p.p. 385—395. — Beitriige zur Geologie von Niederlindisch-Indien. Palaeon-
toeraphica. Suppl. 1V. Stuttgart. 1904, p.p. 6, 13—14.

) Maatschappij ter beverdering van het Natuurkundig Onderzoek der Neder-
landsche Kolonién. Bulletin No. 48. 1905. — Bijdrage tot de kemnis van het eiland
Taliaboe der Soela-groep (Moluksche Zee). Tijdschr K. Nederl. Aardrijksk. Genootsch.
(2) 27. Leiden 1910, p.p. 945--976, 1173—1196.

5) Beitriige zur Geologie von Niederliindisch-Indien. Palaeontographica. Suppl. LV
1912, p.p. 123177.

227

Taliabu is a longitudinal island extending in the direction from
East-West between 124°8’ and 124°41’ E. and 1°50’—2° S. Whilst
the length amounts to 117 km., the width is no more than 387'/,
km. A mountain range of an average height of 1000 to 1200 m.
extends over its entire length. The formations of the northern part,
hitherto little known, are restricted to old slate-rocks, quartzites,
granite-porphyry and coral limestone, whiist on the southern part
moreover extensive strata are found containing numerous fossils
from the Jurassic system those of the Berriasien ineluded '). Among
the eruptive rocks occurs especially much granite. Younger forma-
tions play here likewise an inferior part, because the coral limestone
is found only in the eastern half of the south-ecoast and no farther
than cape Kona | Mantarara| ’).

Granite. Van Novuvys already called the attention to the fact
that the granites of Taliabu have much similarity with the granites
deseribed by Verberk of the Banggai Islands, which are situated
westward from the Sula Islands. They are characterized by the
occurrence of dark red orthoclase, greenish dull white plagioclase,
white quartz and black biotite*). Rocks in which the orthoclase is
of a lighter colour are however not wanting in Taliabu. They are
contrary to most granites of the Indian Archipelago, which as a
rule are rich in plagioclase, to be regarded as normal biotite-granites,
in which a more subordinate place is assigned to oligoclase. It
appeared that mikrokline was always absent. The red colour of the °
orthoclase is caused by a finely distributed reddish brown substance,
which disappears however as soon as the feldspar is altered into
kaoline. Biotite is indeed always present, but sometimes very scarcely
represented. It also occurs that by alteration it has been changed
into chlorite, and then, at the same time, rutile-needles appear.
Brown iron ore (limonite), in the shape of irregular flakes and aceu-

1) J. Antpure asserts (Versuch einer geologischen Darstellung der Insel Celebes.
Geolog. und paleontolog Abhandl. herausgeg. von J. F. Pompecxi und F. yon Huens.
N. F. 12. Jena 1913, page 110), that among others also Lias is found in Taliabu. Most
likely he mistakes — he is not so very particular — this island for Misol. Further,
he says, with regard to the demarcation strata of the Jurassic and the Cretaceous
system, that they “allerdings nach neueren Untersuchungen der Trias angehéren’’,
There can neither be question of this, as is clearly proved by G. Borum’s essay
(Palaeontographica. Suppl. IV. 1904, pp. 1—46). Most likely Antpure has in this
respect mistaken Taliabu for Buru. (Vide: Centralblatt f. Mineralogie 1909,
p. 561; 1910, p. 161).

2) According to a communication of Mr. van Novnavys the coral limestone reaches
only a height of + 10 m.

8) Molukken-Verslag, p. 218,

228

mulations along the fissures is rather widely spread as a product
of alteration. Apatite and titanite occur only sporadically.

Van Novnvys has already aequainted us with the finding-places of
the granites.') In the western part of the island we must mention
the territory of Lekitobi in’ the first place. The hill westward from
the entrance to the lagoon, the hills of the island Kona in the lagoon
and likewise Tandjunge Merah the red cape — at the east side
are all composed of this rock. The second granite-territory was
found on the upper course of the Wai fa, where it borders upon
strongly folded phyllite.

The third region is situated northward from the Wai Taha and
extends in the N.E. till beyond the left bank of the Wai Kabuta.
A fourth area occurs on the upper course of the Wai Najo, where
it borders the strata of the Jurassic system. South of this river rises
moreover a granite-hill on the coast in the neighbourhood of cape
Pasturi. The erratics that were found, besides in the rivers mentioned
above, also in others namely Wai Miha, Wai Kilo, Wai Ila, Langsa,
Wai Tabana and Wai Kasia point to the fact that granite is widely
spread over the interior. H. Bickine finally mentions a biotite-granite
containing hornblende from the Wai Husu °). :

The contactmetamorphical formations, which have been caused
by the eruption of the granites, deserve attention however in the
first place, especially because both old slates and jurassic sediments
have been concerned in it.

On the northside of the lagoon Lekitobi an andalusite-mica-rock
is found as a rock. In the pink compact rock macroscopically only
numerous silver-white laminae of muscovite can be detected which, also
according to the microscopic examination, form also the chief con-
stituent. Besides the aggregates of these colourless laminae there are
also those of irregular grains of quartz.

The elongated prisms of andalusite are already to be recognized
by their relief, they are nearly colourless in the thin sections and
show no perceptible pleochroism. Rather numerous are the fluid-
inclusions which they contain. As an accessory constituent tourmaline
is present in the form of little strongly pleochroitical prisms (O = yellow
to greenish-brown, E almost colourless). Ore is irregularly scattered in
the form of black grains, and occurs moreover as a fine dust

1) Bijdrage tot de kennis van het eilland Taliaboe, p. 949, 951, 963, 967, 971,
972, 1174, 1178, 1180, 1184, 1185, 1190, 1191, 1193—1195.

2) G. Bornm. Geologische Mittheilungen aus dem Ind. Australischen Archipel.
Neues Jahrbuch fiir Min. Beil. Bd, 27. 1906 p. 93.

229

between the muscovite-laminae. As a product of alteration finally
brown-iron-ore (limonite) is found.

Andalusite-mica-schist. This hard, distinctly schistose, reddish-grey
rock, in which the naked eye discerns only silvery muscovite-laminae,
was found as a boulder only in the Wai Miha. In the thin sections
the rock, of which quartz forms the principal constituent, shows a
erystalloblastic structure. Numerous are likewise colourless laminae of
muscovite, and besides those of a greenish mica. Andalusite is found
in the form of colourless prisms stringed together and in grains,
whilst prisms of tourmaline scarcely ever occur. Rutile forms dark-
brownish red, very strongly refractory grains and knee-shaped twins.

Mica-quartzite-schist. A boulder from the Wai Kabuta, a hard,
grey and very fine-grained, distinctly stratified rock. Under the
microscope we perceive that quartz, which is usually accompanied
by muscovite, is the chief constituent, whilst in strata of a darker
colour, but restricted to these, biotite is likewise freely spread.
Moreover andalusite occurs in the form of aggregates of prisms, with
numerous Ore-grains and further occasionally garnet, rutile, titanite
and tourmaline.

Mica-quartzite occurs among the boulders of the Betino, a left
tributary river of the Wai Miha. In this fine-grained, reddish-grey
rock numerous muscovite-laminae can be discerned by the naked
eye. As appears from fig. I the quartz individuals do not exhibit,
“Pflasterstructur’ under the microscope, but they engage into one
another like teeth. Further it must be remarked that finely distributed

16
Proceedings Royal Acad. Amsterdam. Vol. XVII.

230

ironhydroxide has penetrated between the aggregates of muscovite.
Though the rock does not contain andalusite, it is yet likely, that
it belongs to the contactmetamorphie formations.

Spotted clay slates such as Verbeek discovered ') in the isle of
Labobo (Banggai Isles) were not found among the rocks of Taliabu.

A group of rocks that have likewise been transformed by contact
with granite, but belong to the Jurassic system, are of a quite different
nature. Van Nounvys indicated already on his map a hornfelsmass
in the region of the source of the Wai Najo, whilst for the rest he
detected normal Jurassic sediments partly covered with alluvial
sediments from the source of the river to its upper course. As
appears from a subsequent investigation these hornfelshike masses
belong to the calesilicate-rocks.*) Van Novnuys collected specimens
of these in the Wai Najo and its right tributary, the Baja, and
likewise in the Wai Tabana and the Langsa. They are all dense,
very hard splintery and usually of a greenish-grey colour which,
in some spots, changes into whitish and occasionally into dark
crey. Some of those rocks as those of the Langsa consist of parallel
strata sharply separated from one another, perceptible to the naked
eye, and of a whitish- and blackish-grey colour.

The epidote is a mineral, which, according to the microscopic
examination, is never wanting, it is almost always represented by
the optically-positive klinozoisite, which is usually colourless but
oceasionally provided with a light-yellow tint. The always irregularly
shaped grains can easily be recognized by their strongly refractory
power and their other optical properties. Some parts of the /me-
silicatehornfels originating from the Wai Najo consist chiefly of
aggregates of this mineral, among which is found a_ colourless
eroundmass that cannot be nearer defined and often contains infini-
tesimal parts of dust. In other parts this groundmass forms the chief
constituent of the rock, in which klinozoisite occurs then only in
the form of isolated grains.

Jesides the many and very little grains of klinozoisite in the
lime-silicate hornfels found in the river Lanegsa, prisms of tourmaline
and needles of rutile(?) were occasionally met with. According to
the microscopic examination the difference between the light and
the dark strata is only caused by the fact that the latter are rich
in infinitesimal parts of dust.

!) Molukken-Verslag, p. 219.
2) Bijdrage tot de kennis van het eiland ‘Taliaboe, p. 1190, 1193, 1194,
map N°, XX.

9314

The composition of a cale-silicate-hornfels from the Wai Najo is,
according to the analysis of Prof. Dr. M. Dirrricn of Heidelberg,

as follows:

SOO Aa ee remem BAe ow Soe 58)
DEG Os ee co ea le tu A tte BOCAS
ATO ar Oe ee Se ee ee
C0) Pee AP es ae ee Ge EOL
C0 ere 1 A Ce
iC Oma etn ee ee I Foe 6,02
Mil Ore ear aey fo ees oh 5 POLS
COD eee a ee OO)
VIG ORE eee ae ne a ES By
Oe pare ice eS ee, gee Tu Ses? OPT
NG OMMe Penna cr wets ew ey, oh OR
PAOD. Apts sh tei ie ee a 2 a hae Pe lee Me OR) Yo)
COE Fee ee a ae) eee AOIGS
PaO = (ind eredlOe\t et enw ee eames = (eI 7,
1GPO (@ver TIO? to 1A). 4 5s iew

100,40

The specific weight is 3.213. From the analysis it appears that
the result of the chemical composition in consequence of the contact-
metamorphosis of the Jurassic marls is the disappearance of CO’,
which, as in other similar rocks, is found only in a very slight
quantity. The water was likewise for the greater part evacuated.
A modification of the composition with regard to the other con-
stituents cannot be observed. The results of the analyses of the cale-
silicate rocks vary greatly, which is not astonishing on account of
the great variety of the sediments that gave occasion to their
formation.

The fact that the youngest strata of the Jurassic system in Taliabu
were interspersed with granite and metamorphosed, is of great im-
portance; its eruption can consequently not have taken place earlier
than during the Cretaceous system.

The occurrence of granite of mesozoic age was hitherto only
stated or made probable in the Malay peninsula by J. b,
ScriveNor*), in Sumatra by Auc. Tosier’*) and R. D. M. Verser’),

1) The Rocks of Pulau Ubin and Pulau Nanas (Singapore). Quart. Journ. Geolog.
Soe. 66. London 1910. p. 429. — The Geologic History of the Malay Peninsula,
Quart. Journ. Geolog. Soc. 69, London 1913, p. 351.

2) Voorloopige mededeeling over de geologie van de residentie Djambi. Jaarboek
van het Minwezen in Ned. Indié 39. 1910. Batavia 1912, p. 18S—19.

3) Koloniaal-Aardrijkskundige Tentoonstelling. Amsterdam 1913. Catalogus, p. 76.

16%

232

their statements were a short time ago confirmed by W. Vortz’). On
the contrary J. Antpure writes: “Was das Verhalten der Gesteine
“der Tinomboformation| zum Granit betrifft, so ist es immerhin von
“Bedeutung, dass woh! nahezu alle echten Granite des Indischen
“Archipels, vor allem die Granite von Malakka, Sumatra,
“und Bangka, ebenso die grosse Granitplatte von Siidwestborneo,
“paldozoischen und zwar in den meisten Fillen nachweislich*) kar-
“bonischen Alters sind.” *)

Mr. AnLBuRG is prudent enough not to mention the names of his
informants.

Graniie-porphyry. Hitherto this rock has only been found as erratic
rock, namely by R. D. M. Versexk on the north coast, near Cape
Damar *), by G. Borum in the Wai Kadai (described by H. BicKtne °)
and by J. W. van Novusuys in the Wai Ha, a tributary of the Wai
Miha. The granite-porphyry of the latter finding-place contains a
yellowish brown, fine crystalline groundmass, in which numerous
grains and dihexaedrons of quartz are inclosed. The light-yellowish

crystals of ortheclase — sometimes twins according to the law of
Karlsbad — are dull and have caused the formation of scaly mus-

covite, as appears from the microscopic examination. They are
moreover filled up with finely distributed brown iron ore. The much
less numerous twinned individuals of plagioclase have caused
similar alteration as the orthoclase. The crystals of quartz are
characterized by numerous fluid-inclusions. Sometimes the intrusion
of the groundmass is perceived, but glassy inclosures are utterly
wanting. Dark constituents were only exceptionally found, and if so,
in an entirely decomposed condition. The previous occurrence of
biotite however is unmistakable, as the shapes of the laminae are
found back in the limonite into which they have changed. The
feldspars which form a part of the groundmass as well as the
porphyrie crystals have caused a transformation into muscovite.
Quartz-porphyry was collected by G. Borum in the Wai Husu
and examined by H. bBickine. In Van -Nounvys’s collection are
two specimens from the boulders of the Wai Najo. One is characterized

1) Oberer Jura in West-Sumatra. Centralbl. f. Min. 1913, p. 757. — Stid-China
und Nord-Sumatra. Mitteilungen des Ferd. y. Richthofen-Tages 1913. Berlin 1914,
p. 37.

2) The italics are mine.

5) Versuch einer geologischen Darstellung der Insel Celebes. (Geolog. und
palaeontologische Abh.dlg. von J. F. Pompeckr und Fr. Von Huens, N. F. 12.
ane 1913, p. 28).

) Molukken-Verslag, p. 223.

5 G. Bornm. Neues aus dem Indo-Australischen Aretipel p. 391.

233

by a light brown groundmass, bearing great resemblance to the
colour of chocolate, whilst that of the other specimen is yellowish
brown. Microscopically the groundmass is like that of the porphyry
from the Wai Husu microgranitic. The porphyrie erystals of quartz
are bluish and attain a diameter of 2—4 mm. The flesh-coloured
orthoclase crystals attain a length of about 1 em. Microscopically
they are covered with a fine brown pigment and partly altered into
an aggregate of little muscovite-scales. The groundmass is micro-
granitic and consists of a fine aggregate of quartz and orthoclase.

Syenite-porphyry. Only one specimen of this rock originating from
the Wai Najo is present. With the naked eye only a few dark
constituents can be detected in the grey to brownish dense ground-mass
showing a somewhat violet tint, with the help of the magnifying glass
likewise little rectangular sections of whitish grey feldspar can be
discovered. From the microscopic examination it appears that they
consist for the greater part of orthoclase, partly however also of
plagioclase (oligoclase). The dark constituents are in the first place
represented by green hornblende. The pleochroism is « = yellowish
sreen, \=dark green, ¢—bluish green; ¢ >) Sa; ¢:¢ = 12°.
Besides this biotite occurred frequently, which was however completely
transformed into chlorite, whilst grains of ore and epidote were
formed. Apatite is found in the shape of little thick prisms. The
eroundmass is entirely crystalline and is composed of aggregates of
particles of feldspar, among which a few little, angular grains of
quartz occur.

From the scarcity of porphyrie rocks in Taliabu may be deduced
that originally they occurred only in the form of dikes.

Diabase. ‘This kind of rock is likewise only represented by one
specimen from the boulders of the Wai Kabuta. It is dull, greenish-
grey and contains a few macroscopically observable dull-white
erystals of feldspar. In thin sections the characteristic ophitic structure
is to be observed, narrow and broader lath-shaped erystals of plagio-
clase, between which the xenomorphic augites appear, which have
undergone however partly an alteration into epidote. Grains of black
ore are freely dispersed. On the fissures of the rock greenish-yellow
epidotes have deposited themselves, which are accompanied by quartz.

The oldest sediments found in Taliabu are represented — in so
far as it is known — by phyllites, which have submitted to a very

strong folding, as was already remarked by van Nounvys at the place
mentioned. An extensive region is watered by the Wai Miha, i.e.
from its source till it leaves the chasm between the Bapen Kudi and
Bono Kedot6, whereupon it reappears again at Nali. In some spots

234

the rock contains strata and lenses of quartz and occasionally much
pyrite‘). A second region that has not been thoroughly explored is
found, according to the map, at the upper course of Wai Kabuta.

Besides the finding-places mentioned above, van Nounuys mentions
the river Langsa, but he remarks emphatically that the phyllites
occur there only in boulders, but nowhere *) in the form of rocks. One
of the specimens is composed of alternating thin, dark-coloured,
almost black strata, and lighter brownish-grey strata more rich in
quartz. From the microscopic examination it appears that biotite
forms the chief constituent, occasionally accompanied by many grains
of ore and fine black particles of dust and only few prisms of tour-
maline and grains of titanite. The lighter strata consist chiefly of
an ageregate of quartz grains among which are numerous little biotite-
laminae. The rock is moreover penetrated in several directions by
small veins of quartz, in which yellowish-green, wormshaped aggre-
gates of little pleochroitical laminae of chlorite (helminth).

Another phyllite is of a blackish-grey colour, dense and rather
hard. In consequence of the decomposition of the rock such parts
as are richer in quartz appear at the surface as knots. Microscopic-
ally the little biotite-lamellae are irregularly spread over the quartz-mass,
and sometimes closely compressed in accumulations. Sometimes a light

1) Bijdrage tot de kennis van het eiland Taliabu, pp. 958, 961, 1174—1176,
1187—1188.
*) Page 1180.

sericitical mica occurs, and further prisms of tourmaline and ilmenite.

The phyllites of the Wai Miha are usually softer than those of
the Langsa, and the microscopic examination proves them to be
different. Because thin dark, blackish-grey strata alternate with light
ones that are rich in quartz, the folding can very distinetly be
observed (fig. 2). The former are composed of closely compressed
aggregates of light-green sericite, as a consequence of the folding
the laminae were likewise bent. Little flakes of brown iron-ore (timonite)
are abundantly spread. The lighter strata chiefly consist of aggregates
of quartz, containing very few fluid inclusions. Further light greenish
mica-lamellae are discerned, floating as it were in the quartzmass
that is as clear as water. In other phyllites, besides grains of ore,
many particles of carbon are spread and further prisms of tourmaline
and needles of rutile.

At the foot of Sangeang, situated on the upper-course of the Wai
Miha, oceurs a black phyllite containing numerous hexaedrons of
pyrite having a diameter of 2 mm., it has great resemblance with
the rock collected by R. D. M. Verserk on the north coast in the
neighbourhood of Cape Damar’). Under the microscope the eye
distinguishes light strata containing much quartz, alternating with
quite dark ones, which are filled with carbonaceous matter in sucha
way that even the thin sections remain in some places opaque. It
appears that the grains of quartz contain few and small fluid-inelu-
sions. The rock moreover contains light-greenish laminae of sericite,
needles. of rutile and

If the quartz predominates a phyllitequartzite is formed.

A similar rock is likewise found as a rock near the Wai Miha

along the fissures — particles of limonite.

and consists chiefly of whitish-grey quartz of a greasy appearance,
interwoven with strata of phyllite. At last there is still a bowlder-
phyllite in itself normal and containing small boulders of white
quartzite and of siliceous limestone. The rock forms a counterpart
of the boulder-clay slate described by E. KaLkwosky’).

Near the upper course of the Wai Miha was found, besides the
rocks described above, a waterworn specimen of clay slate which
is strongly folded and apparently belongs to the same system of
strata as phyllite. Microscopically it behaves as a common rooting-
slate, contains as the latter numerous needles of rutile, a few prisms
of tourmaline, and black widely distributed carbonaceous matter.

1) Molukken-Verslag, p. 223.
2) Uber Gerdllthonschiefer glacialen Ursprungs im Kulm des Frankenwaldes
Zeitschr. d. D. geolog. Ges. 45. 1893, p. 69—86.

256

Van Novnvys moreover collected in the bed of the Wai Miha a
phiyllite-breccia consisting of numerous angular, sometimes a little
rounded fragments of phyllite having a diameter of at the utmost
3 cm. They are usually strongly altered, and have consequently
given occasion to the formation of chloritic minerals. As appears from
the microscopic examination the white quartz-cement is composed
of some grains of quartz as clear as water, the angles of which
engage into one another like teeth.

In the neighbourhood of Cape Pasturi boulders were found of a
hard, grey, distinctly strated quartzite, containing moreover a great
number of small hexaedrons of pyrite. Under the microscope the
eye discovers, beside the grains of quartz which are as clear as
water, green lamellae of chlorite, little titanite and a few black
erains of ore.

For the present moment it is still impossible to determine the
age of the strata of phyllite. It is certain that the folding they have
been submitted to, has taken place before the deposit of the Jurassic
sediments which show nothing of this nature. Petrographically some
fragments are completely identical to some Cambrian rocks in the
Ardennes, especially those belonging to the etage devillo-revinien.
Much nearer to hand is a comparison with similar rocks of the
continent of Australia. Whilst there the Cambrian sediments are
chiefly represented by limestones, those of the Praecambrium contain
not only similar rocks as those of Taliabu, but it appears that they
are likewise strongly folded all over the continent.

In the strata of the Jurassic system found in Taliabu, a few rocks
are found which, also from a petrographical point of view, draw
special attention. Van Novunvys reported already that S. E. from the
mouth of the Wai Najo cliffs are found consisting of “iron-hard
“dark rock having on the fracture entirely the appearance of con-
“olutinated gun-powder. This reck contains belemnites, which are
“however as a rule badly conserved, and are often cemented with
“the inclosing rock. Moreover the rock behaves entirely like granite,
“as it is split into steep perpendicular prisms divided into blocks
“by cross-fissures. This rock likewise changes into another of a
“lighter colour, in which on the weathering-planes reddish quartz-
“orains are found.” *)

The rock that is meant here, is a chloritic iron-odlite (chamosite)
dull, of a deep blackish-green colour, and containing numerous
small grains, which have indeed great resemblance with gun-powder.

1) Bydrage tot de kennis van het eiland Tahaboe, p. 1195.

237

As the colour makes us already suspect, in the thin sections under
the microscope it is to be observed, that the rock is chiefly composed
of fine dirty-green chloritie particles, which have been altered in
the same way as those of the Chamoson-valley’). They contain a
fine black dustlike matter, furtber pretty large grains of ore and
moreover a few angular splinters of quartz. Some cavities are filled
with erystals of calcite.

As to the odlite-formations they distinguish themselves only from
the other mass of rock by their structure. In the thin sections they
are always of an elliptical or circular shape (diameter 0.08—0.6mm.)
and consist of very thin green successive coats. The nucleus usually
consists of a stranger body, as a rule of quartz, the grain of which
occasionally becomes comparatively large (fig. 3). Though its shape
may be ever so irregular the coats of the chamosite are always

arranged in such a way that the unevennesses disappear, and the
result is in the end a regular odlitic body. There are however
likewise fragments of quartz in which every trace of a chamosite-
edge is wanting. Exceptionally the fragment of the skeleton of a
sponge serves as nucleus of an odlite. In consequence of an altera-
tion the odlites change into a yellow- to red-brown mass.
Formations of chamosite were also met with in other Jurassic
sediments of the Najo-region. As van Nounvys has already remarked
the chamosite-rock changes into another rock of a lighter colour ‘in
which on the weathering-planes reddish quartz-grains are found”.
The rock meant here, is a rather course sandstone, the quartz-grains
of which have a diameter of 2 mm. The cement is of a greyish-
green colour and effervesces strongly by treatment with hydrochloric
acid. In thin sections one consequently perceives much calcite, partly
in the shape of grains, in which the rhomboedrical cleavage is very
obvious, for the greater part however in that of a fine scalish mass
forming the real cement. The green chamosite is spread as in the
above mentioned rocks, but odlites are only met with as a great

1) G.Scummr. Ueber die Mineralien der Kisenoolithe an der Windgille im Canton
Uri. Zeitschr. f. Krystallographie. XI. 1886, p.598. — Geologisch-petrographische
Mittheilungen. Neues Jahrb, f. Miner, Beil. Bd. 4. 1886, p. 395.

238

exception. Parts of the skeletons of sponges have also been changed
into chamosite in these rocks.

Another sandstone of the same finding-place is more compact
and contains much less calcite. Microscopically it appears to consist
of angular and rounded quartz-grains, the intervening spaces of which
are filled with fragments of sponges, the skeleton parts of which
have been altered into chamosite. Odlitic formations are scarce.

In connection with the rocks described above attention must
be paid to a Limestone that was found in the Wai Najo in bank-
shaped flakes. The greenish grey fine-grained rock leaves at the
solution in hydrochloric acid a green sandy residue which appears
{o consist of quartz and chamosite, the latter at the same time as
petrifaction-material of numerous skeletons of sponges. In the thin
sections of the rock the grains of calcite show rhomboedrical cleavage
and form partly also polysynthetic twins. They likewise enclose
particles of chamosite. Odlitie formations are not rare, but in this
case only the outer zone consists of chamosite, whilst the inner
part is still caleite, in which the rhomboedric cleavage-planes of
the neighbouring grains of calcite have found their immediate con-
tinuation, so that they form with these one individual. The skeletons
of the sponges have been metamorphosed into pure green chamosite,
whilst the intervening spaces are filled with limpid calcite. Besides
ihe constituents mentioned numerous quartz-grains are present. From
the above it appears that the limestone contains the same constituents
as the sandstones that contain chamosite, and that there exists only
a quantitative difference.

As regards the formation of odlites, there can be no doubt that
they have come into existence in the still soft mass of rock during
or after the sedimentation. In my opinion they have originally con-
sisted of carbonate of lime. That chamosite is no original mineral
is already proved by the metamorphosed parts of the skeletons of
sponges. It remains still unexplained which chemical processes have
operated to bring this metamorphosis about. E. R. Zarinski has given
an excellent summary of the different theories regarding the formation
of thuringite and chamosite'), but it appears that none can be regarded
as valid.

Finally a few annotations about crystallized minerals of Taliabu
may follow:

Pyrite occurs — as has already been mentioned — in the shape

‘') Untersuchungen tiber Thuringit und Chamosit aus Thiiringen und Umgebung.
Neues Jahrb. f. Miner. Beil. Bd. 19. 1904, p. 79—82.

239

of cubic crystals in phyllites and quartzites of the Wai Miha region,
whence also pseudomorploses of limonite originate.

Quartz was found in limpid and dull-white crystals, attaining a
length of 9 cm., found near Pela, situated between the Wai Miha
and the Wai Ha. The shapes are the usual combinations of xf,
Rand — R.

Calcite. Elegant skalenhedrons 3 were found in a concretion,
originating from the river Kempa, a tributary of the river Wai
Miba, and likewise in a cavity of a geode with Macrocephalites.
Small rhombohedrons are present in the cavity of the chamosite-rock
in the neighbourhood of the mouth of the Wai Najo.

Rhodochrosite occurs in the shape of small rhombohedrons on the
walls of the air-chambers of a Macrocephalites from the Betino.

Siderite was detected in a boulder of quartzite, originating from
the upper-course of the Wai Miha, in the shape of yellowish rhom-
tbohedrons. Brown rhombohedrons together with calcite were found
in the chambers of an Ammonite from the Wai Galo.

Barite. All the chambers of Macracephalites keewwenis G. Bown
are sometimes filled with limpid barite in such a way that the
whole mass forms one individual.

Chemistry. — ‘Studies in the Field of Silicate-Chemistry.” 1.
On the Lithiumaluminiumsilicates whose composition corresponds
to that of the Minerals Eucryptite and Spodumene. By Prof.

F. M. Jancer and Dr. Anr. Stwek. (Communicated by Prof.
P. van RompBurGH).
(Communicated in the meejing of May 30, 1914).

§ 1. In connection with the study of the ternary system, whose
components are: Lithiwmovide, alumina and silica, it was necessary
for us, to obtain the compounds, whose composition corresponds
with that of the minerals ewcryptite and spodumene, in a perfectly
pure state, and to investigate their characteristic properties. The
third ternary compound, corresponding in its Composition with the
mineral petalite, will be taken in account only afterwards, as for some
reasons it is better to deal with it, when the experimental study of
the ternary mixtures themselves shall have proceeded some-what further.

The eucryptite: LiAlSiO, belongs to the series of silicates, whose
other members are: nepheline, kaliophilite, ete. In nature the said
compound occurs in the form of microscopical, hexagonal crystals, e. g.
in the albite of Brancnmvittn (Conn.) ; albite and eucryptite both take
their origin here from spodumene, decomposed by solving agents.

240

The spodumene LiAlSi,O, is a monoclinic lithiumpyroxene. The
mineral is found in several places, in the form of colourless or feebly
tinged, glassy crystals of prismatic habitus, or in the form of opaque,
eryptocrystalline aggregations. The transparent or coloured varieties,
which are strongly dichroitic, are used as a beloved precious stone ;
they are: called: triphane, kunzite, hiddenite, ete. Their properties are
mentioned further on.

§ 2. As was already pointed out, in a previous paper *) on
lithiumsilicates, the synthesis of the pure compounds offered severe
difficulties, caused by the volatilibility of the lithiumoxide at higher
temperatures. The composition of the mixture is thus altered during
the synthesis, and the quantities of all three components must there-
fore afterwards be corrected, after being accurately determined by long
and troublesome analysis. A relatively small loss of the lithiumoxide,
is of considerable influence on the meltingpoint and other properties
of the investigated compound, because of the very small molecular
weight of the oxide. The analysis offered many difficulties: for
notwithstanding all care and all arrangements’), it often happens,
that some A/,O, is found in the silica, and some SO, in alumina,
so that afterwards a controlling determination of these admixtures
must be made, which takes a lot of time. The small amount
of Li,O is furthermore hardly determinable under the colossal excess
of Na,O in the liquid; therefore, being determined as the difference
of 100°/, with the sum of the percentages for S’O, and A/,O,, all
mistakes and inaccuracies of those determinations are summed up in
the number for L7,0, so that the correction of the preparation after-
wards, often depending on very slight differences in the amount of
Li,OQ, is a hazardous and not very amusing task. So it takes much
time to obtain products, which will not differ appreciably im their
constants and properties from those to be expected for the true pure
compounds, the criterium being given by the perfect identity of the
products, prepared in several ways.

§ 3. Synthesis and Properties of the Pseudo-Kucryptite.

The materials for this and other syntheses were the same,
whose purity was before tested and described; the alumina used
was also provided by Bakrr and ApaAmson. It was necessary to heat it for
a long time in a platinum dish on the blaze, and often to stir the
powder with a platinum-wire, to allow the watervapour and the nitrous
gases, which the preparation evolved, to escape completely. The

1) FE. M. Jaeger and H. §. Knoosrer, these Proceedings p. 900, Febr. (1914).

241

heating was checked when the weight of the dish remained constant
after repeated heatings. Analysis then showed, that an almost pure
Al,O, (100°/,) was present; even no appreciable trace of iron could
be demonstrated with the usual reagents.

To point out the change of composition, taking place on heating
mixtures of known composition during the melting of the mass, the
numbers here following can serve very well: a mixture of 6,23 gram
Li,CO,, 8,61 gram Al,O, and 10,16 gram SiO,, was melted in
a closed platinum erucible in the Frrrcumr-furnace at 1500° C.
After crystallisation, the mass was finely ground and sieved, melted
again, and this process repeated three times. Instead of the expected
composition /, the composition // was found by analysis to be:

/ IT
SiO, A7,7°/, 48,6°/,
Al, 0, 40,4°/, 40,9°/,
Oe 11,9°/, 10,5°/,

As there was thus 1,5°/, Lz,O0 too little, 0,055 gram Al,O,
and 0,718 gram dry Li,CO, were added to 18,92 gram of the
resulting product, and this mixture was then heated four times in
platinum crucibles, by means of small resistance-furnaces, at 900° or
1000° C., the mass being finely ground and sieved after every
melting. Then the preparation was again heated once at 1450°C.
in a resistance-furnace. Analysis gave:

Odserved : Calculated :
SiO, 47,9°/, 47,7 °/,
Al,0, 40,1 °/, 40,4°/,
Li,O 12,0°/, 11,9°/,

The deviation from the exact composition is so slighf, that this
preparation could safely be used for the study of the properties of
the compound,

§ 4. The meltingpoint of this preparation was determined several
times by means of a calibrated thermoelement (N°. ///). The mean
value of all readings was 14200 M.V. + 2 M.V.; as the correction
of this element with respect to the standardelement, which was
standardized by means of Sosman’s element G, was -— 12 M.V.;
the meltingpoint of the substance, in terms of the Washington nitro-
vengasthermometerscale, can be fixed at 1888° C.

The heat-effect on melting is only small; as a result of that, on
cooling down the molten mass, one finds a retardation of its erystal-
lisation up to about 12840 M. V.; then crystallisation takes place
while the temperature increases only to 1306° C. The point of

242

solidification therefore is found 80° or 90° below the true tempe-
rature of equilibrium: solid = liquid, although the velocity of crys-
tallisation can by no means be called very small. From this faet
also the discrepancies in the data of different authors are to be explained :
1330° C. (Dirrier and Baio), 1807° C. (Ginsprre), etc. In this case
also, the usual method of cooling appears to give no reliable results.

A remarkable fact is the relatively appreciable cncrease of the
volume of the molten mass on crystallisation; it is immediately
observable by the deformation of the platinum-crucible. (fig. 1). That
really this phenomenon is caused
in this case by a volume-change like
that of water into ice at the freezing-
point, and that it need not be explai-
= i. ned in the manner mentioned in the

Fig. case of the spodumene, can be demon-

Increase of the volume of molten ‘Strated by the determination’ of the
Eueryptite on crystallisation. specitic gravities of the erystallized
mass, and of that of the beautiful, colourless ‘glass’, obtained by
suddenly chilling the liquid. The expansion seems to be about 3°/,

of the original volume.

§ 5. The crystallized substance, obtained by slowly cooling the
liquid, is opaque and greyish white. Microscopical investigation
showed it to be a eryptocrystalline aggregation of irregularly shaped,
erain-like crystals, which are so small, that even with an 800-times
enlargement, they can hardly be seen; they possess a very weak
birefringence. Greater pieces seem to be built up between crossed
nicols by innumerable lighting points ; such aggregations always show
an undulatory extinction. In no case erystals with determinable
borders were found. As a ‘mean’ refractive-index the value:
Ny = 1,531 + 0,002 was obtained.

The specific gravity at 13°,6 C. was pyenometrically found to be:
do 2,365, and at 25°, C: dy = 2,362 ; we used orthochlorotoluene
(1,0825 at 25°,1 ©.) as immersion-liquid.

As follows clearly from those values for the refraction of light
and for the specific gravity, the natural eweryptite must be another
modification of the compound Lz AlSiO, ; therefore we will distinguish
the artificial silicate by the name: pseudo-eucryptite. *).

1) Ginspera (Zeits. f. anorg, Chem. 73. 291 (1911)) describes his preparation in
the followmg manner: completely isotropous, uniaxial negative in convergent pola-
vised light, with a birefringence smaller than that of nepheline. Weypera asserts
to have obtained an “eueryptite” of rhombic symmetry, by the reaction of Li,SO,
on kaoline in solution. Cf. also the experiments of Tuuaeurt, Zeits. f. anorg. Chemie
2. 116. (1892).

245

§ 6. The glass, obtained by suddenly chilling the molten mass
in mercury or cold water, is colourless, perfectly clear and exceed-
ingly hard. It can be removed from the platinum-crucibles in an
easier way than the crystallized mass, which fact is connected with
the volume-change in crystallizing.

The refractive index of the glass appeared to be: mp) = 1,541.
We have prepared several glasses of varying chemical composition,
all in the vicinity of the composition of the pure compound, with
the purpose to measure accurately the refractive indices and the
dispersion, in order to get information about the influence of the
chemical composition on the optical behaviour of these glasses. They
were ground in <a flat cylindrical form, and in all directions care-
fully polished; then they were investigated by means of an ABBE-
erystalrefractometer in light of different wave-lengths.

For pure pseudo-eucryptite-glass of the composition LiAlO,,
we found:

Wavelength in A\.U. Angle of Total- Refractive A:

reflection : Index :

Ii: 6708 62am 1.5450
0,0040

Na: 5893 61°54’ 15410
0.0056

Sips 5350 Olson 1,5354

In the following are summarized the measurements with the glasses :
LT. Compos: 47,5°/, Si O,; 40,0°/, Al, O; ; 2 Dif ta),

HEE Compos: 42°55), Su Onc 30:0° (Al O, > 18,99 /5 ha. C).
i VesCompos:, 48.4°/- S71 Obs 39:39), Al. 0, > 1 i RO!
Gt.
Wavelength in Angle of Refractive Ne
eet Oe Totalrejlection : Index:
Li 6708 62°26’ 1,5484
0,0047
Na 5893 G2ebr ie 1.5437
| 0,0044
Tl 5850 61°47’ 1,5395
LUE
Wavelength in Angle of Refractive aN
INGE dee Totalrejlection : Index :
li 6708 63°36" 1.5647
0,0048
Na 5893 Gave 1.5599
0,0039

fl 5390 62°58’ 1,5560

244

LV
Wavelength in Angle of Refractive A:

ICE Oa Totalrejlection : Index:

li 6708 61°50’ 1,5400
0,0046

Na 5893 61°31’ 1,5354
0,0053

fh) 5350 Gie97 1,53801

It is difficult to deduce a simple relation of chemical composition
and optical properties from these data. Generally speaking, an
increase of the amount of 7,0 seems to cause an_ increase
of the refractive power (except in JV), while a larger amount .
of SO, appears just to diminish the refractive index, the exceptional
case /V could be explained by the superposition of these two causes.
This dependence of the quantities of the oxides present, appears to
bear some connection with the relatively higher refractive power of
the lithiumoxide, and the smaller one of the silica ').

The pseudoeucryptite-glass is, with respect to the opaque, erystal-
lized compound, a typical metastable phase: already on heating the
glass during a very short time in a Bunsen-gasburner, the pieces of
glass become primarily yellowish, then they become opaque,
and finally they appear under the microscope wholly changed into
the mentioned cryptocrystalline aggregation of birefringent grains.
If heated only for ten minutes at 900°C., they are completely -
changed, and the same occurs, on heating the finely powdered glass
during some time with molten LiCl or LiF in a platinum crucible.

The specific gravity of the pare pseudo-eucryptite-glass was deter-
mined by means of the method of swimming, in a mixture of
bromoform and benzene, at 13° C.; it was found to be : dy = 2,429.
Thus both the refractive index and the density of the glass are
somewhat higher than for the crystallized compound.

§ 7. Finally we have compared the artificial product with a
natural eueryptite of BrancunviLLe (Conn.). The mineral, of which
a thin section was prepared, looked as an aggregation of erypto-
crystalline, homogeneously extinguishing fields: however, although
they had superficially some analogy with the artificial product, they
must be considered as composed of much larger crystals, showing
apparently the kind of structure, somewhat similar to the so-called
“schrift”-granite. Locally it is intermixed with a much more strongly

1) fF, M. Janeen and H. S. van Kuoosrer, these Proceedings, loco cit. (1914).

245

birefringent mineral; although the eucryptite is here generated from
spodume. with deposition of albite, the properties of the inclusions
did not agree with those of the two lastnamed minerals. The
specific gravity was pycnometrically determined to be dyo = 2,667
at 25°C.; the available data show the composition not to be the

proper one, the S’O,-amount being 0,6°/, too high and that of the

LiV,z about 1°/, less than the theoretical value. The fig. 2 and 3
represent two microscopical preparations of the thin section between
erossed nicols; in the fig. 3 the preparation is turned over 30° with
respect to that in fig. 2; — this fact pointing to a trigonal twinfor-
mation. Also the very peculiar structure of the crystals is shown
in fig. 3.

The refractive index was microscopically determined on : 2p = 1,545
+ 0,002. A definite meltingpoint could not be fixed by the usual,

dynamical method; at about 1120° C. the mineral gradually changes
into a viscous mass, which, on cooling, becomes a glass. The refrac-
tive index of this glass appeared to be: np=1,506 + 0,001, it is
thus evidently lower than that for the glass of psewdo-eucryptite.
On being heated it is devitrified only slightly; there seems to be no
doubt, that the natural mineral and its glass are other than the
corresponding phases of the artificial product. As also never any
indication of an oceurring inversion could be found, it is highly
probable that eucryptite and pseudo-eucryptite are in relation of
monotropic modifications to each other.

§ 8. Synthesis and properties of (?-Spodumene.

The compound, ~ whose composition is: LiAlS7,0, was prepared
17

Proceedings Royal Acad. Amsterdam. Vol. X VIL.

246

by us in four different ways, just to get information on the final
identity of such preparations:

a. By melting together calculated quantities of Li,CO,, Al,O, and
SiOQ,, repeating this manipulation a few times, after thoroughly
erinding and sieving the crystallized masses. Analysis and correction
were made as usual.

b. By starting from pure Lz,S70,, Al,O, and SiO,.

ce. From LiAlSiO, and Si).

d. From LiA/O,, the lithiumaluminate, and S7O,.

The four preparations, thus obtained, were used only for the
definitive measurements after it had been proved by repeated ana-

lysis and correction, that their composition did correspond, within
the limits of error, with that of the formula. AIl these experiments
were made in electrically heated furnaces with oxidizing atmosphere ;
the preparation of these substances took a long time, because of
the volatibility of the 7,0, and the fact, that only small devia-
tions in the content of 7,0 showed themselves of appreciable
influence on the meltingpoint and properties of the compound.

§ 9. The purest preparation we got, was obtained from synthe-
tical eueryptite by admixture of SvO,. Analysis gave the following data:
I. 1 Caleulated :
SiO, 64,39 °/, 64,438 °/, 64,6 °/,
AlsOe 227,000), 27,66 °/, 27,4 °/,
I1,O 8,05 °/, ieoies 80°75
The mass was kept during a longer time at a high temperature,
to allow it to erystallize totally. Then the meltingpoint was deter-
mined in the usual way, by means of thermoelement ///; we found :
14353 M. V.
14341 MM. V.
Mean: 14347 J/. V. (without correction),
if the rate of heating was about 65 M.V. pro minute. As the correction
for the thermoelement was — 12 M. V. at this temperature, the
meltingtemperature is 1400°C., in terms of the nitrogenthermometer.
As a check the mellingpoint was now again determined by the
statical method: very small quantities, wrapped in platinum folium
were heated during a considerable time (from half an hour to one full
hour) at a certain and accurately constant temperature, and then,
after suddenly chilling *) in cold mereury, investigated by means of
1) F. M. Jareer, Kine Anleitung zur Ausfiihrung exakter physiko-chemischer
Messungen bei héheren Temperaturen. Groningen, 1913, Seite 73, 74.

947

the’microscope. We found that after heating at 14340 M. V. (element IIT)
the whole preparation was again crystalline, although it had the
outward appearance of a glassy, half-opaque mass; but on heating
at 14360 M. V., all had been changed into a real “glass”. The
meltingtemperature therefore must be fixed at 14850 M. V. As the
correction for the used quenching-system (vid. the determinations of
the meltingpoint of natural spodumene of J/adagascar) was shown
to be practically equal to zero, we can conclude from this, that the
meltingpoint thus determined is in full agreement with that found
by the dynamical method, and can be put at 1401°C.(G Th.). The
crystallized product appeared to be identical with the /?-modification,
later to be described, the refractive index was about: » = 1,521;
the specific gravity at 25° C: dy = 2,411.

2. In a similar way the preparation, obtained from lithinmaluminate
and SiO, was investigated; analysis gave the following data:

I Il Calculated:
StO, 64,80°/, 64,07°/, 64,6°/,
AGO 2S Os fae 205092 2 e
Li, O Cpa edie a liptess sali 8,0°/,

This preparation therefore evidently can also be considered as a very
good one; it contains ca. 0,4°/, 17,0 too little, and ca. 0,5"), Al, O,
too much.

Fig. 4.
Artificial 6-spodumene, obtained from LiA/O,
and Si0,; melted and slowly cooled.

CX Nicols).

248

The meltingpoint, determined after the dynamical method (element
IT]), was found:
14463 M. V.
14481 M. V.

Mean 14472 M. V. = 10 M. V. (without correction) ;
after correction, the meltingpoint can be fixed at 1410° + 1° C. (G.Th.).
After the statical method, the meltingpoint was determined at
14450 M. V., corresponding to 1410°C. The small excess of A/,O,
has evidently caused an ncrease of the meltingtemperature, of about
9°C. The erystallized product again was shown to be /?-spodumene
(n= 1,519); a photograph of it, taken between crossed nicols is
reproduced in fig. 4.

3. An analogous result was, in both ways, obtained with a pre-
paration, prepared from Li,S/0,, Al,O, and SvO,. Analysis of this
product gave the following data:

] II Caleulated :
SiO, 64,7°/, 64,48°/, 64,6°/,
Al,O, 28,4 °/, 28599) 2a ye
1,0 G95 Ce S076

The content of S/O, is here the right one, but the Ad,O, is 1°/,
too high. The meltingpoint determinations gave as a mean value:
14456 M.V. (uncorr.) after the dynamical method, and about: 14450
M. V. after the statical method. The meltingpoint is therefore :
11092 (Ch(Gelhe):

4. Most deviating from the composition: Li AlSi,O,,. was a pre-
paration, obtained from the melting together of £7,C0,, SiO, and
Al,O,. Analysis gave the following numbers:

I II Caleulated ;
SiO, 64,44°/, 64,88°/, 64,6°/,
Al.O,, J2T09/. SEAT Uh eno Ane
Li,0 —*847 > S795 eS Sey)

Evidently it contains about 0,21 °/, Z7,0 too mueh.

After the first method the meltingpoint was found at 14552 M.V.
(uneorr.), and after the statical method: 14550 M.V. The true melting-
point can thus be put at: 1417° C. (G.Th.).

§ 10. Although in most eases perfectly colourless products were
obtained, which evidently were identical to and independent of the
particular manner of preparing them, and which all represented the
8-modification, —- we succeeded however in several cases in obtaining
beautifully erystallized preparations, which locally or also totally were

249

tinged with a nice, reddish lilac hue; they were in most cases
obtained by longer heating, somewhat below the meltingtemperature.

The meltingpointdetermination with such an intensively coloured
product, prepared from L7A/O, and SiO, and showing by analysis
the following composition :

I. Me Caleulated :
S72, 64-92) o)s NEARY. F< Gd6/5
Al,O, 28,10°/, 27,94°/, 27,4 °/,
ROTC OSS 29) SOR
and thus evidently containing about 0,68°/, too much alumina, gave
the following results (statical method) :
After heating at 14660 M. V.: all glass.
14640 M. V.: all glass.
14600 M. V.: all glass.
14500 M. V.: all erystallized.
14560 M. V.: all crystallized.

The meltingpoint is thus situated at 14580 M.V., corresponding
with 1420° ©. (G.Th.).

Such lilac coloured preparations present in most cases rather
larger individuals of the 2-modification, which possess a tabular shape
with appreciably stronger birefringence than the common erypto-
crystalline masses, although the mean refractive index is the same.
While commonly this birefringence varies between 0,001 and 0,008,
it amounts in these preparations to about 0,007 ; the principal refrac-
tive indices are about: 1,520 and 1,527. In convergent polarized
light, at the border of the field an interference-image is partially
visible, giving the impression of that of an uniaxial crystal. However
on moving the table of the microscope, one can easily observe the
curvature and even the hyperbolic form of the dark beams; undoubtedly
an optically biaxial erystal with a very small axial angle, is present
here; while the position of the first bisectrix and the character
of the dispersion, point to monoclinic symmetry, with a strong
tendency to tetragonal forms. This last pecularity can be deduced,
— besides from the apparent uniaxity — from the fact, that rectangular
plates are not rare, which possess an extinction under right angles
or parallel to a diagonal, and a system of cleavage-directions under
45° with the optical sections. The specific gravity, like the refractive
indices, does not differ appreciably from that of the common @-form,
and was determined at 25° C.: d» = 2,401 + 0,008, measured with
several preparations. We obtained these same apparently uniaxial
plates, also from natural spodumenes by melting and slowly crystal-
lizing; there is no doubt whatever about the fact, that these tabular

250

crystals are identical with the common g-form, which represents
the stable form at the meltingpoint; the plates must be a peculiar
kind of erystals of this g-modification.

However we have till now not succeeded in giving a final explan-
ation of the remarkable reddish-lilac colour of many of these pre-
parations. It is quite sure, that it does not depend in any way on
the admixture of certain metallic impurities, solved from the crucible-
walls; on the contrary it appears to be connected with the macro-
crystalline strueture of the preparations. The nearer the chemical
composition came to the theoretical one, and the slower the crystal-
lisation of the mass takes place, by heating during a long time at
a temperature just below the meltingpoint, the more the appearance
of the violet tinge seems to be probable.

The same colour appears, if spodumene-powder or the pulverized
“glass” of it, are brought into liquids of about the same refractive
index (e. g. inta orthochlorotoluene, with n= 1,522); in that ease
the wellknown phenomenon of the “monochromes” (CHRISTIANSEN)
will appear. It is not impossible, that in our case the colour is
produced in An analogous way by the presence of the tabular, very
thin crystals amidst spodumene-glass, which possesses about the
same refractive index (1,519) as the ecrystal-tables (1,520 till 1,527),
or Yeversely ; these tables would be therefore quite invisible in the
surrounding medium. It could be understood in this way also, why
in the uncoloured mass in some cases locally smaller or larger
pink spherolithes are produced, making the impression, as the molten
mass were locally inoculated with germs of the violet substance.

By means of the ultra-microscope we were able to show, that the
preparation was not “optically empty”, as a great number of differ-
ently coloured lightspots, which do not move however, could be
observed; they are manifesting a structure of some particular kind,
without it being possible to ascertain of what kind the imbedded
particles are.

§ 11. As it follows from these investigations, in connection with the
meltingpoint determinations of natural a-spodumene later to be described,
that the chemically pure compound LiAlSi,0, has a meltingpoint
considerably lower than the natural spodumene-minerals, — we made
a series of investigations to find out, what admixtures of the natural
spodumenes might canse the mentioned increase of the meltingpoint.
Therefore to an artificial product, whose composition was:

StOp Ie oder
ALO; Dida fe
Li,O 8,2) /6

we added successively in concentrations of 1 mol. percentage, the
following chemically pure preparations :
Observed and reduced
Meltingpoints:

1. Jadeite: NaAlSi,O,, synthetical. elas SMe —— 382°
2. Leucite: KALSi,O,, synthetical, anhydrous. 14506 M.V. = 1414°
3. Lithtwmowide: Li,O. 14304 M:V. = 1397°
4. Alumina: Al,O,. 14585 M.V. = 1420°
5. Silica: SiO, (quartz). | 14530 M.V. = 1416°
And in concentrations of 2 mol. pere.: |

6. Pseudowollastonite: CaSiO,, sy nthetical, 14357 M.V. = 1402°
7. Siliimannite: Al,SiO,, synthetical. 14593 M.V.=1421°

Keeping in mind, that the pure substance melts at 1417° C.
(G. Th.), we can deduce from these experiments, that :

a. An excess of L7,0 lowers the meltingpoint of the compound
LiAlSi,O,, while the influence of an excess of S’O, is somewhat
uncertain, but seems to produce a slight increase.

b. That a lowering of the meltingpoint is also produced by an
excess of synthetical jadeite, leucite and pseudowollastonite, which can
be considered as the principal admixtures of the natural kunzites
and spodumenes.

c. That on the contrary, an dncrease of the meltingpoint is produced
by an excess of alumina and of alumosilicates, like e.g. pure
sillimannite.

In how far these facts, which of course will be studied more in
detail, when the ternary system: Li, 0—A/,O,—Si0, is investigated
completely, can be used for the explanation of the phenomena,
observed in the case of the natural spodumenes, will be shown in the
next paper.

Groningen, May 1914. Laboratory of Inorganic Chemistry

of the University.

Chemistry. — ‘Studies in the Field of Silicate-Chemistry. UL. On
the Lithiumaluminiumsilicates, whose composition corresponds
to that of the Minerals Eucryptite and Spodumene”. By
Prof. Dr. F. M. Janeer and Dr. Ant. Smek. ( Continued ).
(Communicated by Prof. P. van Rompureu.)

(Communicated in the meeting of May 30, 1914).

§ 12. For the purpose of comparison of the properties of the
described artificial product with the mineral itself, we have inves-
tigated a number of natural spodwmene-species in an analogous way.

252

We obtained a number of very pure funzites, and some good
spodumenes:

1. An almost colourless, somewhat lac tinged, strongly dichroitie
kunzite from Rincon in California.

2. A completely transparent, glassy, pale rose tinged kunzite from
Suhatany-valley on Madagascar.

3. <A beautiful, transparent pale greenish yellow kunzite from
Minas Geraés in Brasil.

4. A transparent, emerald-green hiddenite from Alewander County in
North Carolina, U.S.A., anda pale yellow hiddenite of the same place.

5. A eryptocrystalline, opaque piece of spodumene from Somerd,
in Finland.

6 An aggregation of opaque, long prisms of spodumene from
Maine, U: oh A.

All meltingpoints of the finely ground material were determined
in exactly the same way and with the same care, as formerly
described. The specitie gravities were determined by means of a
pycnometer, with ortho-chlorotoluene as an immersion-liquid; the
oravity of this was: dy = 17,0841 at 25°,1 C.

Most of the optical data were obtained by microscopical investi-
gation; the values of the refractive indices are determined at 16°
oye AY (Ce

specific

1. Kunzite of Rincon, Cahfornia.
Big, very feeble lilac colours, very lustrous and perfectly trans-
parent crystals, evidently with a cleavage parallel to the vertical prism.
An analysis of Davis, made with the same material, gave the
following results :
Calculated: Impurities :

70. : 64,05°%/ - 64,64), CaO R10; Sif: MnO : 0,11°/,
A,O, : 27,30°, 27,45, Na,0:03 °°, NeOmmomegn
TOO 388.5) S01. ZnO: 0,44°/, K,O : 0106

Total: 0.78 °/,.

The crystals show a strong fluorescence under the influence of

RONTGEN-rays.

The meltingpoint determinations gave, with thermoelement IV, the
following results: as a mean value of a greater number of obser-
vations, we found: 14683 M. V. + 4M. V.; as the correction of the
thermoelement at this temperature was — 8M.V., the melting-point
is thus: 1428° C. (G. Th.). It is very sharply localised on the
heating-curves.

253

The specifie gravity at 25,1° C. was: dy = 3.204 + 0,008 for the
natural, not yet melted compound; after solidification of the molten
mass, one obtains, after slowly cooling, a colourless, finely crystal-
lized mass, whose density differs considerably from the original mineral;
itis dqi==92, cor a 2o>,1aC.

The refractive indices of the molten and solidified substance are
considerably different from those of the original mineral. While tor
the unmelted substance we found respectively: 2, = 1,658 + 0,008;
— ARGE9H= = O1O03 Zande rie —1nGi-2) = 01003 2) for: the solidified
mass we found an extremely feeble birefringence of about 0,001,
and a mean refractive index of: 2p —= 1,518. The erystalpieces showed
an irregular extinction, evidently by very complicated intergrowth
of several individuals.

On rapidly cooling, an isotropous glass was obtained, with a
refractive index of m, = 1,517 + 0,001, being about the same as
for the crystallized mass. The specific gravity was at 25°,2 C.:
d,o = 2,388 + 0,003. When heated during a longer time at 1300° ©.,
it becomes erystalline; even at lower temperatures the glass gets
soon opaque and like porcelain by devitrification; but glass and
crystalline product obtained from it, evidently do not differ in their
properties to any appreciable amount.

Il. Kunzite of the Sahatany-valley on Madagascar. Big, clear and
completely transparent crystals; they are dichroitie and tinged with
a pale rose hue. Locally the environing rock-material is again
discernible, as a rusty coloured, finely divided substance. The erystals
were carefully cleaned from it; then they were ground and sieved,
after which the investigation proceeded in the usual manner.

As a mean value for a greater number of determinations, we
found the meltingpoint at: 14683 +5 M.V.; as the correction of
the thermoelement was —8M.V. at this temperature, we can adopt
the value 14675 M.V. of the E.M.F. of the thermoelement at the
ineltingpoint, corresponding with: 1428° C. (G. Th.); in this case
the meltingpoint is also very sharp.

Evidently this kunzite differs only slightly from the preceding
mineral of Rincon. With respect to its chemical composition, we
have some data, given by Lacroix’), who investigated colourless,

1) In a liquid of nm» = 1,670, composed of methylene-iodide and monobromo-
naphtaline, the crystalpowder showed a very beautiful reddish-violet colour, just as
some of CuristIANsen’s “monochromes”. The same phenomenon was observed fo1
the glass and the @-modification of artificial spodumene.

2) A. Lacroix, Minéralogie de la France et ses Colonies, [V, 775, (1910).

254

greenish-yellow and rose kunzites (triphane) from Maharitra on
Madagascar; the lilac and rose kunzites of Ampasihatra are im-
bedded in a kind of kaoline-earth, generated from the spodumene
by decaying-processes. The green kunzites possess the greatest values
of their refractive indices, however only little differing from the
other ones, while the rose tinged erystals have a smaller, the colour-
less ones yet smaller values for those constants.

We found by means of the immersion-method n, = 1,658 and
n, = 1,673, which values do not differ appreciably from the mean
values: n, = 1,6588, n, =1,6645 and n, = 1,6750.') For the ana-
lysis of the red and greenish crystals, the following data are given
in literature; they are reproduced here for comparison with the
composition of the Californian kunzite :

rose cristals: | green cristals:
SiOz :63,85% 9 CaO : 0,529) MnO : trace | SiO, :62,21%9 CaO :0,50% MnO : trace
AlyOy:29,87%\y NagO: 0,98) Fe,03:0,15%) | AlzO3:29,79%) NaO: 1,03%y) Fe03: 2,489/g
Li0 : 3,76%9 MgO :0,13°%/9 KoO :0,13%p Li,O : 4,02", MgO : trace K,O :0,212%p
Residue : 0,37%. | Residue: 0,25%p.

From these data results, that the quantity of S’O, in the rose
crystals is about the same as for the pale rose kunzite of Rincon;
but the content of A/,O, is much greater in the mineral of Mada-
gascar, and thus the 2,0 appreciably less than in the American
kunzite. The sum of those three constituents does not differ very
much in all these cases: 97,5°/, for the kunzite of Madagascar,
95,2°/, for that from Rincon. The specific gravity of the rose species
is about 3177: a value, only slightly different from the value,
determined by us: d,e = 38,3801 + 0,005, at 25°,1 C.

The refractive indices of the melted, feebly birefringent produet,

were found to be n, = 1,518 and n, = 1,520; the birefringence is
not greater than 0,002.

At 25°,1 ©. the specific gravity of the melted and solidified sub-
stance was determined: d,° = 2,373, when the preparation was heated
during several hours at a constant temperature, just below the
meltingpoint; under the microscope the obtained product then showed
the typical aspect of the aggregates of scales, which are always found
with the @-spodumene; they have a weak birefringence, and an
irregular, often undulatory extinction. When «-spodumene was not
melted before, but only kept at a constant temperature below the
meltingpoint, the substance appeared to be wholly transformed into
the same @-modification, with a specific gravity of: do = 2,376 at

1) Duparnc, Wunper et Sasor, Mém. de la Soc. physique de Geneve, 36, 402,
(1910).

259

25°,1 C. In both cases the mean refractive index for sodiumlight
was: ny = 1,518 + 0,001. From the molten mass therefore no other
phase is deposited than the mentioned 8-modification.

The fig. 5, 6, and 7 may give an impression of the manner, in
which the transformation of the e-, into the /?-modification gradually
occurs. In fig. 5 the original kunzite of J/adagascar is photographed
between crossed nicols, when heated only during 2 hours at 975°C.,
and showing no trace yet of the @-form; in fig. 7 the same heating,
but prolonged to 15 hours, has led to complete transformation of the
erystals into the #-form. The fig. 6 represents the crystals, after 8
hours heating at 975° C.; they show a partial transformation, and
the gradually occurring differentiation of the originally homogeneous
crystals into an aggregation of the felty needles of the @-modification.

Ill. Greenish-yellow Kunzite of Minas Geraés, Brasil.

This kunzite appears also in the form of large, very transparent
crystals, having a pale greenish or yellowish hue. This colour is
caused by a content of /eO, which in melting the mineral, is con-
verted into: Fe,0,; thus the solidified mass being always tinged
with a reddish-brown colour. The analysis of this mineral ') gave
the following data :

SiO, : 63,3— 64,3°/, CAOr 02-00
Al,O,: 27,7—27,9°/, Na,O: 0,6—1,0 °/,
1,0, : i 7,4°/, FeO ° O12 WE

This kunzite therefore is also relatively close in composition to
that of Rincon, approaching in its content of L7,0 closer to the
theoretical value; the sum of the principal constituents is 97,7 °/,.

The meltingpoint of this mineral was determined five times; the
results were, with thermoelement IV:

14643 M.V.
14646 M.V.
14650 M.V.
14639 M.V.
14646 M.V.

Mean value: 14645 M.V.;
after correction: 14637 M.V. (G. Th.)
The meltingpoint, reduced on the nitrogengasthermometer, lies
thus at 1425° C., i.e. about 3° C. lower than for the kunzite of Rincon.
The specific gravity of the substance before melting, was deter-
mined at 25°,1 C. to be: dy= 3,262; the data, given in literature
for the specific gravity of natural crystals, vary between 3,16 and

% 1) CG. Hintze, Handbuch der Mineralogie.

3,174. The refractive indices of the original substance were: 2, = 1,661
and n, = 1,669, with apparently a somewhat weaker birefringence

as for the already deseribed kunzites.

Fig. 5. Fig. 6.
Kunzite of Madagascar, heated tor two hours Beginning of the transformation of z-spodumene
at 960° CG. and not yet perceptibly transformed, (Madagascar), after being heated during eight hours
(X Nicols). — - at 975° CG. (X Nicols).

Fig. 7.

Kunzite of Madagascar, completely transformed into
the 6-form, after being heated at 975° C. (< Nicols).

257

After being melted however, the reddishbrown, crystalline product
had _a specific gravity at 25°,1 C.: dy = 2,463, while the refractive
indices of the feebly birefringent grains were found to be about
1,522 and 1,527. There is no doubt whatever about the fact, that
the solidified product is again a modification absolutely different from
the original kunzite; moreover it is evidently identical with the
already mentioned @-spodumene.

IV. Hiddenite from Alexander County, North Carolina, U.S.A.

Long, needle-shaped, pale green crystals, and emerald-green crystal-
fragments, which are transparent and dichroitic. The specific gravity
of this mineral at 25°,1 C. was found to be: dy=3,295 + 0,002 ;
the refractive indices were: n, = 1,664 and n, = 1,674. The data
for the specific density, given in literature, vary between 3,152 and
3,189. Of a hiddenite from Alevander City, with specitic weight

of: dy= 3,177, the analysis gave the following results :
SUON 2. 63595.9/5 Pe Oraey lelve of.
Al,O, : 26,58 °/, Na,O: 1,54 °/,
iO G82), CaO: no trace.

The sum of the principal constituents is here 97,35 °/,; the hue
of the erystals is caused by the admixture of /eQ, which is oxydized
in melting to Fv,O0,, giving a brownish-black or chocolate-brown
colour to the solidified mass. Another hiddenite of the same locality,
but of a paler colour, had: 64,35°/, SiO,, 28,10°/, A/,O,, and 7,05°/,
Li,9, — consequently together: 99,5 °/, ; moreover: 0,25°/, LeO
and only about 0,38°/, Na,O. The differences of the meltingpoints
of these two kinds of hiddenite, were about 1° C. or less. In a
series of observations, made with thermoelement IV, the melting-
point was fonnd at 14565 M.V. + 410M. V.; after correction, this
corresponds to 1418? + 41°C. , x.Th.). On cooling down the moiten
mass, first an undercooling is observed to about 1255°C., if the
temperature-fall was about 4° pro minute; then the temperature
rose to 1262°C. during the solidification of the mass, being 150° C.
lower than the real equilibrium-temperature.

Another time we found an _undercooling to 1208°C., then
solidification at 1214°C., — this being 204°C. lower than the true
meltingpoint! Although this point of solidification is lower than that
for the pure kunzites, it can have no essential signification whatever,
being wholly dependent on the speed of cooling and other accidental
circumstances.

V. Spodumene of Somerd, Finland.

A white, opaque eryptoerystalline and very hard mass. It was
finely ground, and investigated in a manner, quite analogous to that for-
merly described. The specific gravity at 25°,1 C. was : dy = 2,997 +
0.050; the refractive indices were about : 2, = 1,658 and n, = 1,669.
With the thermoelement /J’ the meltingpoint was found at 14649
M.V. +5 M.V.; being, after correction, 1425° C. on the gasthermo-
meter. Because of the inhomogeneity of the material, the meltingpoint
is here not so sharply localized on the heatingeurves, as in the
cases of the kunzites; on cooling the molten mass, solidification
oeeurs in the neighbourhood of 1298° C.

The substance solidified and heated for some hours below its
meltingpoint, had a specific gravity at 25°,1 C. of: do = 2,398 ; the
refractive indices were about: 1,510 and 1,518 for sodiumlight,

just a little smaller than commonly with the -spodumene. The
substance always shows very complicated aggregations of feebly
extinguishing scales with undulatory extinction.

If the original substance is not melted, but only heated during a
longer time below its meltingpoint, the erystals are converted into
the aggregations of the B-spodumene ; the specific gravity at 25°,1 C.
was now: dy— 2,412 and the refractive indices about: 1,519.

VI. Spodumene from Maine, U.S.A.; perhaps from Windhain.
This mineral consists of long, opaque, prismatic crystals, looking

Fig. 13.
Dense #Spodumene of Someré, Finland. (X Nicols).

259

like porcelain, with predominant cleavage. The carefully selected
material was finely pulverized, and investigated as described before.
The specific gravity at 25°41 C. was: d= 3,154 + 0,002; the

refractive indices were about: 7, = 1,656 and n, = 1,672. A micro-
photograph of it between crossed nicols is reproduced in the fig. 13.

The meltingpoint was determined several times with the thermo-
element ///; the following results were obtained : 14669 + 13 M.V.,
being after correction: 1427° + 1° C. on the gasthermometer. Also
in this case the meltingpoint is not quite so sharp as with the kun-
zites, just because of the chemical inhomogeneity of the material.

The obtained product had a specifie gravity : dyo = 2,336 at 25°,4 C.;
the weakly birefringent, irregularly extinguishing scales, had refractive
indices of about: 1,517 and 1,520; the birefringence is not greater
than: 0,008.

In fig. 8 a microphotograph between crossed nicols is given of
the dense a-spodumene of Jaine; in fig. 9 the same preparation,
molten and solidified into the 3-form is reproduced in the same way.

’ The strong analogy witb the image of fig. 4, representing an arti-
ficial 3-spodumene, made from L7AlO, and LiQ,, is obvious.

Another preparation was not melted, but only kept at a constant
temperature of about 1200°C. for some hours. The original «@-form
appeared to be totally converted into B-spodumene ; the volume of
the mass had increased then in such a degree, that the platinum-

Fig. 9.
Dense z-Spodumene of Maine, between crossed 6-Spodumene obtained by melting and crystallization
Nicols. of the z-modification (X Nicols).

260

erucible was wrecked during the process. The substance showed the
typical granular strneture of the crystal converted into p-spodumene
with undulatory extinction and a mean refractive index of: 1,518.
Phe specific weight at 25°,7 C. was determined to be : dy = 2,309,
and. tobe 2oi7, at ood:

§ 18. In all these experiments it was observed by us, that the
platinumerueibles, in which the silicate was melted and solidified,
showed a strong deformation, which increased every time that the
experiment was repeated. As fig. 10 shows very clearly, this observed
deformation is of such a kind, that it always appears as a dilatation,
as if the silicate, like water, solidifies under a volume-expansion.
The values obtained for the specific volumes of the erystals
and of the g/ass, seem however to make this explanation rather
improbable. We have tried by a series of systematic experiments to
find out, ahen really this increase of the volume sets in, by measuring
the diameter of the crucibles, after their contents had been subjected
to different manipulations. In this way, we found, that by far the
largest deformation of the crucibles took place, at the transformation
of «, into 3-spodumene, which is accompanied by a volume-increase
of about 30°),. When the substance is then melted once more, and again
solidified, the deformation already present will be increased by the

thermal expansion of the mass, and because the liquid substance is

|o\3.b4

1|\2
Fig. 10.

Deformation of the platinum crucibles after melting and solidification
of the natural Spodumene.
0. Origmal form of the platinum-crucibles.

1. Pale yellow spodumene of Minas Geraés, Brasil.
2. Kunzite of Sahatany-valley, Madagascar.

3. Dense Spodumene of Someré, Finnland.

4. Kunzite of Rincon, California.

enormously viscous, enclosed air-bubbles are hardly squeezed out,
but will rather expand in the mass itself, while the surface of the
liquid can change its height only with extreme slowness. In repeating
snecessively the melting and solidifying of the substance a number of
times, the deformation-effect will be gradually increased to such an extent
that, as fig. 10, N°.2 shows clearly, at last the crucible bursts. The
gradual lowering of the liquid surface in successive experimeuts
can be seen in those crucibles; in such a manner it often happens,
that with a strong deformation of the platinum vessels, when they
finally look like inflated balloons, the junction of the thermoelement
emerges at last out of the surface of the liquid mass, so that the heat-
effects on the heating-curves get gradually worse and will finally
disappear totally.

§ 14. To control the found meltingpoints, we have made a series
of experiments to determine it once more (with the kunzite of
Madagascar) by means of the quenching-method, which is to be de-
scribed afterwards in connection with our experiments for fixing the
temperature of beginning transformation. The quenching-system was
first calibrated by means of meltingpoint-determinations, made by
this statical method with lithiummetasilicate (1201°) and: diopside
(139L°); the corrections to be applied to the measured temperatures
appeared however to be practically zero.

We found in successive experiments :

Kunzite, heated during half an hour atl4600 M.V.and quenched in mercury: All crystallized

7 P » Fe PAO ENS 5 Pee ee eAlleolasce

” ” 2 Hp py LEOO MWS. 4 Js JN lbs:

” ” ” Be unr AONE ~ Sa aor alleclasss

” ” n Sut ay nee GSO en. ‘ ee i Glassand
crystals.

, . , PTE OOUIMEN Gear, F » » ? Allerystallized

” > > m3 wae 14690 M.V. ) > > ” : All glass.

Thus, the meltingpoint was found to be 1428° C. (G. Th.), quite
in accordance with the direct meltingpointdeterminations after the
dynamical method. In these experiments we once obtained a product
after longer heating on 14600 M.V., — just somewhat below the melting-
point, — consisting of somewhat larger individuals. They appeared to
be large, homogeneously extinguishing plates, whose birefringence
was about 0,007, and with refractive indices of 1,518 and 1,519,
like those of the 8-spodumene, obtained from artificial spodumene after
melting and cooling. In convergent polarized light the same inter-
ference-image as in the former case, was observed ; there can thus

Proceedings Royal Acad. Amsterdam. Vol. X VIL

262

hardly be any doubt, that the spodumene-modification, which is
deposited from the liquid mass, is quite the same as that, which is
discerned by us as 3-spodumene. There are no reasons to adopt the
existence of a third modification, which on cooling should be con-
verted into the 3-form, as occasionally has been done.

§ 15. Before describing our experiments with this compound with
respect to the study of the transformations into the solid state, the
determined values are once more recapitulated in the following table.

From this table (next page) we can see, that in general the melting-
temperatures of the natural kunzites are considerably higher than those
for the synthetical products, and further we can, generally speaking,
deduce, that the meltingpoint of the kunzites are decreasing at the same
time with the increase of specific gravity. (The specific gravities of the two
first mentioned kunzites differ too little to give any certain argument
for this view). Of the two kinds of dense spodumenes however, the
mineral of higher specific density seems to have the higher melting-
point also, although in this case the meltingpoints are too close
together, and are moreover not sufficiently sharp, to give any certain
argument for an eventual rational relation between the two mentioned

constants.

§ 16. Now we will proceed to the question, in what relation
the different modifications of the compound LiALSi,O0, stand with
respect to each other. That there are several of these modifications,
can already be deduced from the mere fact, that the product o7
solidification of the natural spodumenes is quite different from the
original substances.

Our investigations moreover have taught us, that there are really
only to modifications, which can be discerned as a- and @-spodumene.
Of these two forms the @-modification is undoubtedly the one to be
considered as the more stable form at temperatures in the immediate
vicinity of the meltingpoint. The question, however, then rises im-
mediately: in what relation are «- and #-spodumene to each other?
Are they enantiotropic forms, like e.g. wollastonite and pseudo-wollasto-
nite? Or are they monotropic modifications, as e.g. they are observed
in some forms of the pentamorphic magnesiummetasilieate ?

After numerous experiments in this direction, we have come to
the opinion that both forms of spodumene must be considered as
monotropic ones with respect to each other, and a-spodumene, i.e. all
kunzites, hiddenites, spodumenes of nature, must be metastable phases
of the compound with respect to the B-form at all temperatures below

263

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264

1400° C. Therefore it is neither possible to indicate an “inversion-
temperature’, below which the e-form, and above which the @-form
would represent the more stable phase: at all temperatures below
its meltingpoint, the @-spodumene is the only stable form of the
compound LZ7AlS7,0,. Under what conditions the «-form was always
eenerated in nature, while it was till now never obtained in the
laboratory from “dry” molten mixtures, may preliminarily be put
aside.

The reason however, that the «-modification, once produced, has
remained so, notwithstanding its metastability with respect to the
3-form, is to be ascribed to the enormous slowness, with which the
transformation «— @ takes place.

§ 17. To give an idea of this phenomenon, we will describe here

a series of experiments, made with the purpose to answer the
question, at what lowest temperature the transformation @a— @-
form again will ocenr with a velocity just observable? Preliminary ')
experiments had taught us that a long and little prominent heat-effect
was. observed between 900 and 1000° C., if a larger quantity of
finely powdered «-spodumene was gradually heated; and the micros-
copical investigation also taught us soon, that within the mentioned
temperature-interval, a transformation is going on with observable
velocity. We therefore made the following series of experiments by
means of the already mentioned statical method. For it is evident,
that just with reactions proceeding so enormously slowly, this method
can be used with great suecess, because 7 permits us to keep the
studied substances at a constant temperature during an arbitrarily
long time; in this way one can be sure that the reaction is thus
completely finished, while the sudden chilling of the preparation in
cold mereury will fix the momentaneous state of it in a most
effective way.
- The following data were obtained by observations with the thermo-
element 1V; because the thermoelement was not placed in the mass,
lut beside it, the whole furnace-system needed to be especially
calibrated for this series of experiments.

The calibration of the used quenching-system was executed by
means of meltingpoint-determinations after the statical method, with
substances, whose meltingpoints in terms of the gasthermometer were
!) Vide also : G. Tawmann, Krystallisieren und Schmelven, p, 114. Spodumene (d=3,17)
was transformed gradually into a much less dense substance (d=2,94), by heating
on a Bunysexbarner during ten hours. The new product was attacked much more
rapidly by HF than the original cubstance.

already accurately known before. Only in this way is it possible,
to find out, what temperature really corresponds to that, indicated
by the thermoelement placed in the furnace. For this purpose we
have made use of the meltingpoints of two compounds: L7,Si0, and
MBoO,; the Li,ScO, melts at a temperature of 11956 M.V. on
our standard-elements, the second at a temperature, corresponding
to an E.M.F. of 7822 M.V.'). In this way we observed:

| T
| LinSiO3. | LiBO>.

| | |
Heating during along | | ‘ Heating during a long J : :
_ time at a temperature, — State of the chilled time at a temperature, | State of the chilled
_ at which the E.M.F. of system : at which the E.M.F. of | system:
| element IV was: | element IV was:
12060 M. V. All glass. | 7800 M. V. All glass.
120205, All glass. TmOOwn All crystals.
11980, All glass. | sors, Many crystals; a
| | little glass.
11940, | Much glass, afew crystals |
TO 5, | All crystals.
11930, All crystals |
\| UTE 9 All glass.
11950 sy, All glass. }
Thus, when the furnace-element indicates 11940 | The meltingpoint of the LiBO, is thus reached,

| M.V., the meltingpoint of Zz-.SzO3 is reached;the || if the furnace-element indicates 7780 M.V.; there-
_ correction of the indicated temperatures at 1201°C. | fore the correction at 845° C. is: +42 MV.

_ to reduce them the nitrogenthermometer, is there- |

fore + 16M.V.

From both these data for 845°C. and for 1201° C., the correction
for every intermediate temperature is found by intrapolation; for a
temperature of e.g. 965° C., it is + 28 M. V.; ete. It is with this
number, that the just mentioned temperature (in M. V.) needs to be
augmented, to be reduced to the nitrogengasthermometer-scale.

Having in this manner determined the temperature-correetions for
the whole quenching-system within the range of temperature from
845° to 1201° C., we have chosen as an object for these experiments

1) With the thermoelement IV three series of experiments were made, with
heating-rates of 30, 40 and 60 M.V. per half minute. lor the lithium-metaborate
we found thus successively as mean values: 7786, 7778 and 7781 M.V., — which
gives as probable value: 7782 +4 M.V. The correction of element IV was + 40
M.Y. at this temperature; the true meltingpoint thus being at 7822 M.V. = 845 C,

(G. Th,).

266

the kunzite of Madagascar, and we tried to find in the described
way the lowest temperature, at which a just discernible transform-
ation of «¢— 3-form yet occurred. The reader may be put in mind,
that the experiments 1—14 were made with a thermoelement,
provided with a very thin protecting tube; in the experiment 14—20,
this protecting tube was omitted, which appeared however to make
no appreciable difference.

Indication of ther-| & | es Z \
moelement IV at) Ga | Soe
No. | theconstanttem-|.EE | Des | Result of the Chilling:
perature of healing Sf | 2S on
| =I a= (=)
(See ee wee Les
| 6510 M. V. | 723° | 2 hours | Only «-modif.; no transformation.
2 6800, 750 oy = idem
Sm S80 S05 a Oe idem
| |
4 8450, COLA ee a idem
ae | 9570, 1000 2 , | All s-spodumene.
6 | O500/ eu wie mousenieoian idem
7 9070 , | 957 CA No transformation; z-modification.
8 9220 ,, 970 he idem
9 9360 982 3 x ‘Partially transform.; «-, and #-form.
|
10 70s s 966 _ Probably the same.
| |
11 9280 , | 9715 Saar Partially 3-spodumene.
12 9280 ,, 975 ey = All ?-spodumene.
yt} 9260 ,, 913 | 4", Probably partially 3-form.
| 14 9260, O73 .aeiSua All 8-spodumene.
| | |
Tis) 9260 , | 973 | 855 | All s-spodumene.
16 |B) 9225 , 9170 | 8 , For the greater part: 3-form.
Ya | |
17 |2& \o160 965 | 4 , | All «spodumene.
ae | |
18 =e | 9200 ‘ 968 4 , Evidently partially g-form.
19 |S8foi70 965.5 | 4 , | Some -modification, many crystals
eae | of «-spodumene.
20 9150, 964 | Was | No #-form; the transformation has
| | not yet begun.
| | |
| | |

In this case therefore an evident transformation has already taken
place at 9170 M. V. (uncorr.), or at 9198 M. V. = 968°C. (G. Th.),

267

Similar experiments with the kunzite of Rimcon taught us, that this
lemperature is situated somewhat higher, at about 995° C.; in all
these cases however, only very long continued heating can lead toa
complete transformation of the «-, into the 3-form. It is therefore
quite evident, that at ordinary temperatures, and even at 400° or
500° C., the transformation-velocity of «-, into @-form must be
practically equal to zero; thus the « and 3-spodumenes can be in
immediate contact with each other, during an undetermined long
time, without transformation taking place.

The transition of «-, into @-form is accompanied by an enormous
increase of specific volume: it is augmented from 0.81 to 0.41,
being about 33°/, of the original value. It often occurred that the
heated and transformed powder had risen over the borders of the
platinum crucibles. In the described quenching-experiments, the trans-
formation could often be stated already, when the used platinum folium
had not yet been opened: it seemed to be inflated by the increase
of volume of the enclosed preparation. Microscopically it is observed
that the larger crystals of the «-form, in this transformation primarily
get innumerable cracks and fissures; afterwards they change into
opaque, no longer normally extinguishing aggregations of fine, felty,
or even broader needles, whose extinction is @/most normally orientated
on their longer direction; they ean be recognized by their weak
birefringence, as well as by their low mean refractive index : 1,519.
The microphotographs fig. 7 and 9 may give some impression of
the aspect of the two modifications between crossed nicols.

§ 18. It may be expected, that the mentioned transformation-
velocity will possibly be affected by some catalysers or by some
fluxes in such a way, that it will show a discernible value already
at considerably lower temperatures.

Indeed we succeeded in proving, that on heating spodumene-glass
with molten sodiumtungstate’) at temperatures between 850° and
920° C., after 32 hours a partial crystallization has begun, which
however was complete only after 65 hours of heating. The ecrystal-
mass had a refractive index of 1,523, and appeared to be no other
thing than B-spodumene; the determined specific weight was at 25° C.:
yo a Devise

1) The great difference between the specific gravities of the silicate and the
molten tungstate, makes it necessary to use a platinum stirrer, to bring the silicate
from the surface into the molten mass again and again. This stirrer was moved
by means of a suitable electromotor-driven mechanism.

268

We then made similar experiments with @-spodumene (of Mann)
in a mixture of 20°/, J/oO, and 80°/, sodiummolybdate at tempe-
ratures below 650° C.; on heating during 122 hours on temperatures
between 595° and 605° C., we obtained birefrmgent aggregates of
felty needles of the @-modification, with often rectangular borders.
The refractive index was 1,527, and while the aggregates of needles
did not extinguish in any position between crossed nicols, the rectan-
gular needles often showed a normally orientated extinetion. As in -
ihe former ease, the product had also a pale lilac hue.

Then we made the same experiment with a-spodumene (of /tincon);
it was heated during 88 hours in the same mixtures at 595° to
GO5° C. The small pieces of the «-form had got opaque and were
converted at their borders or totally into the @-modification; the
refractive Index was 1,519.

More experiments were made, which all taught us, that from
molten magmas, cooled under manifold varied circumstances, never
was another thing produced, than either spodumene-‘“glass’, or
B-spodumene; however we did not succeed in getting the a-form
from dry magmas even a single time. As devitrification of spodumene-
glass appears also never to give another phase than @-spodumene,
— we are of opinion, that it may be considered as sufficiently
proved, that the @-modification is the only stable modification below
the melting point. The spodumenes of nature therefore certainly
cannot be produced from dry magmas; they represent metastable
forms of the compound, which are very probably generated from
circulating solutions, that is by so-called “hydrothermal” synthesis;
the natural forms of the compound only appear to be preserved
by the enormously retarding factors, which prohibited the transfor-
mation into the more stable €-form. Experiments are going on, with
a purpose to produce the «-modification of the silicate by such
hydrothermal synthesis. The results of these experiments will be
discussed in a following paper.

§ 19. Finally we can here give some data, concerning the lithi-
wmnaluminate: LiAlO,. This compound was prepared by heating in
platinum crucibles the weighed, finely ground and well mixed com-
ponents, — lithiumecarbonate being taken instead of L7,0, — in
our resistance furnaces once at 900° C., then at 1200° C. After the
resulting mass had been pulverized, the heating was repeated and
these manipulations repeated four times. Analysis of the beautifully
crystallized, homogeneous mass gave the following numbers;

269

Observed : Calculated :

Al, O7: 76,8 °/, TOL Uae fe

LEOr: 23,2 °/, 23,0 °/, 22,7 °/,

100,0
Although a small excess of 47,0 was still present, the substance
could be considered as -practically pure Z7A/O,, — the more so,

as on heating, a certain amount of Z7,0 always volatilizes gradually.
A preparation, heated only shortly at 1600° C. contained, as ana-
lysis showed us, only 19,34°/, Li,O and 80,65 °/, Al,O,; no further
change had occurred than that the crystals of the original prepa-
ration had got inuch larger dimensions, while preserving their gene-
ral properties. At 1625° ©. the substance shows no trace of melting,
but decomposes partially, by the volatibility of the Z7,0. The pla-
tinum is strongly attacked, 27,0, being formed, and thus the alumi-
nate cannot be heated at higher temperatures, without changing its
composition. The meltingpoint can thus be hardly determined; the
substance must have been changed a long time before already into
Al,O,, with perhaps a slight admixture of some lithitumoxide. Even
in a “hollow thermoelement”, we were not able to melt the substance,
notwithstanding it being heated up to 625° C.

Microscopically the aluminate shows large, round-edged, hexagonal
or octogonal plates (fig. 12), with a relatively high birefringence

Fig. 12.

Crystals of Lithiumaluminaie. (X Nicols).

270

and high interference-colours between crossed nicols. The refrac-
tive indices were determined toe be: n, =1,604 + 0,001; n, =
1,615 + 0,001 for sodiumlight; the birefringence was about: 0,012.
No axial image could be observed. The specific gravity of the erys-
tals at 25°,1 C. was: d,o = 2,554.

In a following paper we hope to be able to give an account of
the formation and the occurrence of the «-modification of the spo-
dumene in nature, and to review the results so far obtained, also
with respect to their geological significance.

Laboratory for Inorganic Chemistry
of the University.

Groningen, May 1914.

Physiology. — ‘On the survival of isolated mammalhan organs
with automatic function.” By Dr. E. Laqunur. (Communicated
by Prof. H. J. Hampurerr).

(Communicated in the meeting of April 24, 1914).

When studying the movements cf extirpated pieces of gut, I was
struck by the following fact: a piece of gut which had contracted
for 9 hours in a Tyrode-solution at 37°, to which oxygen had been
added, and which had been left to itself at room-temperature, began
to move again the next morning, after being heated and after a
renewed addition of oxygen. However frequently such experiments
with pieces of gut — in the way suggested by Magnus — have
been carried out by various investigators, yet the possibility of
keeping the gut alive for so long a period seems to be unknown.
~ Further researches show, however, that the automatic movements
of such pieces of gut are of much longer duration than one day
and one night. The longest period, as yet observed by me, runs to
more than 3 weeks. As many as 21 days after the death of the
individual the movements of the piece of gut could be observed.
This time probably exceeds everything hitherto observed in this
respect on mammalian organs working automatically.

We may compare with this, for instance, how long after the death
of the individual the beart can be made to contract. The heart is
indeed the only automatic organ, as far as | know, on which
experiments have been carried out in this direction. KuLIABKo, for
instance, discovered that when the heart of a rabbit, after being
kept for 44 hours after death in an ice-chest, was perfused with
Lockn’s solution, contractions again manifested themselves. The heart

274

sometimes beat for several hours at a stretch; certain parts of the
heart are even said to beat on the 3, the 5, and the 7" day
after death. It is a well-known fact that, when at the obduction
air can penetrate into the cavity of the chest, this may give rise to
spontaneous contractions of the right atrium — the w/timm moriens
Halleri ov vather Galent. Vunrran states that he has observed these
contractions in the dog for 93'/, hours after death. Rovussnau main-
tains that he has seen these movements in an executed woman,
29 hours after death.

The human heart has also been made to contract independently
after death. These attempts have never succeeded with adults when
the individuals had been dead for more than 11 hours. (H. E. Herina).

This could be done with the heart of a child 20 hours after death
and in the case of a monkey as many as 53 hours after death.
(KuntaBko, H&rtNa). ')

Recently Carret and INnGrsrictsEN have stated that some tissues
ean be kept alive for a long time after the death of the individual ;
the tissues could even become differentiated under these circumstances.
These experiments, however, have been taken partly with very
small pieces of hardly differentiated tissues: this applies for instance
to the muscle-cells of the embryonic chicken heart, contracting 104
days after the death of the animal. (Carrer). And partly they relate
to parts of organs (bone and skin) where it is not so easy to
determine whether the cells are living still. To ascertain this the
“surviving” tissues must be transplanted on another animal. It must
be taken into account, however, that these tissues may have
permanently lost their independence. Only with the assistance of the
normal tissues of the animal on which they were transplanted, they
had regained life.

With regard to the following experiments on the movements of
isolated intestines, the investigations of MaGnus have shown. that
automatic movements are only met with, when besides the musele-
cell the nervous system of Awerbach’s plexus has retained its activity.
The phenomenon is, therefore, of a complex nature.

Intestines can be kept alive longer than usual (++ 12 hours) only
when the periods of activity are alternated with long periods of rest.
This can easily be done, as we know, by lowering the temperature.
At body-temperature the isolated gut works itself, sit venia verbo,
to death, within from 10 to 14 hours,

1) See the Summaries by O. Langenporr in Ergebnisse der Physiologie 1903
and 1900.

272

For various reasons the intestines of smaller animals, mouse, cavia,
rabbit, were chiefly experimented upon. The method followed here
keeps the intestines longer alive in proportion as they are thinner.
In reality this method is a very primitive one. In the intestinal wall
there is no longer any circulation and the metabolism is therefore
restricted to the diffusion through the whole thickness of the wall.
Hitherto I have not succeeded in keeping the gut alive in ftyrode-
solution, a medium particularly fitted for intestine-experiments, for
a longer period than 5 days. Pieces of intestine which no longer
moved in the solution in which they had been placed immediately
after the extirpation, began to move again when the solution was
refreshed. This can easily be explained.

The experiments carried out by collaborators of Magnus, WEINLAND
and Nwuxirch have taught that when the intestine is placed in a liquid
medium, substances are formed which stimulate the intestine. That an
accumulation of these stimulating substances, besides the usual decom-
position products, and more especially besides the bacterial decom-
position products, unavoidable in intestine-experiments,should impair
the activity of the intestine in the long run ean easily be understood.

If the temperature of the pieces is kept particularly low (+ 3°),
then the intestine keeps alive much longer than if the temperature
remains but litthe under the limit at which activity still manifests
itself. Pieces of ecavia gut in tyrode-solution at 15° were already
dead on the 38" or 4% day.

If the temperature of the tyrode-solution was + 3°, the gut died
only on the 5% day.

To keep the gut alive for a longer period a medium is required
resembling more than tyrode-solution the normal body-fluids. For
this purpose I took Aorse-serum’*), the serum of the small animals
experimented upon not being obtainable in sufficient quantities.

Since oxygen must bubble through the fluid in which the gut
has been placed, a great quantity of froth is formed if serum is
taken instead of tyrode-solution. This can be avoided, however, by
pouring a thin layer of olive-oil on the serum. It might be assumed
as probable that serum would prove a better medium than a salt-
solution on the strength of the many experiences obtained with the
surviving heart. (Wurre, Howni., Greex, Wanpen, with hearts of
warmblooded animals, Guririm and Pike with hearts of mammals. *)

1) Horse-serum can be oblained by the method, described by HAMBURGER and
often applied in his laboratory, | take this opportunity of again thanking my
colleagues De Haan and Ouwewwen for the readiness with which they always
provided me with horse serum,

It is true, cases have been mentioned where a frog’s heart, which
beat no longer in sheep serum and could no longer be stimulated
mechanically, was made to contract again by Rtina@ur’s” solution
(Waxprn). Yet the possibility is net excluded that in these cases the
strange serum has gradually had a poisonous effect. Therefore I
shall also leave it an open question if the time during which the
eut keeps alive would not be longer still if, instead of horse-serum,
serum of the same animal, if possible of the same individual, were
used.

The experiments of INGrBeiarseN with tissue-cultures in auto-,
homo- and hetero-geneous sera have demonstrated the relative
superiority of autogeneous serum to serum of other individuals of
the same kind, and of these two sera to heterogeneous ones. INGr-
BRIGTSEN has not used horse-serum; this seems to be a particularly
indifferent medium. Numerous experiments have shown that this
serum is a much better medium for the gut than tyrode-solution.
The gut of a cavia, for instance, kept in tyrode-solution, was dead
after 5 days; when kept in horse-serum another piece of the same
gut still moved after 21 days.

The experiments were carried out in the following manner.

The animal, a cavia for instance, is killed by decapitation,

+ 20 em. behind the stomach a piece of the small intestine, long + 40 c.m.
is cut out and divided in Tyrode-solution into 8 pieces long 4—6 c.m., called
a—h. 4 of these (a, b, e, f,) were placed in Tyrode-solution, 4 others (¢, d, g, /)
in horse-serum.

Oxygen is led through the 8 glasses. The pieces a, e, ¢, g, are connected with
a writing apparatus lo a cymographion (method of Magnus)

To ¢ and g olive-oil is added. The movements of these 4 pieces having been
registered at + 37°, they are slowly cooled down. Then the current of oxygen
is stopped. The glasses a, e, and the reserve-experiments b, f, remain at room-
temperature (+ 15°), the glasses c, g and the reserve-experiments d, h are exposed
lo a temperature of + 3°. The pieces a7};, eT, ¢T\, and g7T, remain connected
with the writing-apparatus or are removed with it.

On the third day after the death of the cavia the pieces a, e, c, and g are
connected wilh the cymographion whilst oxygen is led through, and are slowly
heated to 40°. All the pieces move, but not so much as the first time except
Sz, the movements of which have become greater. The fluid in all 8 glasses is
refreshed after being cooled down and saturated with oxyen as on the first day.
On the sixth day all are heated ete. just as on the third day. Piece 77; moves
no longer now, not even after the Tyrode solution has been refreshed. The reserve
piece “7); does not move either: therefore in Tyrode solution at + 15° the gut
dies before the 4th day The three other pieces ¢7, °S);, and 9Ss still move,
the first two less again than last time. On the 6th day everything is heated again
etc. Piece e7; moves no longer, not even after the Tyrode-solution has been
refreshed. Nor does the reserye-piece /7'; move: hence in Tyrode-solution at + 3

D174.

the gut dies before ithe 6th day. Piece “S|; does not move either. On the other
hand the reserve-piece 4S), is still in motion. Movements of 7Sg are still greater
and have the same frequency as before. The three fluids are renewed etc. On the
Sth day only “S; moves distinctly: hence in horse-serum at + 3° death before
the 8th day

On the 10, 13, 15, 17, 20, 22ud day 7S; moves distinctly, but the movements
have become smaller. On the 25th day no movements. The reserve-piece 2S; got
fresh serum for the last time on the 24nd day and is for the first time connected
with the cymographion on the 27th day. It does not move; only its tension
decreases when heated. Hence in horse-serum at 3° the intestine dies after the
22nd and before the 25th day.

Hunan gut can also be kept alive for a comparatively long
time ‘). A piece of colon, obtained after an operation, moved still
after 86 hours. And an appendix, kept in horse-serum, described
no straight line on the cymographion after as many as 6 days.
There were slight but distinet contractions, which ceased when the
intestine was cooled down to 25°. Finally I may mention that a
human vas deferens was still alive in tyrode-solution after 30 hours.

Summary.

Isolated pieces of mammalian gut can be kept alive during a long
time, much longer than the periods found hitherto for other auto-
matic mammalian organs. For this purpose the medium in which
the gut has been placed must occasionally be refreshed whilst it
is of great importance that the temperature of the solutions should be low.

In Tyrode-solution of 15° the gut dies after 3 days, at 3° after
+ 5 days, in horse-serum at 15° after + 7 days, at 3° after more
than 21 days.

Also pieces of human intestines still showed signs of life after
they had lain for 6 days in horse-serum at + 14°.

Groningen, April 1914. Physiological Laboratory.
'!) I am indebted to Prof. Kocn for his kindness of providing me with pieces
of human gut.

975

Physics. — ‘/sothermals of monatomic substances and their binary
mintures. XVI. New determination of the vapour-pressures
of solid argon down to — 205°’ Comm. N°. 140a from

the Physical Laboratory at Leiden. By C. A. Crommenin.
(Communicated by Prof. H. Kamernmen Ones).

(Communicated in the meeting of March 28, 1914).

The vapour-pressures of solid argon, which are communicated
below, form an extension of and have partly to replace those published
on a former occasion. ')

The measurements were made in the usual vapour-pressure apparatus
for low temperatures. *)

The manometer on which the pressures were read was constructed
after the model used by G. Hots for his measurements on ammonia
and methyl-chloride to be published shortly: this form of manometer
gives perfect security against leakage.

The method of conducting the measurements gives no oceasion
for special remarks: we refer the reader to the previous paper. It
may be mentioned however, that the temperatures were measured
with a gold-resistance thermometer, as below — 200° gold is preter-
able to platinum. This thermometer was very carefully compared
with the standard-platinum-thermometer Pty.

I am indebted to Mr. P. G. Carn assistant in the physical Labo-
ratory for the measurement and calculation of the temperatures and
for the comparison of the two resistance-thermometers referred to.

Table I contains the results of the observations and the deviations
from the Rankru-Bose-formula :

log Peoex. =arnB + bra T—! + erp T—-2 + dep T-3,

with the following values for the coefficients

agp + 6.6421 crg = — 0.677438 x 101
bea = — 3.7181 10? dre = + 0.280384 « 108

1) CG. A. Grommetin, Comm. Leiden. N°. 138¢c. The measurements were repeated
because shortly after the publication doubt arose as to the accuracy of the determi-
nations at the lowest temperatures (see note on p. 23 of Comm. N®. 138c). The new
measurements showed this doubt to be justified, the observation at — 2069.04
being found altogether wrong and the one at — 179°.62 not very accurate. The
remaining observations of Comm. N® 188¢ correspond well to those published
here. The probable cause of the errors must be air having leaked into the argon
at the low pressures: but [ cannot explain how it is that this was not noticed
during the measurements.

*) H. KamertinaH Onnes and C. BraaK, Comm. N°. 107a.

bo
~f
o>

TABLE |. Vapour-pressures of solid argon.

pat @ (Celsius | ia | Percentagerdeviations
ig | Ne SN cae) TUT eee ee
Ceyesee | | MCCAY: formula. | formula. |
26 Nov. | XXIII ~189.64 | 0.6554 | 49.78 | +0.20 | +1.33 |
| XX |” 191/31 | 0:5175. "|" 39.30 ot oa

XXVI 195.60 | 0.2749 | 20.88 | +0.35 Ss

XXVII 197.25 | 0.2153 | 16.35 | 2.16 +0.15

28 Nov. XXVIII 200.97 | 0.1113 8.456 | —0.94 |) ==o029
XXIX | 202.21 | 0.08931 | 6.783 | —0.89 —1.49

XXX | 203.78 0.06740. 5.119 | —0.04 +0.59

XXXI 205.32 | 0.05043 | 3.830 | 10:36 [|p ="2:79

and from Nernst’s formula (treated simply as an empirical formula)

log Peoex. = 7 Se SUR es Ding Ps <G)
with the coefficients

A= — 907.49 G — -+f- 20.851

B= + 0.010899 D = — 6.9057.

The values of the coefficients in both formulae hold for p in ems.
mercury.

The comparison with the formula which Sackur has deduced
from Nernst’s heat-theorem

a en pene (oft a
( SS = SS UG — SSS = a0) =
pe ewan wa 23k) T 23R

is given in table II.

For details as to the manner in which the various values have
been calculated the reader is referred to the previous paper. It will
be seen that the agreement is satisfactory at the higher temperatures
while at the lower temperatures the deviations become very large.

Finally 1 have caleulated the heat of sublimation of solid argon
from the simplified CLapryron-Crausivs-formula

RT? (dp
Aso .Vvap. = — == °
P dT CO"X.,

| TABLE II.

| ue A

Pee pW) p(R)
—189.64 | 0.655 0.618

191.31 0.518 0.507

| 195.60 0.275 0.286 |
197.25 0.215 0.226 |
200.97 | 0.111 Onin
202.21 | 0.089 0.124

| 203.78 | 0.067 0.107
205.32 | 0.050 0.094

Calculating (Ge from the above Rankrve-Bosz-formula the
c coex.

following values are found for the heat of sublimation expressed in

calories per gramme of substance at the various observation

temperatures

TABLE III.

Calculated heat of
| sublimation of argon.

In coneluding [ am glad to express my hearty thanks to Professor
H. Kamertincu Onnus for his continued interest in my work.
19
Proceedings Royal Acad. Amsterdam. Vol. XVII.

278

Physics. “Further experiments with liquid helium. J. The ime-
tation of an Amekre molecular current or a permanent magnet
hy means of a supra-conductor. (Cont.). By Prof. H. KAMERLINGH
Onnes. Communication N°. 140¢ from the Physical Labora-
tory at Leiden.

(Communicated in the meeting of May 30, 1914).

§ 5. The main experiment repeated. Although the original experi-
ments on the persistence of a current which is started in a closed
supra-conductor have established the fact that the diminution of the
current with the time is very small (at least if it is assumed that
in the phenomena hitherto unknown magnetic properties do not play
an important part), still for the magnitude of the change only an
upper limit could be fixed. As no change of the current was obser-
ved, this upper limit was determined by the uncertainty in the
measurement of the current. The only fact established so far was
that, if the change had been greater than 10°/,, it would have
been observed.

In repeating the experiment it was attempted to determine the
change itself or otherwise to reduce its upper limit, in so far
as the conditions under which the experiment had to be made
allowed this. The same supra-conducting lead-coil was used. As before
the current was produced in the closed conductor by induction in
order that the circuit might be kept free from connections other
than of lead fused together‘). The current was again measured by
compensating the action of the coil on a compass-needle by means
of a current in a subsidiary coil. The arrangement was however
improved by this coil (of insulated copper wire) being placed in a
small vessel with liquid air in a fixed position with respect to the
needle. When the compensation was obtained, the experimental coil
was turned 180° about a vertical axis and again compensated with
the current in the second coil reversed, the magnetic moment of
the experimental coil being deduced from the mean of the two
observations.

If the diminution of the current can actually be calculated
from the residual micro-resistance given in Comm. No. 138, viz.
10.8 K. ;

———_=—0)5) <10—®, oriawith Topo K. 134 2’): riog x, = 37, the time
19060 Kx.

1) An attempt is at present being made to manufacture a supra-conducting
current-key.

2) This value given already in Comm. N® 1406 is a more accurate value than
the one given in Comm. N°. 153.

of relaxation, with 1 = 10%, would come to about 270000 seconds
ovr 75 hours. In that case the current would fall by 4°/, in three
hours. It was hoped that it would be possible with the improved
arrangement to establish a diminution of that amount.

The experiment was made with a field of 189 gauss at a tempe-
rature of 1.°7 K. The current amounted to about 0.4 amp. (as
before no account was taken of the possibility of magnetisation or
of induced circulating currents inside the supraconducting material)
and during about 2'/, hours no diminution of the current was
observed; it was then necessary to admit a fresh supply of helium
into the cryostat: during this operation the temperature rose tem-
porarily to 4.925 K. During the next hour the current was found
to undergo a gradual diminution and to approach asymptotically a
new value of about 0.56 amp. which did not show any further
change for 1°/, hours. The observations during the two periods
mentioned render it probable, that the change does not attain the
value of 4°/, in 3 hours as calculated above.

It was considered possible, that the changes of shape of the
helium-liquefier and the cryostat during the process of condensation
and transfer of the liquid helium, as well as a possible change of
zero of the compass-needle which after the magnet has been removed
is still near various iron parts of the apparatus, might have had an
influence on the values of the current as measured at different
moments. Judging by the correspondence of the various readings
the accuracy was smaller than had been expected. In again repeat-
ing the experiment therefore two compensating coils were used by
which compensations on the east and on the west could be effected.
They were mounted each in a small vessel with liquid air on a
fork-shaped stand and could be rotated about vertical axes in such
a.manner that the distance of the axes could not change. The same
needle served for the compensation on both sides. Guiding pins
guaranteed the same position cach time of the needle relatively to
the compensating coil which was being used. The common support
of the two coils was moveable parallel to itself in a horizontal
direction on a slide and by means of marks it was possible to place
it each time in the same divection and the same position relatively
to the vertical axis of the experimental coil. The axes of the three
coils were provided with horizontal divided circles moving along
fixed pointers. Each measurement consisted of 8 readings in the
obvious combinations of 4 positions both with compensation on the

left and on the right.
In the experiment with this improved method of reading care was
19*

280

also taken, that the current did not rise above the value at which
no further change had been observed at 4°.25 K. The current was
therefore raised to only 0.22 amp. (approximate value calculated
as before from the observed magnetic moment of the coil), so that
the supply of a fresh quantity of helium would probably not have
the disturbing effect which had been noticed in the previous expe-
riment. The temperature used was 2° K. In the beginning again a
fall of current was noticed which must however be considered as
uncertain, inter alia owing to the possibility of the changes of shape
of the apparatus and the change of zero of the needle not having
been sufficiently eliminated yet in these observations. In the three
hours subsequent to the initial period no further diminution was
observed, the last observation even giving a small increase. Still in
this experiment the accuracy could not be considered greater than
about 2°/, of the measured moment and, as it was found impossible
to continue the experiment, beyond three hours, again only an upper
limit for the change could be established, to be put at about */, °/,
for current and induced magnetisation combined. Taking all the expe-
riments together it may be considered as probable, that the change
of the current is less than 1°/, per hour which raises the time of
relaxation to above 4 days.

§ 6. Upper limit of the residual micro-resistance according to these
experiments. So far no contradiction has arisen in reasoning on the
assumption of the existence of a residual micro-resistance whieh
below the threshold-value’ of the current again obeys Onm’s law.
On this view the upper limit of this micro-resistance for lead, which
in Comm. N°. 188 was placed at 0,5 10—!° of the ordinary resi-
stance at 0’, can now on the basis of the above observations be
moved further back to about 0.3 10~!" or 0.2 10—!" of the resistance
at the ordinary temperature.

§ 7. Some of the control-experiments repeated. In the previous
paper a few other experiments beside the main experiment were
described : some of these have now also been repeated.

Again we did not sueceed in conducting the experiment in which
the windings are placed parallel to the field, the coil cooled below
the vanishing-point while in the field and then the field removed
in such a manner, that the compass-needle, when brought near the
cryostat after removal of the electro-magnet, did not show any
deflection. After the action of a field of 400 gauss at 4°.25 K. a
current of O.1 amp. was found in the coil. This would give 0.045

281
amp. with a field of 189 gauss, the same as used with the other
experiments, whereas the main experiment at the same temperature
and inducing field had given 0.4 amp.

More satisfactory was the experiment in which first a current is
produced in the coil — analogous to the currents in resistance-free
paths as imagined by Weser for the explanation of diamagnetism —
and then destroyed by the removal of the field: an almost complete
compensation was obtained in this case. The experiment was made
with a field of 189 gauss. This result is of special importance as if
practically disposes of the supposition mentioned in the previous
paper as possible, although very improbable, that magnetic properties
of the material of the coil might play an important part in the
phenomena.

The current in the coil changes with any new magnetic field
applied and with any further change in it, or with any change of
position relatively to the field. In this respect the influence of the
earth-field may be noted. The current in the coil, when placed with
its windings at right angles to the meridian, will assume a slightly
smaller value in the one position North-South and a somewhat larger
value in the opposite position Sout-North than in the position East-
West, which is practically the position in which the experiments
were made. In our experiments this action was however too small
to be taken into account considering the accuracy which could be
attained at the most.

It may be observed that our conductor carrying its current in the
absence of an electromotive force, when undergoing the relatively
small action of the field of the earth, is analogous to the AMPERE
molecular currents (in the form of circulating electrons) which play
a part in LanGrvin’s theory of magnetism, when they experience a
diamagnetic action on being brought into a field, in accordance with
Lorentz’s theory of the Zrrman-effect.

§ 8. The experiments repeated with the circuit open.

So far it has been constantly assumed, that the magnetic properties
of the material of the coil play but a secondary part in the pheno-
mena observed, when the experiments were arranged so as to
produce a permanent current. This view was based firstly on the
difference in the results with the windings parallel and perpendicular
to the field during the cooling in the field and secondly on the
compensation found on applying and removing the fiela after the
conductor had already been cooled to helium-temperature. Further-
more that the part of the effect which is independent of the circu-

289

lnting current must be ascribed to the lead itself, was to be inferred
from the fact, that the current is quenched, as soon as the tempe-
rature of the coil rises somewhat above the boiling point of helinm
and passes the point which, as being the vanishing point for lead,
has a special physical meaning for this substance.

In order to obtain further information as to the part of the
phenomenon which depends upon the material itself, the experiments
were repeated after the lead-wire connecting the ends of the coil
had been cut, so that the circuit was no longer closed (apart from
possible short-cirecuits in the coil).

This time the experiments with the exception of one could only
be performed at 4.°25 K: still there does not seem to be any objection
to applying the results for the explanation of the irregularities which
had been left unexplained in the main experiments, although these
had been mostly carried out at a lower temperature.

In all the experiments a certain residual effect remained, which
was reduced to about one tenth when the windings were parallel
instead of at right angles to the field and in the latter case was
fairly well independent of the field. The amount of this effect cor-
responded to a moment which was equivalent to a current of 0,05
or 0,06 amp. in the closed circuit. In one of the experiments, the
only one in which the temperature was lower than 4.°25 K., viz.
about 3° K., the moment was estimated to be equivalent to as
much as 0.07 amp. The effect with the circuit open is thus very
much smaller than in the main experiments. The share born in the
effect by the frame of the coil and the lead independently of closing
the circuit may therefore be put at less than '/, of the total effect
in the main experiment.

As a check on former experiments the following additional expe-
riments were made with the coil with the lead wire cut.

In the first place at the ordinary temperature after joining up to
a ballistic galvanometer the induction was measured arising from
putting on or taking off the field with the windings in the position
in which they were supposed in the previous experiments to be
parallel to the field. The induction was found to be '/,, of the effect
in the position at right angles to the field. This observation may
contribute to the explanation of the residual effect observed in the
experiments in helium in the position with the windings parallel to
the field.

In the second place a known current was sent through the coil
and its strength measured by the same method as used in determining
the moment of the experimental coil in the experiments with the

Z 283

lead cireuit closed. Although the matter requires further elucidation,
it would seem to follow from this measurement, that a few of the
layers of the coil are short-circuited. After opening the cireuit a
residual moment remained in the coil as before which was destroyed
on raising the temperature slightly above that of the helium-bath.

Physics. — “Further experiments with liquid helium. K. Appearance
of beginning paramagnetic saturation.” By Prof. H. Kamertincu
Onnes. Communication N°. 140d from the Physical Laboratory
at Leyden.

(Communicated in the meeting of May 30, 1914).

The question, whether paramagnetic substances would show a
saturation-effect at high field-strengths, has always been considered
a very important one. Although it could hardly be assumed, that
the susceptibility would remain independent of the field at higher
strengths than were attainable, still so far at the highest fields
available if appeared to be the case. Lanervin’s theory brought
the explanation, why so far all attempts to find paramagnetic satu-
ration-effects had remained unsuecessful. According to this theory
the magnetisation appears to be determined by the expression

a= ——, where 6, is the magnetic moment of the molecules per

eramme-molecule, A the gas-constant, 7’ the absolute temperature
and #H the field. As long as a remains below 0,75, the changes of
the susceptibility with the field escape the ordinary method of obser-
vation and at the ordinary temperature even a substance as strongly
paramagnetic as oxygen gives for @ with a field of 100000 not more
than about 0,05. As I pointed out at the 2°¢ International Congress
of Refrigeration at Vienna (1910) this theory shows that lowering
the temperature is the means by which the observation of para-
magnetic saturation might be attaimed and that helium-temperatures
are the most suitable for the purpose. In fact as the absolute tem-
peratures to which one may descend by means of helium are 70
and even 150 times lower than the normal temperature, the result
will be equivalent to raising the magnetic field at which the obser-
vation is made 70 or 150 fold.

I have lately at last been able *) to fulfil my desire to attack by

1) Viz. by the acquisition a short time ago of an electromagnet (built according
to Weiss’s principle and utilising his friendly advice) the interferrum of which
leaves sufficient room at fields of 20000 for experiments with liquid helium,

284

this method the problem of paramagnetic saturation which is also
fundamental to Wriss’s theory of ferromagnetism. In the first place
it was necessary to have a substance which might be expected to
obey Curt’s law, which also follows from Lanervey’s theory, down
to helium-temperatures ; in the second place the substance must have
a high value of 6,. Botb properties I hoped to find combined in
crystallized gadolinium-sulphate, a quantity of which Professor URBaIN
some time ago had very kindly put at my disposal.

Earlier investigations in conjunction with Purrter and Oostrrauis had
shown, that gadolinium-sulphate follows Curte’s law down to the free-
zing point of hydrogen and does not show any sign of saturation, which
as LanGEvin’s theory shows, if it existed at that temperature, would
be ferromagnetic in its nature, as paramagnetic saturation at the
value of a which could be reached would not yet be clearly obser-
vable. The number of magnetons calculated according to Weiss is
large (38). That gadolinium-sulphate would still obey Curm’s law at
helium-temperatures I felt justified to infer from the fact, that it is
a “diluted” paramagnetic substance. The gadolinium-atoms, separated
as they are e.g. by the water of crystallisation, are at great distances
from each other, and this Dr. Oosrrrauis and I in Comm. N°. 139e
found a favourable cireumstance to Curim’s law being valid down to
very low temperatures.

The experiments have given a confirmation of LanGevin’s theory
which is at least qualitatively even now complete. Before an opinion
can be formed as to the quantitative agreement various corrections
will first have to be investigated. The most important of these which
must not be neglected, especially when the validity of Curte’'s law
is to be tested, is the demagnetising action of the paramagnetisation
itself, as the latter attains exceptionally high values. As an instance
I may mention that with 0,345 gram of gadolinium-sulphate at 2° K.
in a field of 15 kilogauss there was observed an attraction amounting
to over 100 grammes. Another circumstance that une should keep
in mind is that the object of observation consists of small crystals
packed on each other.

The measurements consisted in determining the attraction in a
non-homogeneous field, the gadolinium-sulphate in the eryostat being
cooled first in liquid hydrogen under normal pressure, next in hydrogen
under reduced pressure, next in helium boiling at ordinary pressure
and finally in helium under 4 mms, the apparatus and the fields
being the same each time.

The measurements at the boiling point of hydrogen (20.°3 K.)
had the object to obtain the force at a given point for a given

285

strength of field for controlling the values derived from ballistic
calibrations. I hope to return to the details of the measurements
and the arrangement of the apparatus afterwards, when an accurate
quantitative comparison of the results with Lancevin’s theory will
have been made. It is as yet impossible to decide, in how far
deviations are present which might be attributed to the existence
of a small zero-point energy which would manifest itself in the
manner in which the saturation changes, as well as in a deviation
from Curtn’s law at weak fields. It seems, however, that these devia-
tions are not sufficiently large to disturb the general aspect.

On this oceasion I wish to confine myself to communicating the
general aspect of the results as laid down in the adjoining graphie
representation on which the experimental numbers may also be read
with sufficient accuracy. The curves represent the observed attractive
force as a function of the square of the field on the axis between
the poles. This field was read as a funetion of the current from a
calibration curve.

Curve I refers to 20.3 K, curve Il to 14,°7 K, Il to 4.°25 K. and

IV to 1.°9 K. Each division along the horizontal axis corresponds to

about 90 kilogauss, along the vertical axis to 25 grammes. The ratio

of the force to the square of the field on the axis of the poles per

unit of susceptibility was about ',, neglecting small changes in the
topography of the field.

286

If the susceptibility does not depend on the field and its topo-
graphy remains the same, the curves are straight lines. The small
deviations from the straight line at 20.°3 K are probably chiefly due
to errors in the topography of the field, seeing that according to
earlier more accurate determinations we had to await within the
limits of the experiments a susceptibility independent of the field and
therefore in this graph a straight line. By means of the deviations
from the straight line at 20.°3 K the curves for the other tempera-
tures have been provisionally corrected. It will be seen that for a
given field these curves are the more strongly curved the lower the
temperature to which one descends, in accordance with LANGEvin’s
theory. Within the limits of accuracy to be expected in connection
with the neglect of the various corrections referred to above the
tangents of the angles of elevation of the tangents to the curves at
the origin appear to be inversely proportional to the temperature as
required by Curie’s law and the deviations of the curves from the
tangents as expressed by the ratio between the ordinates of both
for a given abscissa are strikingly similar to the deviations of
LANGEVIN’s curve for the magnetisation as a function of the field
expressed in the same manner. The nature of paramagnetic magne-
tisation is very clearly revealed in these measurements at helium-
temperatures.

Mathematics. — “On some integral equations.” By W. Kapreryn.

1. In a memoir “Recherches sur les fonctions cylindriques” (Mem.
Soe. Roy. Se. Liege dime Série t. VI 1905) we gave the solution
of the integral equation

(2) = J 918) Lei ds Perce so 3 (i)
0

in this form

a) ae
Q(z) = ae La fro —— — CP Meomo. 6 3 4)

where the functions /;, represent Beenie functions of order &.
This solution rests upon the relation
,

: Ela 1G BOC) fib 1 Bic Bo.
{Zo = aoe HGS a ) i es

xf n
0

from which the following theorem may be deduced.

If
F(z) = ¢,1 («) + ¢,£,(e) + ¢f,(@)+--.- »- + + (4)
then
P a 3) ; :
fr (2) er SE es eed) ane eG)
0 te
The object of the present paper is to show that more general
integral equations may be solved in the same manner.

De Tet

am
.

Fe) = | vA) (eA. a 2 6)
6
where p represents an integer, and let
F(®) = Cptilp4i(#) + ¢pelp+o(%) + .---
(3) = 6,2,(8) + 6,4,(8) + 6,2,(3) 4 ---

then
-
S Oe) = ss by, Jue I, (@—8) dp. = - . = (7)
p+ 10) e

0 o
Therefore the integral equation (6) will be solved if we can
determine the coefficients 4 in function of the coefficients c.
We shall first show that

u =| I,()L,(«—p)adg

can be expressed in a series of Bessei’s functions.
By differentiating we get

d . U,(e—P
Sel yr (7) at (@—P) ap
da. da

raf I, (8) — NS) ag

d3 3?
Now
2 ia = 2
aC) Ces) iy Fy se Se
da® «—p dx ( )B?
or
ad? I,(a« —p) p 1 dl(«—Pp)
} ( /
= (a6 (e—6)— — -
da? st Epa D) (w—p)? p28) p da

288

where the second member may be reduced by means of the relations
P

aan L, (ew—B) = 3 [Lp41 (@—B) + Ips (e—B8)]
d
re I, (c—6)=4 [Zp—1 (e—p) — Ip4i («—)].
Therefore
int 3) (= 1 1,1 (w —8) pti, 1 («—B)
eas I, (e—8) =- ! = pana!)
div a a—p 2 z—Pp
and
du p-l (4. 1p-1(e-8) Bet Ty41 (e—8)
: =— —— | /7,(¢e — dp + — 3) ——__— _ dp
pare oer elf eee
0 0

or, according to (3)

dt } i L{l n+p—1 (w) 4e Ln4p4i (a ‘)]

au p) te (w) Ds

This differential equation holds also if eer
Now the general integral of this equation

u=Asine + Boose + (n+p) fon aah). ate ®) as

gives the required value of w, a the constants A and B are
determined by the conditions

du
z= 0 i ==) ——*()
dx
du
A=) u = 0 = == Il (== 709 = 1)
da

Thus we obtain generally

4 = (n+p) fis (av 8) = ae 8) a

and when n= p=0
SINK
Introducing now the known expansions
sin (e«—B) = 2 [J, (e —B) — I, (e«—8) }|- J, (e—B) — ...]
and
sin & = 2 (I, (x) — J, (x) + J, (2) «. |

we have according to (3)

289

== Leer (2) — Ln4p+s (#) + Intpts («) — seo)
thus in all cases
x
Tk (3) Ly («—6) dg = 2 [Zn t (x) — L,4p+3 (2) ap dl ntp-ts ( az (5)
0
Applying this result, the equation (7) takes the form
2) enim (w) i by [Lntp+t (2) aaah Ent p43 (x) =e cod]
p+ n=0
and comparing the two members we have
Cp+1 — 2b,
Cp+2 —— 26,

CS ta 26, + 26,
Cp-+4 = 26, oo 2b,
ete.
thus
ip a hee eae sacl ee
OSes 2 PS 2 Di Chae 9 7 25. 5 z
and
2 bi F ep --3 ; ae 4
gx (3)= ig) sae £(8)+ wana ED fe (gaan Eee (ay. (Q}

The solution of ih integral equation (1) in the form (2) may be
easily deduced from this equation. For putting p= 0, we obtain

1O=2 0+ Ot ros

In this case

SF (#) =e, +, (@) + 6, LZ, (x) + ¢s 7, (%) + ---

I, (2) +.

thus
df Cy C3 C4 ©,
== Sh) +240) +2 10+ 5740+...
and
df
@p («) — — =e, J, (2) + ¢, J, (&) +
dau

which, according to (5) may be written

I («—p
vont (10 Po.

3. We shall next show that the solution (9) may be written in
the same manner as the solution (2). It is however convenient to

examine first the special cases p= 1, 2, 3.

290

I. — |
Let @)= | ¢ (8) 1, (a — B) dp
‘0
then

f) (#) = 2 g (2) =| ¢p (8) [8 Z, (e —- 8)-— 1, (x — B)] dB.
0

Multiplying these equations respectively by 1 and 4

and adding
we find

fey

2? f%) (w) + 4 f (0) = 2p (e) 4 fv (8) [1, (@—@) + 4, (@—8)] ap

0
esriGeee
= 2p (#) + 7 y (3) pus ip
10)
thus
. I («—B
2 (@) — [2/9 (ON — 4 LF = — 4 f 9)” ap.
1)

Now, according to (5
> 5D

i I («—p
2| p (@) = Pas = byl, - Od, se bef, ee
e WOK

or, with the values of 6 from (9)

=tlel, +¢4+¢%+-- 1]
+ $[e.7, tet, +¢,2%, + --]

which by means of (5) may be written

Therefore the solution may be put in this form

2g(w) — [2° fFE(@)| — 3 [fo] = — ofan Me me dp . (10)

yo ee
Differentiating

291

P= (v (8) Z, (e—8) a

we obtain

2f(2) =r (8) (1,—1,] 48

29H 200 + fi (8){— 47, + 312,—J,] dp.

Thus

ak a? TA. eee
227 Me)+ 2AM Bele) — [HOLL +L MP=24 (0) —8 (6G)

e &
0 0

where

1 - 1
=> flew = ec. eal, es... <i]

1
see Les l + ¢f, + ¢,I3 +...]

— 3) I,(2«—B)
= |e) —e at > sf fe) dB
0 0
This gives the solution
me =v se I (ie
24 (0) — [24f)(2)] —4[2/M(a)] =f jG)" aa fi (0) ap
—p z—Pp
U U

i pc.
By differentiating

J(#) = Jv (B) Z, (eB) dB

we obtain

247° (a) = {o(B) 21, + 1.) a8

292

27 (o) = 2 (0) + f(B)L— 51, + OL —A1, + La
0
Multiplying these equations respectively by 4, 5, 1 and adding
we get ‘

[247 (@)J 4- 5[ 2277 (@)] + 4[ A(2)] = : v)| wi fu ee
ue 8
= 2y (x) + 12f) (8) a = dg
0
where
if tle 8)
6 fv) gy BL, EOL, + OT +
e vU—t
0
== i(C, I. sp os Sp Oar ao)
SF $ (cl, = cL, == ORI + -.-)
ae a I (#—p) 4 7 , L(e7—B8),,
= » {78 per dp + 2. WO ane
0 0)

In this case therefore the solution takes the form

2y (a) — [24a] — 5 BVO) — 4 el =
48 oe fre Pa, (12)

4. Proceeding now to the general case, we may expect, A;{”) being
constants,
ly (w)-A,' P ) Paes AC )(x)} =A i Pp) [2P—1f pt \(x)] -A, (p)[2P—3 fP = 3)(x)} =
Bs
= (—1)?. 4p [vi 3)

I2,(«@—8)
ee . (18)

If p be even the last term in the first member is — AY [27 (w)],

and if p be odd it is ~ Able v)].

The second member now reduces to
> (z—B
2pfutey™ vie ae = b, 1 Ta, bate ela ee

293

= $ [pile, + p4olo,pi + cp43lopte + . |
+} [ep4itopte+e42lopt3t+¢,43lots + ---]

thus
zr z

on (nc. t2(@—B) 1p P—! (re — p+l Ty 4i(a-

2p fate) a PP (ray ae Baas EA gyi = V3 (14)
0 0

Substituting this value in the equation (13) we see that g(x) may
be expressed in differential coefficients of the function J(2) and two
integrals. To determine the law of the coefficients A,(”), A,”, A\™,
A,)... we put together the values for p=1, 2,...10 in the
following table:

p AO SAC VAG) | 2A) A VA) AG)
1 1 3

2 \ 4

a 1 5 4

4 1 6 8

5 1 7 13 4

6 1 8 19 iz

7 1 9 26 25 4

8 1 10 34 44 16

9 1 11 43 70 41 4
10 1 12 53 104 85 20

Examining this table we see that
A,(P) = A\P-Y + AS p—®)
A,r) = As ps) of A ip 2)

A,(p) = A,(r—1) 4+ A,fp—2)
(p even)
OD) —— y—1) (p—2) __ (p— 2)
AY, — is + Ape =4+ A
(p odd)
(p) =.
Ay = 4

If therefore the coefficients of order p— 2 and p —1 are known
those of order p may be found. To verify the results we may
remark that if

TAM=S,
we must find
Sp = Sp—2 aia Sp—1 .
The resulting values of these coefficients are as follows
20
Proceedings Royal Acad. Amsterdam. Vol. XVII.

294

AK (p12 ed.22)
A?) ==/)) + 2 — 1a -)

1
A= > (p?+p—4) (p=3.4.5...)

rare Bye
Ae) 31 (p—4) (p?+-p—6) (p=5.6.7...) . (15)

1 PORK 5
A fp) = ai (p—5) (p—6) (p?+p—8) (p=7.8.9...)

1
er (p—68) (p—T) (p—8) (p?+-p—10) (p=9.10.11..) |

where the law of succession is evident. With these values the equa-
tions (13) and (14) give the required solution.

4. To generalise the preceding results we will proceed to examine
the more general integral equation.

f(a) =[9(@)K(@—A)dB . . . . . . (16)
J

assuming that the functions f(z) and A(x) may be expanded in series
_ of Brssex’s functions
Se) = ¢,1,(@) + el .(w) + e,2,(@) + «.
K(«) = a,l,(e) + a, f,(e) + a,1,(a) +...
which is the case if these functions are finite and continuous
from O to 2.
If now
—p (x) = b,L,(x) + b,1,(x) + 6,7,(x) + ...
the second member reduces to

x
S355) yl. I, (8) L) (e—8) a8 =
U

2S ayy pyle) — Lp-+943 1b Iptags — +]
Thus, comparing the two members, we find
= 10-
» = 2a,b,+2a,),
c, = 2 (a,—a,) b, 4+ 2a,b, + 24,6,
c, = 2 (a,—a,) b, +2 (a,—a,) 6, + 2a,b,-+4 2a,,
etc.

Cat

which give

‘ 1
26, = —e,
ay
ob ee a, C, |
2b, = —_,
Dx Ce Os)
1 4 Oc!
26,=>— 4, a, ¢,
ay
g,—4, a, ¢,
a, 0 C;
1 fa a 0c
1 0
2b, =— ;
a,’ |a,—a, a, i, Cs
a,—a@, 4,—a, @, ¢,
ete:

Therefore g(v) may be written in this form

ay 0 0 0
a, 00
] a, 0 1 1 a, a, 00
24(«)= —e,?1,+ == (aie ee Cp hy OT ipee
a, Gea anic. a, Gy \a,-a, a, a, 9
a,-a, &, Cy
@,-@; @—a) a, ¢,
‘ a, 0 00
a, 0 0
1 Gace 1 1 a, ay 0 0.
“tee ott gal PANEL Ul i It.
a, |a, V| a, a |a,-a, a, a, Cy
a,-a,a, 0
a,-@, a,-a, a, 0
ay 0 0 0
a 0 c, |
iT 1 \4, a, ONG:
= 0,/,+— iD
a 311 GON ae 7 sche.
a," a a,-a, a, a,0
\a,-a, a, 0)

@,-4, a,-a, a, 0

0 1
1 a; ae, ADD)

+ > z J,+-.
0 |a,—a, a, a, 0

a, 4, a,-a, a, 0

or
20%

296

1
2¢(«) = lan (1,42, | c,l,+ “M :)

0
We
0 (c,2,+¢,2,+-¢,2,+ a)
ke,
1
+s make a, 0| (¢,f,-+-¢,2,+¢,1 4.4 - -)
: a,—a, a, 9
\d, 0 0 1
pie. Ol |
+ ar | (c,I,+¢,1,+¢1,+--)
a, |a,-a,a, a,9
a,-a, a@,-a, a, 0}
+ ete.
If now
f(e)=eJ, + Cale aie Cas ci
we have

df
pa am Sead ie SS Gye

da
= (c,1, 33 ty, =e o,f, a as -)

thus, according to (5)

c.J,tel, +¢/, +... = 0th frosts ap

and by the same formula

In—\(e@— 8) dp

e,In + ¢Inpi + eslng2 + ++ = 0) {7 259
0

Introducing these values we have

ee a ee ae

Remarking that
nIn(a« —B)
«—Bp

this result we may write

= $ [Znsl@—8) + Ing (eB)

497
2¢(2) = = 2 a aes Ane ae $ J@l—A AGS BAC er dg ar
0

: | (18)
ASME rAnane—oa|
0

When the integral equation

2D («) = | W(8) K (« —8) dp
0

is given, we find by (18)
eo = A, /,(«) + A,4(e) + 4,4,(2) + --

Therefore = = (A,+-A,42)4, pov) be expressed in function of wp.

For

LETTS a hey WI oma eo Pea fae aa)
and, differentiating again

ee a -B)
A,I,(a) | AD, +A TD, +-.=4 = +29+-A,F,—A,7,—2 | w8)— a
av a — Bp

0
thus

2 Ged mal Ij(e—f) _,
(Ay 4 Appa) = 475 + Bh + A, AL —2 | WG) 7 a3
: . assy

e
0

5. We now proceed to give some applications of formula (18).
First let the integral equauien be

a=fu (3) I, (e—8) dB

then
Gy SS ly Gh = 0 So SW)
hence
A =I ARO AL ale A =A! 10)
thus
x
9 9 df % ) 5)
2p (e) = 2 + 4 (F(8) (22, (@—B) + 22, @—B)] 4B
0

998

oli" f+ fan se
—p
which agrees with (2).
Considering the integral equation
z
Ho) = [x (3) 1, ayaa
0

the formula (18) is not applicable because a, — 0. In this case and
assuming a, =— 0, we have

1
2p) (@) = ae (Ql ORIEN 55)

Ie as
— Notre vom ae ee)
a, aa
; a Oma
tall 4s Gen0> (0,0 geri)

where

PY Di ce Ie er i

oe . T, («—f)
oy Be =e ~ = Gi
tah $n = 2S r ff @) ee
0
I, esl, 4 pals 2 2) as
c | oe == 4 —— + 27 — 2 f 7 (8B) ——_ c
TO Sik dx? “oe fi Bp t

. af —8)
2p (x) = B, se : afi (8) ee pe

aah
+ B, 17 (8) 1 fe—8) 13
w—B
0

299
or

—é)

af i ‘ (@
+(2B,+B,)/—2 rf) oe a+

2g (7)=4B, an? +2B, Ie
)

a A RB
+f me [(\B,4+B,)1,(e—p)+2B,1,+3B,1,+. Jade.
0
Now putting

we have
Bell Bi) 13). == 1 Bi == == eat 0
thus
xr
: Gap > fj.«—B
24(«)=4 de ok 2 K(8)- <> d3

e
(

which agrees with (10).
Finally let the integral equation to be solved be

¢(@) cos (e—B) dg
In this case

thus
i — Av —=0 , Ano 7 A= 0h, ALS Aes er eel peel

and, according to (18)

ie
24 (2) = 2 ay ence @)+ 80,4 87,4 °8/,+...] de
0
which, by means of the known relation

Pia DT (aya Tey ee SS

may be written

300)

Geodesy. —- “Comparison of te measuring bar used in the base-
measurement at Stroe with the Dutch Metre No. 27”. By H. G.
vy. p. Sanpe Baknuyzen, N. Winpesorr and J, W. Dinewrink.

In the summer of 1918, the Government-Commission for Triangu-
lation and Jevelling measured a base of about 4320 metres, under
the direction of Prof. H. J. Hruvenmk, on the high road between
Apeldoorn and Amersfoort, near the Railway-station Stroe.

The measurements were made with the base-apparatus of the
“Service géographique de Varmée” at Paris, which was lent through
the courteous help of the Director of that service to the Government
Commission by the French Government.

The measuring bar of this apparatus is an H-shaped invar-bar_ of
four metres length, provided with two very sharp end lines at the
extremities, between whieh three intermediate lines are drawn, which
divide the measuring bar into four parts, a, 6, ¢ and d, each one
metre long. :

Previous to the base measurement here, this measuring-bar had
been compared several times with the métre international at Breteuil ;
these comparisons had shown, that the length had undergone some
slow changes, as is often the case with invar-bars; it was therefore
important to determine the length shortly before and after the base-
measurement.

In April 1913 therefore a comparison was made at Breteuil, but
as the comparator there had to undergo some repairs, the comparison
could not be repeated in the autumn of 1918; it was therefore
decided to compare the measuring bar in this country with one of
the two Dateh platinum-iridium metres, viz. with No. 27, by means
of the comparator which had been supplied by messrs. RepsoLp and
Sons in 1867 with the base-apparatus for the triangulation in the
East Indies, and which is now mounted in the geodetic buildings in Delft.

From the experience gained in previous measurements we did not
consider that sufficient accuracy could be obtained with this compa-
rator, especially on account of the inferior quality of the microscopes ;
on this account it was decided to order two new micrometer-miecros-
copes from Zeiss (in Jena) which were delivered in the autumn of
1913, so that in December the comparator was ready for the comparison.

We are very much indebted to Prof. Hruveninx, who arranged
everything for the measurements and placed a room in the geodetie
buildings, and an instrument-maker at our disposal for some weeks ;
and further to the ‘Commission for the preservation of the stan-
dards”, who allowed us the use of metre 27.

301

il Arrangement of the comparator.

A complete description of the comparator can be found in Dr. J.
A. C. Ouprmans, “Die Triangulation von Java, erste Abteiling”’ ; we
may therefore confine ourselves here to a short account of the
arrangement.

A wooden case over four metres long inside, contains a long iron
carrier, which can be moved upon rails from one side of the ease to the
other, at right angles to the length. Upon this carrier the measuring
bar and the metre with which it is to be compared, are placed
parallel to each other, while the metre with the box in which it
is placed can be moved along the carrier in the direction of its
length, and can so in turn be placed opposite to each of the four
parts a, 6, c, and d of the measuring rod.

The wooden case is further provided with a strong iron frame
to which the micrometer-microscopes are attached at a distance of
exactly a metre and which can be moved upon rails, independently
of the carrier, above the measuring bar and the metre.

The first thing to do is to place the metre opposite the first part
of the measuring bar, parallel to and at the same height as the
bar, and to push the carrier upon which they both le as far as
possible sideways across the case, until it touches a pair of correc-
tion screws. If everything is properly arranged, the microscope
frame upon its rails can then be placed so, that the two microscopes
are just above the end lines of the metre, or the part a of the
measuring bar. If the carrier is then moved to the other side of
the case, where it similarly touches two screws, the microscopes
will be directed just above the end lines of part a or of the metre.

By focussing with the micrometers accurately upon the end lines
of the metre and of part @ in both these positions, it is easy to
find the difference in length between them, expressed in micro-
meter-divisions. By subsequently placing the metre successively opposite
to the portions 4, c, and ¢ of the measuring bar, and making the
same observations, the data are procured, by which the length of
the measuring bar can he determined in metres. :

In order to be certain that in the successive measurements of
portions a, 6, c, and d the microscopes were each time directed
upon the same points of the division lines, small brass plates
provided with a point in the middle were fixed on the middle of the
bar near the division lines, in this way fixing a line along the middle
of the measuring bar. The correction screws at the sides of the case,
(against which the carrier moves up in ils sideways movements)
were so adjusted, that these points came exactly under the fixed

802

horizontal wires in the two microscopes. As care was taken, that
the moveable micrometer wires were parallel to the division lines, an
influence of a small deviation of the point upon which the micros-
copes are directed need not be feared.

2. Microscopes. At our request the microscopes were so con-
structed, that on the obiective-side the course of the rays is tele-
centric; they have a 30-fold magnification, and the illumination of
the division lines is not sideways but central, by means of a prism
with total reflection, which is placed behind the objective in the
tube of the microscope, and occupies half of the field. The light
from a small electric lamp falls through an opening in the tube of
the microscope upon the dull face of the prism, is then reflected by
the prism vertically downwards through the objective, falls upon the
reflecting surface of the metre or the measuring bar, and is thus
reflected vertically back into the microscope. With an electric lamp
of a few candles the illumination was excellent, and the division
lines were seen as very fine black lines.

3. Temperature. The exact determination of the temperatures of
the metre and the measuring bar is a matter of great importance.
In order to make the changes of temperature as small as possible
we endeavoured, in the first place, to keep the temperature of the
room as constant as possible. For this purpose the windows were
covered with thick curtains, and the central heating was shut off. As
only a small amount of heat was conveyed through the floor and
walls, the temperature did not change much, and only rose a little
from the presence of the observers, and the burning of a few gas lamps.

All the metal parts of the comparator were shut off from the
outside air by wood and other badly conducting material, outside
which only the eye-pieces of the microscopes protruded ; the measur-
ing bar was moreover entirely enclosed in a thick aluminium case
and the metre in a brass box, in which there were only small
openings for the reading of the division lines and the thermometers.
The protection of the metre from the radiating heat was less effective
than that of the measuring rod, so that in half of the measurements,
during which the observer was on the side of the comparator nearest
to the metre, it was found advisable to cover the outside wall of
the comparator with a layer of badly conducting material, which
gave a greater constancy of temperature.

For the determination of the temperature of the metre and mea-
suring bar, upon the horizontal faces on which the division lines are
drawn a thermometer A was laid upon the metre, and on the measur-

303

ing bar two thermometers B and C, the last two about a metre from
each extremity. Moreover there were placed in the comparator case
a registering thermometer ), two thermometers // and F upon the
outside of the aluminium case about above the thermometers B and C,
and two thermometers G and #/ at the two extremities of the comparator,
which were read through glass-covered openings in the end-walls.

On the whole the temperature readings were of such a nature,
that there is every reason to believe that the readings of the thermo-
meters A, B and C may be taken as the temperatures of the metre
and the measuring bar.

4. Programme of the measurements. It was arranged, that the
measurements should be made by the two engineers of the Govern-
ment Commission for triangulation and levelling, A. Winprsorr and
J. W. Dieprrink, and a member of the commission, H. G. v. p. SANDE
Baknuyzen. Each of these made a complete series of measurements.
Mr. Witprsorr and Mr. Dirprrink arranged everything beforehand,
so that (1) metre and measuring bar were parallel to each other
and at the same level, (2) the micrometer wires were parallel to the
division lines and showed no parallax with regard to the division
lines, (8) in the extreme positions of the carrier the division lines of
the metre and of the measuring bar appeared in the correct position
in the field of the microseopes. In the adjustment of the level of
metre and bar, so that no parallax could be detected of the micro-
meter-wires with respect to the division-lines, the adjustment of one
of the observers was always checked by a second or third.

When the carrier had been placed in one of the extreme positions
and the microscopes were therefore directed upon the end lines, say
of the metre, the observer placed the micrometerwires of the left-
hand microscope twice in succession upon the line, then took four
readings with the right-hand microscope. and finally two with the
left-hand one. In the middle of these eight readings the thermo-
meter on the metre was read. The carrier was now brought into
the other extreme position, so that portion a of the measuring bar
came under the microscope. In the same way as for the metre, 8
readings were taken with the microscopes, and readings of the
thermometers. The observer then returned to the metre, and in the
same way took seven sets of observations in succession, alternately
upon the metre and the selected portion of the measuring-bar, each
consisting of 8 readings.

A series of observations of this kind, which lasted about a quarter
of an hour, we shall henceforth call an observation-series.

304

Hach of the three observers made two of these observation-series
in succession.

After these six series, the metre was turned round in its case, so
that the mark which first showed on the left hand side now lay
on the right hand side; and in the same way as at the beginning
of the measurements, the position of the metre with regard to the
measuring bar and the microscopes was then properly regulated. As
the comparator case had to be opened for this, there was a disturb-
ance in the equilibrium of the temperature. An hour or 1‘/, was
therefore allowed to pass before fresh measurements were begun.
As in the first position, each of the three observers then took two
series of observations in this second position.

For the determination of the temperature in the comparator, at -
the beginning and at the end of the 6 series with the same position
of the metre, the thermometers /, /’, G, and H were read. These
readings served only to ascertain, whether disturbances of tempera-
ture had oecurred in the comparator. In none of the series which were
used for the determination of the length of the measuring bar was
this the case; there was therefore no further use made of the
readings of the thermometers 1, /, G, and H, any more than of
the records of the registering thermometer.

As in the computation of the results the differences of the readings
of the right-hand and left-hand microscopes are used, the influence
of a personal error of adjustment will disappear from the results,
if both end lines, the micrometer wires and the optic images in the
two microscopes are exactly alike. This complete equality however
does not exist. The lines are, as far as can be seen, all equally fine
and faultless, but the distance of the micrometer wires is smaller
in the one microscope than in the other, so that the appearance of
the line, when it is placed between the two micrometer wires, is
different in the two microscopes. In order to eliminate the personal
error arising from this, the observations would have to be repeated
after exchanging the microscopes, or else with the microscopes in
the same position, but the observer standing the second time on the
other side of the comparator, so that the microscope which was first
on his right hand, is now on his left.

The latter method is simpler than the former, and had the further
advantage (over the changing of the microscopes) that the observer,
who first stood nearest to the measuring bar, is now nearest to the
metre, and an irregular influence of the heat radiated by the observer
will thus be also, at least partially, eliminated.

On these grounds the observers, after they had compared each of

305

the 4 portions of the measuring bar with the metre, while standing
on one side of the comparator, repeated the observations standing
on the other side.

To distinguish the observation-series from each other, we shall
call those which were made while the observers were in their original
position with respect to the comparator, A, those in which they were
on the other side, £6, the series in which the mark on the metre
lay to the right of the observer 7, that in which it was on the
left 7, while the first of two identical series we shall call 1 and
the second 2. For each portion of the measuring bar each observer
therefore took 8 series of observations Ar,, Ar,, Al,, Al,, Br,, Br,,
Bi,, Bl,. Care was taken, that when the first series was begun
with the metre, the second identical series should begin with the
measuring bar.

5. Runs and errors of the micrometer screws. For the purpose
of determining any possible changes in the runs of the micrometer
serews, the length of the millimetre divided into 10 marked on the
measuring bar near the end lines was measured every day before
and after the measurements, with both of the microscopes. From
the results it appeared, that the value of the run, which was approxi-
mately 200 micromillimetres, did not change perceptibly. As, however,
it was not certain, that the millimetres on the measuring bar were
of exactly the correct length, the absolute value of the run was
afterwards determined by measuring out a distance of 1 centimetre
divided into millimetres on a measuring rod of nickel-steel belonging
to the Observatory in Leiden, supplied by the Société Genevoise,
the errors of division of which had been accurately determined in
Breteuil. For all the measurements the same value of the run is
assumed, viz. 198.69 micromillimetres for the microscope marked I
and 199.82 micromillimetres for the unmarked microscope.

Moreover the periodic errors of the micrometer screws were
determined in the observatory at Leiden, by measuring distances
equal to a half and a third of a turn. The continuous errors were
determined by measuring a larger distance, with portions of the serew
situated symmetrically with respect to the zero.

For micrometer | the correction formula of the readings in parts of
the divided head, was found to be: 0.18 Sim (wu + 17°); the influence
of the term dependent on the double of the reading was imperceptible.

In the unmarked microscope no periodic errors could be detected
by the observations.

The continuous errors were imperceptible in both microscopes.

306

6. Reduction of the observations and results obtained. The micro-
meter readings are all reduced with the above mentioned values
for the run of the screws in micromms and for the periodic errors
in micrometer I.

The errors of thermometer 4570 belonging to the Dutch platinum-
iridium metres, which was used for the temperature-determinations
of metre No. 27, were determined by comparison with two thermo-
meters standardized at Breteuil, and by separate determinations of
the freezing point. It appeared, that between 0° and 30° the ther-
mometer is free from errors, except the error of the freezing point,
which was —0.48°. The determinations were made by Mr. H. C.
Vorkers, lecturer at the Technical University at Delft.

For the thermometers 153855 and 15356 belonging to the invar-
bar both the errors of division and the correction for the zero are
negligible.

In the reduction of the length of the metre and the measuring-
bar the following coefticients of expansion were used. For the metre
the value communicated by Bosscua in his paper: ‘Relation des
expériences qui ont servi a la construction de deux métres étalons en
platine iridié, comparés directement avec le metre des archives” and
which from 0° to ¢° gives an expansion for the metre in micromms
of:

8.4327 ¢ + 0.00401 7’.

For the measuring bar, the determination made at Breteuil was

used, which gives for the expansion per metre in micromms;
1,6245 ¢ + 0.001065 ¢?.

After the introduction of these reductions, the three observers
obtained the following results for the lengths of the 4 portions of
the measuring-bar, each about a metre in length, diminished by the
length of N°. 27 both at the temperature of zero. These results
are the mean of the observations of one series.

Portion O—1.
WILDEBOER DIEPERINK BAKHUYZEN

Position A Position B Position A Position B Position A Position B

1, —29.70 —27.43 —26.65 —27.39 —27.93 — 26.40
l, 28.25 27.84 28.28 27.19 28.60 27.13
1, 29.25 28.39 28.85 27.94 29.89 27.96

iP 29.01 28.95 28.89 28.23 29.49 27.91

307

Portion 1—2.

WILDEBOER DinPERINK BAKHUYZEN
Position A Position B Position A Position B Position A Position B
i, —99.31 —95.46 —98.59 —96.73 —97.96 —96.10
E 99.61 95.28 98.64 96.02 97,65 96.22
iP 98.82 95.338 97.95 96.99 97.30 95.69
ip 99.96 95.18 98.50 96.7 97.69 94.94

Portion 2—8.
WILDEBOER DIrPERINK BAKHUYZEN
Position A Position 6 Position 4 Position B Position A Position B
Poe ee —— 12200) 12.2570) 1.23.64 2352) 199-95
i 22.25 122.22 122.26 123.00 12239 123.03
r 122.72 AO ioe, 121.18 121.04 122.85 1:23:35
7 122.00 121.46 120.75 122.24 121.96 122.83

Portion 3—4.
WILDEBOER DIEPERINK BAKHUYZEN
Position A Position B Position A Position B Position A Position B
1, —144.49 —14348 —143.28 —143.45 —144.09 —143.22
i 144.55 143.58 143.96 143.37 143.938 143.28
ry 144.91 144.00 144.09 143.69 145.10 144.57
r 143.70 144.08 143.98 143.65 144.44 143.48

In order to eliminate the effect of personal errors the means
were now formed from the observation-series A and JB, those
two series being combined in which the metre was in the same
absolute position in space, not relatively to the observer, i.e. Al,
with £r,, Al, with Sr,, Ar, with Bl, and Ar, with Bl,. In this
manner the following results were obtained :

WILDEBOER.
Portion O—1 Portion 1—2 Portion 2—3 Portion 3—4

—29.04 —97.32 —122.24 —144.20
28.60 97.39 121.85 144.31
28.34 97.14 122.36 144.19
28.42 97.62 122.11 143.64

Mean 28.60 97.37 122.14 144.08

308

DIEPERINK.

Portion O0—1 Portion 1—2 Portion 2—3 Portion 3—4

——Ora9 9) 1187 —143.48

28.25 97.70 122.25 143.80

28.12 97.34 122.41 143.77

28.04 97.26 NSH 143.67

Mean 28.18 97.52 122,10 143.68
BakHUYZEN.

Portion O—1 Portion 1—2 Portion 2—3 Portion 3—4

—27.94 — 96.82 — 108} 144033

28.25 96.29 122.61 143.70

28.14 96.70 122.90 144.16

28.29 97.45 122.49 143.86

Mean 28.16 96.82 122.86 144.01

If the sum is

taken of

the lengths of the 4 portions of the

measuring-bar, we get for the length of the whole measuring bar at O°:

Measuring bar = 4 x Metre 27—392.19 WILDEBOER
4 So Metre2 (=a Oras DIEPERINK

”

55 = 4 xX Metre.27— 391285
Mean for the three observers :
Measuring bar = 4 « Metre 27—391’.84.

BAKHUYZEN

7. Mean errors. The errors in a series of observations are caused
by the pointing- and reading errors of the microscopes, the change
in the distance of the microscopes, erroneous determinations of
temperature and personal errors of observation.

Owing to the excellent optical qualities of the microscopes and
the fine sharp end lines, the errors in the reading and pointing of
the microscopes are small. From the observations for the determination
of the periodic screw-errors we found for the mean reading-error,
from the mean of two observers, + 04,32: this error leads to a
mean error of + 0,17 in one series of observations.

The influence of other sources of error are difficult to determine
separately. We shall therefore try to calculate their combined effect,
in different ways, in order to find out, what systematic errors are
to be feared, and how the series of observations are to be combined
in order to obtain a result in which the effect of the systematic
errors will be as far as possible eliminated.

309

In the first place it was investigated, whether there was a systematic
difference in the results of a series of observations according to
whether the microscope was pointed 8 times on the metre and
4 times on the measuring-bar, or 4 times on the metre and 3 times
on the measuring-bar. For this purpose the mean was first formed
of corresponding series in the positions A and #4, in which the
number of times that the microscope was pointed on the metre and
therefore also on the measuring bar, was the same. According to

these averages the mean error of observation in micromms was:

WILDEBOER DIgPERINK BAKHUYZUN Mean
Ott 0.366 0.509 0.420 (I)

After this the average was formed of corresponding series in
A and & in which the aumber of times pointed on the metre and
on the measuring bar was unequal; according to these averages the
mean error of observation for a series was :

WILDEBOER DinperiInk BAKHUYZEN Mean
0.496 0.330 0.440 0.428 (IT)

From the agreement of the two means we may infer that there
is no systematic difference in the series with 3 or with 4 pointings
on the metre or measuring bar.

It was next investigated, if there was a systematic difference in
the results of series in which the metre was in a different position
relatively to the observer, i.e. in the results of the series / and 7.

This was done in two ways.

1. The differences were found of the corresponding series in
Which the observer and the metre were in the same position in
which differences the systematic error referred to plays no part. The
mean error for a series 7 deduced from this is:

WILDEBOER Divperink BAKHUYZEN Mean
0.450 0.346 0.492 0.434 . (IIT)

After this the mean was formed of all the corresponding values
found with the same position of the observer, in position / as well
as position 7 of the metre.

The deviations of all these values from their mean, in which the
influence of the systematic error is present give the following values
for the mean error of a series.

WILDEBOER DiePERINK BAKHUYZEN Mean
0.454 0.594 0.636 0.564 (IV)

2. The means were found of an observation-series in position
A and in a corresponding series in position B, in which the metre

24
Proceedings Royal Acad. Amsterdam. Vol. ¥ VII

310

Was in the reversed position relatively to the observer, i.e. 7 and /.
In these averages the systematic error is thus eliminated. In this
way the mean error of one series was found to be

WILDEBOER Dinprrink BAKHUYZEN Mean
0.370 0.296 0.507 0.401 . (V)

If on the other hand a series in position A was combined with
one in 4, in which the metre was in the same position with regard
to the observer, so that the systematic error was not eliminated in
the mean, the mean error was found to be:

WILDEBOER DinpuriInk BAKHUYZEN Mean
0.424 0.755 0.768 0.666 . (VI)

Both the double sets of mean errors (III) and (IV), and (V) and
(VI) show clearly, that there is a systematic difference in the results
of the series r and /, or with different positions of the metre relatively
to the observer. In order to remove the error, therefore, the mean
of two corresponding series of observations must always be taken,
in which the metre is in different positions with regard to the
observer.

We further computed the mean error from all the series of ob-
servations for the same portion of the measuring-bar, without regard
to the position of the metre or of the observer, in which therefore
the influence is present both of the position of the metre and of
the observer. First the mean errors were computed for each observer
separately. This gave

WILDEBORR DIuPeERINK BAKHUYZEN Mean
16222 0.805 0.955 1.009 , (VII)

Finally the results of the series for the same portion of the
measuring bar in all positions of the metre and of the observer for
all three observers were averaged, and the mean error determined
from the deviations of each of the results, which must therefore
contain (1) the influence of the position of the metre (2) the influence
of the position of the observer, (3) any other possible influence of
the observer. The mean error was then found to be:

15002, 0, on te 2 Se ODL

The difference of the mean errors (VII) and (IV) shows, that the
position of the observer has a marked influence, on the other hand
the agreement of the mean errors (VII) and (VIII) shows, that there
does not appear to be an influence due to the observer other than
that which depends upon the position of the metre and observer.

We may further conclude from the values found, that if the two
systematic errors mentioned are elimimated, the mean error of a

oll

series of observations is the mean of the values: 0.420 (1), 0.428 (IN),
0.434 (IIT) and 0.401 (V) therefore:
m— a= O42

As the measurement of each portion of the measuring bar was
obtained for each observer by taking the mean of 8 series of obser-
vations, the mean error in the length of each portion measured by
one observer is:

0#.421
ae Se ea
V8
and as the whole measuring-bar consists of four portions, the mean
error in the length of the bar for each observer is
UPA (7 4 = SOK 298.

If the value of this mean error is formed by comparing with each
other the lengths of the measuring-bar according to each of the three
observers, we obtain:

= 0#2355.

From the agreement of the last fwo values we may conclude,
that in the results obtained the influence of the observer and of the
position of the metre and the measnring-bar is eliminated, and that
therefore, beyond the influence of the temperature determination and
errors in the coefficient of expansion, the mean error in the length
of the whole measuring-bar expressed in the length of metre 27,
determined by one observer, is equal to

: == (04.36.
and is therefore for the mean of the three observers:

0.36
= — = 04205
V3
Geodesy. — “Comparison of the Dutch platinum-iridium Metre

No. 27 with the international Metre M, as derived from the
measurements by the Dutch Metre-Commission in 1879 and
1880, and a preliminary determination of the length of the
measuring-bar of the French basc-apparatus in mternational
Metres.” By Prof. H. G. van pe Sanpe BAKkHUYZEN.

The main object of the measurements made by the Dutch Metre-
Commission (BosscHa, OvuprMans and SramKart) at Paris in 1879
and 1880 was an accurate comparison of the two Dutch metres
19 and 27 with the Métre des Archives, the various papers published
by Bosscna on the subject show, how very well this object was

214

3li2

attained. As we shall have to refer to these papers more than once
we shall quote by volume and page from “Bosscua’s Verspreide
geschriften” (B.’s collected papers) published in three volumes.

The importance of a comparison of the Dutch metres with the
International platinum-iridium metre kept in Paris was, however, not
lost sight of by the Commission. It was probably by their request,
that in the protocol drawn up of the handing over of the two
metres by the French Section of the international Metre-Commission
to the Duteh delegates BosscHa and OvupgEMANs it was specially stated :
Cette remise est faite sous la réserve du droit qu’aura le Gonver-
nement des Pays Bas de faire effectuer les comparaisons entre ces
metres et le prototype du Bureau international des poids et mesures
pour la determination de leurs equations a VPégard de ce metre.

However, not only did the Dutch Commission leave open the
possibility of obtaining a direct comparison with the international
metre later on, but also by making determinations at Paris of the
differences between the Dutch metres and metres which are in their
turn connected to the International metre, they took care, that the
relation between the lengths of our metres and the International
metre can be calculated.

Although all the observations which are required for these caleu-
lations are fully communicated in Bosscna’s papers and only very
simple caleulations are sufficient to obtain the relation in question,
the results have not been published either by Bosscua himself or
as far as I know by anybody else; and as they are needed in order
to express the length of our base-line in international metres, I shall
here shortly communicate them.

The relation to the International metre is obtained not only through
the metre des Archives A (see further down), but also through the
two Metres /, and 20, both of the second alloy of Marrnry, of
which .J/ is also made; in addition use is made of the two metres
23 and 27 both of the first alloy (metal du conservatoire).

For the reduction of the difference of length of 23 and /, the
difference of the coefficients of expansion of these two metres is
reqnired, and I shall therefore try to derive its most probable value
from the results communicated by Bosscna.

In the first place we may conclude from BosscHa’s calculations,
that the metres of the second alloy have all got the same coefficient
of expansion (Vol. III, p. 74—76). The equality of the coetficients
of expansion of the metres 1, 3, 12, and 13 of the first alloy is
also demonstrated (Vol. I[l p. 77). According to Fizeau’s measure-
ments the coefficients of expansion of the metres 19, 27, and 23 of

the first alloy would also have very approximately the same value
(Vol. Il, p. 314), whereas according to the measurements of the
Dutch Commission the difference in expansion of the metres 19 and
23 is too small to be observable. (Vol. II, p. 314, 315). This is
not quite in accordance with Fizwau’s results (Vol. II, p. 823) obtained
at 12°, 42°, and 62°, as these give for 19 and 27 somewhat different
values. but if the quadratic term is taken into account, the coeffi-
cients of expansion at 40°, the mean temperature used by Fizvav
in his measurements, would be according to his formulae 8’.74 for
49, and 8”.75 for 27, so that in connection with the equality men-
tioned above of the expansion of the 4 first-named metres of the
“metal du conservatoire” and the equality of the expansion of 19
and 23 found by the Dutch Commission it may be inferred, that all
the metres of the first alloy have also the sume coefficient of expansion.

The next question is, what the difference is between the coefficients
of expansion of the first and second alloy.

According to measurements by Brnorr and GuiLLaume with Metre
6 of the 2°¢ alloy the mean expansion between O and 20° per
degree and per metre is 8’.617; according to measurements by
Fizeau the mean of the same expansion for metres 19 and 2
the first alloy is 87.537, i. e. a difference of 0.408. It is necessary,

© i
however, to observe, that the two values were obtained by altogether
different methods, that of Brenorr and GuiniaumE by ordinary measure-
ments of length at different temperatures, that of Fizeau by his
well-known interference-method.

Against these we have the determinations of the differences in
expansion of metre 6 of the 2°¢ and of metres 1, 3, 12, and 13 of
the 1s* alloy (Vol. IIL p. 77) all from ordinary measurements of
length at different temperatures. As the result of these 0”.02 is
obtained as the average of the differences.

Taking into account, that, where the methods of observation differ,
systematic errors in the differences are possible, it seems to me
probable, that the latter result is the more trustworthy.

In the reduction of the Dutch metre 27 to the International metre
the difference in length of metres 23 and 27 also plays a part.
For this difference two values have been determined; in 1879 the
Dutch Commission found 27 — 23 = 0.92 + 0*.031 (Vol. I, p. 297)
and in 1880 the same commission found 27 —- 23 = 0.41 + 07.073
(Vol. If p. 334). Of the latter value no further use has been made
by Bosscua; it seems to me, however, that it is preferable to use
the mean of the two results, taking into account the respective
weights. In that case the result is

Reduction by means of I,. From several series of observations at
a’ mean temperature of 16°.44, Tresca found (Vol. III, p. 14)
23 = J, + 14.24.
Adding 0°.02 < 16.44 = 07.33 for the reduction to 0° the equation
becomes

93 = 1, 1657,

further 27 = 23-+ 0.84 (see above}
and I, = M- 5.94 (Vol. Ill, p. 70),
so that 27 = M+ 8.35.

Reduction by means of 20. From three series of measurements
one by Bosscua and two by Tresca, follows :

23 = 20 + 7#.19 (Vol. III, p. 24),

further 7} ee 23 ais Or. can (see above)
and Fol. Til, pesto}
so that 27 = M 4 8.99.

The mean of the two reductions is 27 = M+ 8+.67.

If the 5 above mentioned different equations containing 4 unknown
quantities, are taken as all equally accurate and if they are then
solved by the method of least squares, obviously the same value
for 27—JV is found, while the mean error of each of the equations
is + 07.32, that of 27 — 17 =8".67 being + O?.45.

A value for 27— J/ is also arrived at by using the comparisons
with the “Metre des Archives’ A, viz.
27 = A+ 64.11 (Vol. II, p. 323),
A=M-- 2.63 (Vol. Ill, p. 24). 70);

Hence 27 —M+ 8.74.

This result agrees very closely with the value found above. But,
as it is largely based on the comparisons which have also served
for calculating the previous result, no particular importance can be
attached to the accordance. Considering the value of the mean
error + 0.45 a direct comparison of 27 and WV would certainly
seem to be desirable.

If the length of the measuring bar of the French base-apparatus
in terms of metre 27, as given in the previous note, is now expres-
sed in International metres by means of the equation 27 = J/ + 87.67
the result is;

L=4 M— 391-84 + 4 & 84.67 =4 M — 3574.16.

The value of Z had been determined several times before at the

“Bureau international des poids et mesures” at Breteuit; on these
occasions the following values were obtained, leaving out the some-
what uncertain correction for the “change in the molecular equilibrium”.

1903 March 4 M—277".6 Breteuil
1904 June —-373 .5 re
1907 February —-363 .7 is
1909 February. —356 .8 7
1909 December —358 .4 3
1910 December —— St ae -
1911 June 515) a) “
1911 Sept.-October - 398 .4 ;
1913 April —348 .7 “
1913-14 Dee.-January —357 .2 Delft.

It appears from these numbers that during the first years up to
1909 the bar increased in length. From that year onwards the length
seems to have remained practically unchanged; only in April 1913
a further very marked increase in length shows itself, of which,
however, no trace is found in the measurement made by us. In
view of this contradiction a new determination at Breteuil of the
length of the measuring-bar is desirable; col. LALLEMAND, chief of
the geodetic department of the Service géographique de l’armée, and
Monsieur Bunorr, Director of the Bureau international des poids et
mesures at Breteuil, have both promised to undertake this comparison
shortly.

Postscript. A few weeks after the meeting of our Academy
I received from Monsieur benoit a letter in which he communicated
the results of an elaborate investigation concerning the length of the bar
of the French base apparatus. He and Monsieur Mauprer compared
in the Bureau at Breteuil first that bar and three other ones each
with the prototype and afterwards the four bars with one another.
Benoit found as final result for the length of the French bar, with-
out correction for the change in the molecular equilibrium:

L, = 4 M — 3487.23 ,
almost exactly the same value as that found in April 1915.

On the average the length determined at Breteuil is therefore 8’.7
greater than that determined at Delft.

In order to find what may be the causes of that difference I

316

used the formula by which the length of the bar at zero is derived
from the measurements.

During the measurements at Breteuil the temperatures of the bar were,
according to Brnorr’s statements, not very different from 15°. I bave
not here at my disposal the data of the exaet values of the tem-
peratures during the measurements at Delft, but I know that they
presented no great deviations and, if I am not mistaken, the extreme
differences from the mean, about 15°. were not greater than about
two degrees. We can therefore combine the observations at Breteuil,
and also those made at Delft each into a mean result, at a mean
temperature, and we then obtain the following equation, in which
the letters without a dash indicate the values determined at Breteuil,
those with a dash the values determined at Delft:
Lp=L tel, T=4l,+48t+S8 , p= +e'Lh | T’=41,'+48t-+S,

L,— bhi eh, Fee Ll Poe AG 1) 468) ae

In these formulae Z is the length of the bar, 7 its mean tem-
perature during the measurements, « the adopted coéfficient of expansion
of the bar, / the length of the comparison metre, ¢ its mean tem-
perature, 3 the mean expansion of the metre for 1°, S the difference
of the length of the bar and the fourfold of the length of the com-
parison metre, determined by means of micrometrical measurements
with the microscopes; 7’ and 0, as indices of LZ and / indicate the
temperatures to which these lengths have been reduced.

The differences of the temperatures 7’— 7” = AT and t—t = At,
and also the differences in the adopted coefficients of expansion
8— p'=Ap are small, and for the value of the coefficient of ex-
pansion «@ and e« the same value has been adopted in Breteuil and
in Delft; the last of the three equations may therefore be put
approximately into the following form:

L,— LL, =4L=—aLAT+ 4Al 4 4pAt 4+ 4tAg+ S—S’.

When A7’, At, Al, As and S—S’ have their exact values, AZ
is zero; the value 8.7 for ASL found from the observations is there-
fore only a funetion of the errors in those values, and putting on
the first side of the formula AZ = 8’.7 the quantities on the second

side represent those errors. We will consider each of the terms
separately.

1. «LAT. T and 7” have been determined in the same manner
by readings of the thermometers laid on the surface of the measur-
ing bar within the thick aluminium case; the temperatures in both
comparators were fairly constant, and the value of @ is small; eZ
for O°. is about 07.7. In view of the great value of AZ, we may
therefore neglect that term.

317

2. S-—S’. Taking into account the precision of the micro-
metrical measurements and the small influence of the systematic errors
in the measurements made at Delft, as appears from the values of the
mean errors, that term may also be neglected in trying to explain
the great value of AL.

3. 484¢. 43 is about 34” and Af is the difference in the errors
of the mean temperatures of the metre, determined at Breteuil and
at Delft. When we assume, that in the perfectly constructed
comparator at Breteuil the error in the mean temperature of the
metre was zero, the effect of an error of 0°,1 in the mean tempe-
rature of the metre at Delft on its length is 3”,4, and in order to
gel a positive value of AZ the temperature of the thermometer
laid on the surface of the metre must be lower than the tempe-
rature of the metre itself.

During the measurements the temperature of the metre was slowly
rising, it is therefore improbable, that the teimperature of the thermo-
meter should be systematically lower than that of the metre, and it
is difficult to explain the positive value of AZ, either totally or for
the greater part by an error in Af.

4. 44/7. I cannot say, what is the real value of A/, the error
of the difference I adopted between the length of metre N°. 27 and the
International metre.. The mean error of the adopted value of 44/
is +1”.8. It is therefore possible that a part of the AZ may be
accounted for by an error in the adopted difference, but it is
improbable, that it should explain the whole value, 8%.7 of AZ.

5. 4t43. We can determine a fairly probable value of that
term. According to a telegram from Monsieur Brnorr, the mean expan-
sion for 1° between O° and 15°, used in the reduction of the
measurements of the prototype, made of the second alloy, is 8’,662, the
mean expansion per degree between the same limits adopted in my
reductions of the length of N°. 27 made of the first alloy is 8’,493 ;
the difference between the two is 04,169. As a_ result of direct
comparisons, the mean difference of the expansion of the metres of
the first and second alloy is 07,02, as I stated above.

If we assume, that the coefficients of expansion of the metres
of the second alloy are really equal and that it is the same with
the metres of the first alloy, which assumption after the researches
of Bosscna is very probable, the error 43 would be equal to 0.169
—(0.02 = 02,15. As ¢ is about 15°, the term 4¢Af is 9”, almosi
equal to the value 87,7 found for AL.

Although I do not pretend, that the assumptions made in order
to explain the difference between the results obtained in Bbreteuil

318

and Delft are absolutely certain, still I believe that the probability
is not small, that the difference between the assumed and the real
coefficients of expansion of the prototype at Breteuil and the
metre N°. 27, is for the greater part the cause of the value of
AL. It remains absolutely uncertain, what the real coefficients of
expansion of the metres are and also whether the coefficient of N°. 27,
determined after Fizuavu’s method, merits greater or less confidence
than that of the prototype deduced, as I believe, from direct measure-
ments at different temperatures. But whatever it may be, it is of great
importance, and it is in my opinion the chief result which may
be deduced from my discussion, that when a direct comparison
of the metre N°. 27 and the international metre shall be made,
according to the right given to our government, it will not be confined
to a comparison at a mean temperature, but that if possible, the
absolute coefficient of expansion of our metre, and certainly the
difference in expansion of N°. 27 and the prototype will also be
determined.
Lenk (Switzerland.

Physiology. — “On the formation of antibodies after injection of
sensitized antigens.” Il. By Dr. L. K. Worrr. (Communicated
by Prof. C. Eyxmay.)

I. As a continuation to my series of experiments given in the first
communication, | have examined the immunisation power of a mixture
of erythrocytes and specific serum with a surplus of amboceptor.

It is generally stated in literature that this power is very slight or
that it does not exist at all; in my two series of experiments I have also
found very little or no formation of amboceptor. I shall communi-
cate one of the series.

Horsecorpuscles — specific rabbitserum */,,, strong.

Binding power of 1 ecm. 5°/, blood + 7 doses.

Mixture of 40 c.em. serum and 20 e.em. undiluted blood i. e.
20 doses amboceptor, so a great surplus.

Rabbit 149, 73 and 76 each get 20¢.em. of the mixture intraperitoneal.

x, ADS Oennavelecale =, - 6'/, ,, undiluted blood only %
Titre after 1 day after 7 days after 12 days
149 Yi) weak ae Ear
(i aif 1/,, weak 1/,, weak
76 “ie ‘/,, weak ha
179 7s ia “en
70 aa iNet Woon

@ re “Laoo AGE weak,

319
/

So with the rabbit 149 and 73 we do not find a trace of active
immunisation, only of passive; rabbit 76 after 12 days shows a
small (active) increase of titre. The controlling rabbits however have
distinetly formed amboceptor.

The second experiment with cattle corpuscles had a_ perfectly
analogous course. With these experiments we cannot inject intra-
venously; the animals which are intravenously injected with such a
great quantity of serum and corpuscles die of anaphylaxis.

II. I have now put to myself the question what happens with
the sensitized corpuscles after the injection into the rabbit or cavia.

Therefore | have for the time being confined myself to the sub-
cutaneous resp. subconjunctive injection; the intravenous one is very
difficult to follow, the progress of the peritoneal one it mostly known ;
besides the subcutaneous is the only one that is to be considered
with regard to man. I expected that in keeping with what happens
in the peritoneum, viz. a solution of the sensitized red corpuscles
in a short time, the corpuscles would also dissolve in the subeuta-
neous tissue. I have taken the conjunctiva as the spot where to
inject: there the phenomena are to be controlled better than any-
where else, and one can easily cut out little pieces for microscopic
examination.

Well then: if we inject foreign corpuscles under the conjunctiva
they are generally gone after one, and certainly so after two days.

As they have no movement of their own, we must assume them
to be led away along the lymphpaths a leading away by phago-
eytes in such a short time is not to be assumed. It is however
different if sensitized corpuscles are injected; these remain on the
spot; they do not dissolve in any quantity worth mentioning, and
if one microscopies the place after a longer or shorter space of time
(after cutting out, fixing, embedding, and colouring) one will find
an important number of leucocytes between the corpuscles.

After 6 to 8 days only the corpuscles have generally disappeared;
sometimes however they are still to be seen after 10 to 12 days.

During the first few days one mostly finds polynuclear small
leucocytes, later more great mononuclear ones.

Now the question is how to explain this conduct. For this we
must examine three things.

Ist. How is it that the sensitized corpuscles which are injected
subconjunctively do not dissolve, while those injected intraperiton-
eally do.

2nd, Why do the sensitized corpuscles remain in the same place,
whereas the normal ones are carried away.

320

3°'. What happens finally to the sensitized cells; what do the
leucocytes do.

Let us first answer the first question.

Here we must ask at once if there is complement in the sub-
cutaneous lymph.

As far as I know H. Scuneiper’s') researches about this subjeet
are the best; he found that the tissue lymph which is obtained by
bringing a piece of cottonwool under the skin, and afterwards
pressing if out, contains very little complement indeed. One always
finds a littlke more complement than would really be the case if
we had pure tissue lymph; a slight mixing with serum can of
course hardly be avoided. It goes without saying that in this
Way we cannot be certain to get a liquid, agreeing with the tissue
lymph; the piece of cottonwool naturally works irritating; an
inflammation arises. But the injection of the corpuscles also causes
an inflammation, and as such these two processes are equal.

I have also made some complement titrations to the guinea pig
and rabbit, of subeutaneous fluids obtained in this way.

For the solution of my haemolytic system I needed :
1/

I. Fresh guinea pig serum Hori Gitte
Subcutaneous fluid “om Cxe lta.
[I]. Fresh guinea pig serum eeGRC NN:
Subcutaneous fluid Win (OsK0e
Ul. Fresh rabbit serum Wf, CxO.
Subeutaneous fluid 0,6 c.cm. no haemolysis !
Siowing fluid 0,6 c.cm. trace of ,,

So we can affirm ScuNemeEr’s experiments and assume very little
or no complement to exist in the subeutaneous cellular tissue ; and
we need not be astonished about the sensitized corpuscles not dis-
solving, when being injected subcutaneously.

Now we must answer the second question. The sensitized cells
remaining in the same place was supposed to be due to the agglu-
tination which always accompanies the sensitizing. I did not succeed
in obtaining an immune serum prepared in the usual way, which
did not at the same time agglutinate. As I did not know any
method to separate amboceptor and agglutinin when I started my
experiments, | took another way to prove that the remaining of the
bloodcells was owing to their being agelutinated and not to the
sensitizing. | therefore agglutinated the bloodecells in a different way,
and now found that clinically and histologically the same was to be
seen after injecting these corpuscles as after injecting sensitized (and

1) Arch, f. Hygiene 70. p. 40 seq.

321

at the same time agglutinated) cells. In the first place T used a
colloidal solution of SiQ, for it.

All the red bloodcells I used (rabbit, guinea pig, horse, cattle, dog)
were agglutinated by it, be it in various concentration. Only the
SiO, had no effect; it caused neither swelling, nor leucocytosis. It
had been prepared by saponifving Siliciumethylether (Itan_BauM) with
greatly diluted hydrochloric acid. Colloidal SiO, prepared in a different
way had the same effect. Now one might object against this
experiment that the SiO, not only agglutinates the bloodcells, but
that it also sensitizes them; for together with guinea pig serum ina
great quantity, it can dissolve some kinds of blood. Therefore I took
refuge to the vegetable agglutinins which are found in the bean,
pea, lentil, and in the seeds of Datura Stramonium. In all these
cases the result was the same: the bloodcells always remained there ;
the conjunctiva also showed the wellknown bluish-red change of
colour after some days, and histologically the image was always the
sane. It goes without saying that with all those experiments the
sterility was taken into consideration as much as possible. *).

In order to make quite sure, however, that only sensitized and
agglutinated corpuscles did not show the phenomenon, I examined
some thirty rabbits out of my collection on haemolysin and agglu-
tinin against sheep-erythrocytes, and I really found some sera which
did contain baemolysin, but only little agglutinin. I repeated the experi-
ments with these sera; but the results were not very distinct : there
sometimes was a difference, but it was not big enough to draw a
certain conclusion from it.

This is because all the sera employed were rather weak (ambo-
ceptor */;,—'/,9.) and so a rather big quantity of serum was necessary
(+ 3 em.) to sensitize the cells. Normal rabbitserum generally con-
taining some agglutinin, we did not sueceed in this way in obtaining
a suspension of sheep-erythrocytes which are sensitized but little or
not agglutinated. Yet I ean communicate one experiment which came
out rather well:

Serum rabbit 73 titre amboceptor ‘/,, very little agglutinin.
cml tt! 87h o, oe srneanly a>, much iy

» 100

1/, ecm. sheep-erythrocytes is digested with += 3 cem. serum 73,
just as ‘/, ecem. with +3 ecm. serum 147. The suspensions are
centrifuged and the corpuscles are taken up in 1 cem. saltsolution.
Erythrocytes 73 are injected on the right, erythrocytes 147 on the

1) I did not use ricine because the poisonous qualities of this substance would
have injured the image.

322

left under the conjunetiva of rabbit 172. The serum of this rabbit
contains neither amboceptor nor ae in a noticeable quantity
against sheep-erythrocytes.

After one day there is a distinct difference. There is very little
swelling and redness (+) on the left, but very strong swelling and
bluish-red change of colour (+-+-++) on the right. The next day the
difference is a little less, but still it is distinet.

Consequently it was desireable to obtain a serum which sensitized
strongly (at least ), but whick agglutinated little or not at all.
As there was no question of a chemical separation — all the litera-
ture tells us that all suchlike attempts lead to no result whatever —
such serum had to be obtained in a different way. In the literature

1000

about the heterogenetical antibodies is mentioned that serum of a
rabbit which had been in some way prepared in order to get hetero-
genetical amboceptors against sheep-erythrocytes, would then contain
no more agglutinins than are found in normal rabbitserum.

My experiments in this direction have however not yet led to the
desired result. One rabbit which was injected with pempeie
had a serum with titre '/,,, against cattle-corpuscles, and a titre */, 999
against sheep-corpuscles. Hoa eet it very clearly contained agelutinins
against the latter. The same thing appeared with two rabbits which
had: been injected with horse-kidney extract. The titre against sheep-
blood was ‘/,,, of both of them. Both distinctly contained agglutinins,
if only little. The sheep-corpuscles treated with this serum remained
for some days in the same place, after having been injected under
the conjunctiva.

So in this way I could not prove awith certainty that the agglu-
tinin is the cause of the prepared corpuscles remaining under the
conjunctiva, *

11. I will now mention some experiments which have been made
in connection herewith, but which do not directly bear upon the
subject mentioned in the title. | have asked myself whether the same
difference as is mentioned above, is also found when non-prepared
bloodeells are injected subconjunctively partly with prepared, partly
with non-prepared animals, and whether here too the agglutinin was
of any importance as to the remaining of the erythroeytes. And this
has indeed appeared to be the case.

Rabbits with serum containing amboceptor (and agglutinin) still
show a strong swelling under the conjunctiva after one or two
days after having been injected with the erythrocytes in question

) Note added during to the correction: Now | had more success with this
experiment. The heterogenetical serum which | now used was '/aoo9 strong.

(in my experiments they were horsecorpuscles), whereas the controlling
animals showed hardly any swelling after one, and no swelling at
all after two days. In accordance with this the tissue fluid (obtained
in the above mentioned way with cottonwool) obtains amboceptor
as well as agglutinin, if they are in the serum.
Rabbit 160 immunized against cavia-erythrocytes.
Serum agelutination '/,, amboceptor ‘/,, weak (+--+)
fluid * oe * ay key aie
Rabbit 192 immunized against horse-erythrocy tes.
Serum agglutination */,, amboceptor
jluid 3 1/7, weak ,, 1/,, nearly

/
/20
Rabbit 147 immunized against cattle-erythrocy tes.
Serum agglutination ‘/, amboceptor */,,
fluid 1 mie ms lee
I have now investigated if it really is the agglutinin which deter-
mines the difference.

Rabbit 116 agglutination strong, amboceptor ',

100°
Rabbit 148 » very weak, fe eee
Both rabbits are subeonjunctively injected with '/, c.em. washed

sheep-ery throcy tes.

After one day there is a very strong bluishred swelling with 116,
with 148 hardly any swelling; after 2 days still a strong swelling
with 116, with 148 nearly all the blood has disappeared.

A stronger proof is given by the rabbits that were injected with
horsekidney extract’). Although the titre against sheepcorpuscles was
not high here (with both */,,,) a great difference was stated with
the controlling animal (titre also */,,,).

After one day hardly any blood was to be seen with the first,
contrary to the controlling-animal. 1 think these experiments are
of some importance. For in the latest great report about the
agelutination known to me, that by Patraur*), the author says on
p. 515: Ob Agglutination auch im Organismus stattfindet erscheint
recht zweifelhatft.

At least I believe I have proved the haemagglutination to take
place in the subcutaneous tissue. [| only want to insert bere that

1) These are the same animals as were mentioned above: their serum did
contain agelutinin, but much less than the animals immunized in the ordinary
way. That here we get no agglutinin effect, and that we did when mixing the
serum with the bloodcells in vitro, may be explained by the fact that the agglu-
tinin can pierce with so much more difficulty into the tissue fissures and reach the
bloodcells than when a great quantily of serum in vitro ts directly added.

2) Kotte und Wasserman, lle Auflage, Il, p. 483—654.

324

the phenomena mentioned above belong to the department of local
anaphylaxis (Phenomenon of Artuus). As far as 1 know they have
not been studied as to the immunisation with bloodeells; they have
with serum or bacteria. This really is only a question of name
however: the essence of local anaphylaxis is still as unknown to
us as that of general anaphylaxis.

In any case we can see by the bloodcells that the disintegration
of albumen is a very slow one; I do not wish to deny however,
that part of the flood of leucocytes is owing to this disintegration.
What has been stated somewhere else viz., a primary necrosis of
the tissue and after that an infiltration of leucocytes '), I have never
observed; I could sometimes also state a toxical influence of the
injection out of an oedema of the cornea: but this happened very
rarely. Then one should not directly compare the phenomena of
subeutaneous injection with those of intracorneal injection (WESsSELY,
von Sziny); in the latter ease the current of fluid is much slower,
so that great differences can occur by this. It would however lead
us too far if we entered into this more closely.

We must now still treat of the third question: what happens to
the sensitized (agglutinated) cells, and what do the leucocytes do in
this process? I must first of all mention that 1 could not find any
difference between histological images when injecting sensitized or
only agglutinated bloodeells. ‘This, however, is in keeping with
other experiments. For, there being a great difference in vitro between
the phagocytosis of sensitized (opsonized) and nonsensitized cells, -—
the former are phagocytated, the latter are not, when brought
together with suitable leucocytes — one does not find back this
difference in vivo when injecting the cells into the abdomen,
previously injected with broth. AcHarp and Forx’*) some time
ago tried to find the causes of this difference, but in vain. I did
not succeed either*). We need not be astonished however, when
finding the same conduct in the subcutaneous tissue as in the
prepared abdomen.

Are the erythrocytes now phagocytated? Notwithstanding my
observing a great many preparations, I did not succeed in getting any
certainty whatever about this in my histological sections; to form

1) H. Fucus und Metter, Z. f. Ophthalmologie. Bd. 87, p. 280.

2) AcwarpD and Forx Arch. de Medecine expérimentale et d’anatomie Patholo-
gique, January 1914.

3) Prof pe Vries advised me to add to the mixture (foreign bloodcells, fresh
serum (without opsonins) and leucocytes) scrapings of the peritoneum endothelium;
with this | had no suecess either.

325

an opinion about it is, however, very difficult; leucocytes are always
among a great number of red cells and the sections are always
thicker than one red or white cell. Anyhow, it seems very probable
to me that this must happen. For:

1. the red cells disappear atter 6—8 days.

2. in vitro they are easily phagocytated.

3. The subcutaneous cellflaid and the leucocyte extract do not
contain an unspecific haemolysin (ScuNumwer: |. ¢.; this concerns
polynucleous (mikrophages) as well as mononucleous cells (macrophages).

I have tried after one or two days to cut out the swelling (after
injecting the sensitized (agglutinated) cells), and then to spread them
out on a coverglass: these preparations too gave bad images; princi-
pally by the stickiness of the substance: I did not see a distinct
phagocytosis.

I have here always spoken about sensitized cells without wishing
to form an opinion about the open question of identity between
amboceptors and opsonins and tropins. (NEUPELD *) SaTSCHENSKO’’) ).

The following experiment will show that there can be amboceptor
as well as tropins in the subcutaneous cellular tissue. A piece of
cottonwool was entered under the skin of the abdomen of a prepared
rabbit (against sheep-erythrocytes) and the fluid was examined after
some hours: in vitro it sirongly stimulated the phagocytosis of
sheep-erytrocytes by rabbit-leucocy tes.

As a summary we can draw the following conclusions:

1. When using red corpuscles loaded with amboceptor as antigen
one should remove all surplus of serum.

2. Sensitized and agglutinated red corpuscles, when injected sub-
cutaneously, remain in the same place for a long time; non-treated
cells are soon led away.

3. This will most probably be the consequence of the agglutination,
not of the sensitizing. The same happens to non-specific agglutination
— also when it concerns the animal’s own cells.

+. With prepared animals possessing agelutinin, the cells injected
also remain in the place where they have been injected. So agglu-
tination in vitro also takes place; this is not the case with animals
which only possess amboceptors (opsonins) and no agglutinins.

5. The subcutaneous lymph contains very little or no complement,
it does contain amboceptor, agglutinin, opsonin (tropin).

The above will show my experiments not yet to be complete.
They require to be completed as to the question to what
“1) Arbeiten aus den Kaiscrl. Gesundh. Bd. 25, 27 en 28.

*) Arch. Se. biol. St. Petersburg. XV, blz. 145 1910. a

Proceedings Royal Acad. Amsterdam. Vol. XVIL.

extent the immunizing power of red corpuscles loaded with antibodies
is related to that of normal cells as to the tropin- and the agglutinin-
content of the serum. We may suppose, also in consequence of the
above mentioned experiments, that the content of antibodies of serum
and subcutaneous lymph goes parallel and so we shall not investigate
this point separately.

IV. After the immunisation with sensitized erythrocytes the one
with mixtures of serum and anti-serum comes next. I have not
stated the amboceptortitre (to be stated by means of complement
fixing) but the precipitincontent. Where the results do not differ
much from the experiments with sensitized erythrocytes, 1 think I
can suffice with only stating the precipitin.

7A Rabbits, injected intravenously with horseserum, 0,5 ¢.c.m. per

ke. (made inactive).
>

Rabbit weight titre after 3days after 5 days after 7days after 12 ds. after 14 ds.
103 26007 3 =— of z Pa t= ae s} "oo hoo
104 2850 — lB ee =) \s | — NE EF Yoo weak — /r900
105 2830 i Ne a A 7 2 ¥ — 5 - Thooo » "/r000
106 1650 tS Zs vee z\ he x "hoo “/iooo Weak
107 2100 — a8 = pe SI Mio) weak Th o00

/B. Rabbits injected, intravenously with 0,5 ¢.em. horseserum
(inactive) + 1 ccm. precip. serum ('/,,,,), after this mixture had
stood for 1 hour.

Rabbit weight titre aft. 3days after 5 days after 7 days aft. 12 days aft. 14 days

8 = 2150 — ges —(og “ho "hoo Yoo
109 2150 = 5 5 5 — E 5 ho Thooo Miooo
a ee — ie 2 © et par = ae some . ‘hoo ‘A000
35 = at ys — ea te — (horse serum
5 a fellas /ho00 / 1000
112 9150 — et = s /ip Weak Mhogo weak 1/009
So here we do not see a distinct difference between the A and B
group.
Il A. Rabbits, injected intraperitoneally 0,4 cem. human serum
>} *
per kg.
Rabbit Weight after 5 days aft. 7 ds. aft. 10 ds. aft. 12 ds. aft. 14 ds.
67 2150 — g ; “= tho 000 Mhonoo
78 2450 — 5 5 = hho hoo T/1o99 Weak
70 1900 — /s 5 = Vio ooo 1 0000
60 2320 — jog Wo? 1/00 1 000 M1000
76 1820 — a 1h hoo hoo 10000

II B. Rabbits injected similarly 0,4 eem per keg. + 3.6 cem.
antiserum (‘/,,,, largely). The mixture had stood for 4 hours, a thick
precipitate has been formed.

O26

alt. 7 dss atte VONdss © Jatt) 12) ds. “aft. 14 ds:

9
=)
or
a
7

Rabbit Weight

2100 —— 5 \ - hoo “hooo 1000
114 3200 — (: 2) = = = “ho
113 2000 — /¢§ i ; = = et tho
112 2550 —_ (2 :| = =a “ooo "/igo Weak
7/Al 1600 pil = Te a 1h ooo 1/0000

After 17 days the titre already went back.

Here we can see that, whereas of the series B three rabbits
distinctly lag behind, two of them reach as high a titre as the A
rabbits. Knowing (UsLENAUTH) that accidental failures in the preparation
of precipitinholding sera are not to be avoided, I should not wish to
draw any other conclusion from this than that a good formation of
precipitins is also possible with mixtures of serum and antiserum.

I have also taken the following series of experiments.

III. Rabbit 140 1 c.cm. horseserum intraperitoneal.

ee kG * 5 » + 1 cem antiserum
(*/1000)
» 142 - ‘ Sng crt, Sha ss
e 99 33 An Wey SIMO! Gata
Perio teas OO 7? este oe
7: 8 2 0 Diet! Ae
i 42 5 x ad foter dy MES,
es 48 3 93 Geeta OV ee
Rabbits after 8 days
140 oe
116 ‘Tipo 4Wweak.
142 a epaiate Mn
v9 Hitent
121 t/acus
8 piaaen
42 aetet
48 —

So here too we find a rather important formation of antiserum
with rabbits, which, with the serum, bad also got antiserum.

IV. Rabbit 155 50 ¢.em. antiserum ‘/,,,, -- 2¢.cm. horseserum intraperil.

per is6: 30, ‘ Fiat alae
57 10) | ‘ nae ‘
marissy On, 3 ia) a :
meson dS. .. y ae ; i

328

Rabbit after 1*/, hour after 1 day after 3 days after 5 days
contains — | » contains / contains / contains
es se serum | horse serum horse serum horse serum

dd - —\+++4¢—\) ++ +
156 Sie aby a ge ++

as, oy < — eee z 4?

Pah ae shaRAE = aioe ++

169 aes :

after 7 days. aft. 10 ds. aft 12'ds. att. 4vdse Vath diadee

contains
horse serum 28
aos
Sk <> 1/ 1) . 1
155 = + ailing BS 5 100 /1000 Ww. nee
LOG Staats > IE a 3 > ‘L100 weak L100 WwW. “hres
Si | 1/ oe) 1 9 1
157 — — fio a oa : ho Ww.
KO 1/ Aes / 1 1/
158 — staat 10 3 a /100 /100 /100

1G eee re a ee ve om

Here too we also see some irregularity: (rabbit 157 immunizes
somewhat less than the other, but even a mixture of 25 times more
antiserum than serum still has immunizing: effect.

I did not try if surplus of serum can do any harm when
immunizing, for one then gets too great quantities so that it is hard
to inject them: 50 ccm. serum is rather much for a rabbit.

These experiments seem to be somewhat contrary to a communi-
cation of Do6rr (report about Anaphylaxis, Kote unp WassrrM.
Ile Aufl.), that the precipitate obtained by mixing serum and _ anti-
serum, has no immunizing effect. But this is only a seeming
contadiction. For, according to investigations e.g. by Wetsa and
CHAPMANN’) this precipitate only contains traces of parts of the
serum and it is almost exclusively formed out of the antiserum.

Thus I have found that of a serum of a rabbit which was
immunized against human serum (titre '/,,,.) 75 ecem. was necessary
to form together with 1 cem. human serum (together till 150 cem.)
a precipitate, so that in the above mentioned liquid no more human
serum could be indicated with my antiserum (’/,,,,). 1 cem. being a
very small dosis to immunize a rabbit, it is clear that not much
can be expected in general from an injection of the precipitate’).

I have now also examined the local effect of serum and antiserum.

1) Zeitsch. f. Immunitiitsf. 9, p. 517.
2) T here give up the question whether there is any human serum at all to be
found in the precipitate, or whether it could be again removed by washing.

329

With this the antiserum and serum were always both inactive, so
that we have nothing to do with any possible anaphylatoxin.

If one again injects the mixture in which a precipitate has been
formed subconjunctively, one will find a rather strong swelling the
next few days, which at a morphological examination again seems
to contain polynucleous cells. The controlling animals which had
only been injected with serum, were normal again the next day.

If one centrifuges the mixture, the above mentioned liquid is not
found to cause a swelling, but the precipitate is. So we have here
an analogous conduct as with the corpuscles’).

I have now tried whether specific albumen precipitations did not
show the same conduct, and for this I chose the precipitates of
horseserum with colloidal He (OH), and S/O,. Both precipitates
gave some swelling and ata morphological investigation polynucleous
Jeucocytosis. This investigation must still be extended.

If one injects a prepared animal with specific serum, one gets
the same phenomenon: swelling and lencocytosis. This phenomenon
is wellknown. I did not yet succeed in proving here as well that
the precipitins hold the serum in its place’*), although | do think it
likely, considering what goes before. For the time being I do not
see a chance of preparing a serum which possesses amboceptor
against foreign albumen, but no precipitin.

Amsterdam. Path. Anat. Laboratory of the University.

Chemistry. — “The Temperature-coefficients of the free Surface-
energy of Liquids at Temperatures from —80° to 1650° C.
1. Methods and Apparatus. By Prof. Dr. F. M. Janeur. (Com-
municated by Prof. P. van Rompuran).

§ 1. The purpose of the experiments here described was to en-
deavour to ascertain the relation between the so-called “molecular
a relation

surface-energy” of molten salts and the temperature,
which has hithertho been studied only in liquids, which possess no
electrolytical conductivity.

1) The experiments are somewhat analogous to those about the local effect of
the anaphylatoxin (fRiepBeRGER), but I always used serum that was made inactive,
contrary to the investigators, into the anaphylatoxin.

2) That is to say subconjunctively. For the cornea other laws probably prevail;
there the serum remains in the same place for rather a long time without there
being any precipitins (WersseLy, von Sziny).

330

A probable relation founded upon the law of corresponding states,
between the value of the temperature-coefficient of the expression :
Ge) , and the degree of molecular association of a liquid was
first suggested by Eérvés*), and later by Ramsay and Saietps*) and
a number of others*). These observations appeared to prove, that
the values of these coefiicients do not differ much from 2,2 Erg
per degree C. for “normal” liquids, while for associated ones they
are considerably less. In any event some definite knowledge of the
dependence of the free surface-energy x upon the temperature will
be of high importance for the consideration of all problems, relating
to the internal state of liquids.

It can hardly be supposed with any probability, that the law of
corresponding states will be found to apply in the case of molten
salts, because they are really electrolytes and more or less dissociated.
Notwithstanding this, if the investigation should chance to reveal
relations in any way analogous to those hitherto supposed to be
characteristic of organic liquids, this fact must carefully be considered
in estimating the significance of the theoretical speculations mentioned,
and especially is this the case, where criteria are sought for judging
about the molecular state of liquids in general. In fact, one can
better hope to elucidate the influence of chemical constitution on
characteristic properties in the case of molten salts, than in the ease
of the much more complicated organic molecules.

These and other considerations, some years ago (1910) suggested
the development‘) of an experimental method, which should permit
the study of the dependence of the molecular surface-energy upon
iemperature, — even up to temperatures in the vicinity of 1650° C.

1) Kérvés, Wied. Ann. 27. 448. (1886); vAN DER WAALS, Zeits. f. phys. Chem.
13. 713. (1894). Erste. Ann. d Phys. 34. 165. (1911-)

2) RAMSAY and Surewps, Zeits. f. phys. Chemie 12. 483. (1893).

8) Vid.: Guyz and collaborators, Journ. de Chim. phys. 5. 81, 97. (1907); 9.
505 (1911); etc.; WaLpEen and Swinney, Zeits. f. phys. Ghem. 79, 700. (1912)
3ull. Acad. St. Pétersbourg, (1914) 405,

‘) Preliminary experiments of this kind were begun during my stay at the
Geophysical Laboratory in Washington, (U.S. A.), in the winter 1910-1911,
and I wish to express my thanks here once more to my friend Dr. A. L. Day
for his kind assistance and most valuable advice in this matter. Through these
preliminary experiments the availability of the method up to 1200° C. was clearly
established by me, and it became quite clear, in what directions improvements
were necessary. The further development was hindered by the building and equip-
ment of the new Chemical Laboratory of the University of Groningen: not earlier
than November 1913 could the first measurements of the present series be made.

With the increase of the temperature of observation, the experimental
difficulties of precision-measurements increase very rapidly : measure-
ments, which at room-temperature are of the utmost simplicity, are
often very difficult at 400° C., and commonly almost impossible
above 1000° C. This fact explains, why it has not been possible
until now, to communicate the results obtained, because only an
extended experience could prove to us the reliability of the method
used and the degree of accuracy obtainable.

§ 2. Of all the methods hithertho deseribed for the determination
of surface-tensions, the one most used is the method of measuring
the rise of the liquid in capillary tubes. Ramsay and Suipips and
most of the investigators who have followed, have used this method.
It can however hardly be denied, that the absolute values of x,
obtained by different observers with the same liquids and at the
same temperatures, show discrepancies of considerable magnitude.
Commonly this lack of agreement is attributed rather to the unequal
degree of chemical purity of the materials studied, than to the methods
employed. In many of the cases, however the discrepancies were
found with liquids, which can be obtained in a state of complete
purity without extraordinary trouble; so that one is easily inclined
to the belief that the method of measuring the capillary column
includes some sources of error which are not yet sufficiently known.
Possibly adhesion to the walls of the tubes plays a certain role in
it, or perhaps the influence of the angle between liquid and
solid material may be not completely negligible, as is ordinarily
assumed.

However there is a decisive argument against the use of the
method of capillary ascension in the following investigations; the
walls of the capillary tubes used, were ahvays damaged in a greater
or less degree by the action of the molten salts. A microscopical
examination of the walls of the tubes readily revealed this fact.
The method cannot be employed therefore at temperatures, exceeding
400° C., because the liquids will always be contaminated and the results
will be almost valueless. Furthermore, the method assumes, that a rather
long column of liquid can be held throughout its full length at a
constant and uniform temperature. At high temperatures this condi-
. tion can searcely be fulfilled. The study of large platinum resistance-
furnaces has shown convincingly, that even in a central furnace-
tube of about 26¢.m. length and 4,5 ¢.m. diameter, with the heating-
coil wound inside, the space of really constant temperature is scarcely

332

longer than 4 or 5 em.') Therefore it is absolutely essential in every
method intended for exact measurement at high temperatures, that
the working-space be reduced to dimensions as small as possible.
With respect to the measurements of temperature under such con-
ditions, the available methods will permit making them with an
accuracy of 0°,1 C.,*) which is more than sufficient for the purpose.
On the other hand, the necessary measurements of the surface-energy
must be made in such a way, that the results will have the same
degree of accuracy at the highest temperatures, which they possess
at lower temperatures, while at the same time the liquid to be
studied must be restricted to a space of one or two cubic centimeters.

§ 8. To fulfill these postulations, there is a method which can_
be used under certain conditions, which was first projected by
M. Srvon, and later developed by Cantor, *) while it was successfully
used afterwards for researches at lower temperatures by FrusTEt. *)
It appeared to be possible to develop the technical procedure in
such a way, that the method could be used, without any appreciable
loss of accuracy, up to the highest temperatures, which can be
measured with the platinum-platinumrhodium thermoelement.

The principle of the method is the measurement of the maximum
pressure HH, prevailing within a very small gas-bubble, which is
slowly formed at the circular, knife-edge opening of a capillary tube
immersed in the liquid perpendicular to its surface, just at the
moment, when the gasbubble is about to burst. The sharp edge
of the capillary tube eliminates the influence of the capillary angle.
In this way absolute measurements of the surface-energy are possible
in Ergs per em’., if the radius » of the tube, the specific gravity d
of the liquid at the temperature of observation, and the depth of
immersion 7 of the tube into the liquid, are known. To obtain the
true value of //, the readings of the manometer require to be
diminished by the hydrostatic pressure, corresponding to this depth
of immersion 7.

The method evidently can only give exact results, if the final state
of the gasbubble represents a state of equilibrium, and is thus reached

1) BorromLEy, Journ. of the Chem. Soc. 83. 1421. (1903) ; Lorpnz and Kaurier,
B. d. d. Chem. Ges. 41. 3727. (1908); Trauss, ibid. 24. 3074. (1891). Vide also:
MoryLewsk1, Z. f. anorg. Chem. 38. 410. (1903). :

*) F. M. JAgaer, Eine Anleitung zur Ausfiihrung exakter physiko-chemischer
Messungen bei hoheren Temperaturen. (1913). p. 36, 43.

3) M. Smon, Ann. de Chim. et Phys. (3). 32. 5. (1851); Canror, Wied. Ann.
47. 399. (1892).

4) FeusTeL, Drude’s Ann. 16. 61. (1995); Forcu, ibid. 17, 744. (1905).

Doo

passing a series of mere equilibria; that is: the method required to
be made practically a sfatic one, the final maximum-pressure being
independent of the special way, in which the pressure in the growing
gas-bubble is gradually augmented.

Thus a very slow rise of pressure in the growing gas-bubble is
necessary, and only in this way does it appear possible to eliminate
the small differences of pressure in the long connecting tubes of the
apparatus. For it is well known, that the adjustment of such small
pressure-differences takes a considerable time, if the connecting tubes
are relatively long.

If the radius of the capillary tube is 7 (in em.), the specific
gravity of the liquid d, and the observed maximum-pressure (in
Dynes) is H, then the surface-energy x (in Erg. pro em’*.) is calculated
from Cantor’s expression (loco cit.) :

oh hat

Dang am
-

The last two terms of the second member of this equation are
usually so small, that they can be neglected in comparison with the
experimental errors, as being corrections of the secondary order.

Nevertheless it has become clear, that a special correction requires
to be applied to the values calculated in this manner, because of
the fact, that in the theoretical deduction of this relation, a simpli-
fication is used, which cannot be considered quite legitimate. We will
advert to this correction lateron. (Vid.: VI; under general remarks).

With this limitation extended experience in the use of the method
leads to the conviction, that in the form it is used here, one ean
obtain reliable and, within narrow limits, reproducible results. It

has the advantage, that the surface-layer of the liquid is continually
renewed, thus the often-observed and troublesome phenomenon of
the alteration of this layer, need not be feared. Furthermore one
can vary the flowing gas at will with the different liquids, to prevent
eventual oxidations or reductions’). With these precautions the
results can be considered as accurate at 1650° C. as at ordinary
temperatures, if only no abnormally high viscosity is encountered
in the liquids; for this will destroy to some extent the reliability of
the measurements. The influence of the viscosity will be discussed
lateron in more detail.

Of all sources of error to be considered: inaccuracy in the

1) As long as the gas is indifferent, i.e. as long as it does not react with the
liquid, the results will be quite comparable, because experience teaches, that the
differences in the values of y, measured with different gases, are vanishingly
small in comparison with the experimental errors.

304

measurements of 7, of d;, of the pressure H/, of the reduction-factor
of the observed pressure on the manometer to mercury-pressure, of
the measurement of temperature, of the depth 7, ete., — the last
mentioned appeared to be the most significant. If all these errors are
assumed to be cumulative, the total effect upon the reproducibility
of the results, even at 1650° C. is still within about 1°/, of the
true value of x, and at lower temperatures about 0.6 °/, of that value.
With many molten salts, where // is very great and the viscosity
very small, the percentage error appeared to be even less than this,
not exceeding 0,4°/,. For our purpose this degree of accuracy may be
considered a very satisfactory one considering the enormous difficulties
of measurements at those extreme temperatures. lt is also question-
able, whether it will be possible to exceed this accuracy at such
high temperatures in the near future. And if this could be
done, it is very problematical whether much would be gained
for the purpose proposed. For experience teaches us, that at those
extreme temperatures all compounds are in a state of more or less
advanced dissociation, and it can hardly be of any significance to
express the surface-energy yx of such compounds in tenths of Ergs,
when the uncertainty in the values of x, caused by the inevitable
admixture of the dissociation-products, will surely be larger than
the correction-factors following from this increase in the accuracy
of the measurements.

§ 4. In this and the following papers we will successively give
an account: (1). Of the experimental arrangements and the manner
of procedure, including some instances, illustrating the general adapta-
bility of the method employed in different cases. (2). The results, obtained
between .—80° and + 270° C. in the study of a great number of
carboncompounds, in connection with their atomic constitution and the
validity of E6érvés’ theoretical views. (3). The experiments made to
determine the free surface-energy of molten salts, by means of the
method here developed. In this connection we will also discuss
more in detail the earlier attempts to solve the problem by the
method of capillary ascension in glass-tubes. (4). Finally a discussion
of the results obtained and a number of considerations of a more
general kind will be given, which are suggested by the study and
comparison of the data now available.

§ 5. Apparatus and Experimental Equipment.
a. In all the measurements pure, dry nitrogen, free from oxygen,
was used, because even at the highest temperatures this gas appeared

335

to be quite inert, and to attack neither the compounds studied, nor
the thermo-elements. Carbondioxyde can be used as a furnace-atmos-
phere up to relatively high temperatures, but is often not very suit-
able to be bubbled through molten salts under these circumstances,
because of its character as an anhydrous acid. Furthermore, at the
highest temperatures a_ slight dissociation is always to be feared.
At the same time the dry nitrogen permitted us to drive out the
air from the glass bulbs at lower temperatures, and completely
prevented the oxidation of the organie liquids studied.

The nitrogen employed was prepared from a mixture of pure
sodiumnitrite and ammoniumchloride, washed by distilled water,
and collected in a gasometer D (fig. 1). It was led through a series
of wash-bottles ¢, filled with an alkaline solution of pyrogailol, then
through otbers, filled with concentrated sulphuric acid (4, and finally
through a tube /, containing a large surface of freshly sublimed
phosphorous-pentoxide. The dried gas was preserved in a collector W,
closed with dry mercury. When needed, it was pushed on into a
inetal reservoir NV by means of a movable mercury-holder 7. Any
arbitrarily chosen pressure could be used which was then read on
the mereury-manometer A. The stopcock / carries a micrometer,
used in the regulation of the gas-current. In the study of the organic
liqnids, this reservoir .V was placed in the oil-thermostate (’, with
the glass-bulbs containing the liquids tod be investigated. In this way
the nitrogen was pro-heated to the temperature of observation, thus
preventing disturbances of temperature in the surface-layer of the

336

liquid due to the small gas-bubbles emerging from the ecapil-
lary tube.

The regulation of the velocity of flow of the gas was obtained
by means of the stopcock /# already mentioned, in combination with
two accurately adjustable pinch-cocks 6, which were inserted between
the reservoir N and the apparatus 2, carrying the capillary tube
and its adjustments. With this arrangement no undesirable cooling
of the surface, nor any lack of adjustment of the gas-velocity need
be feared as a considerable source of error.

b. The apparatus R consists of an upright rod H (fig. 2a), about
1 meter high, and made of brass heavily plated with nickel. It rests
on a heavy iron tripod fitted with three levelling screws. The vertical
rod can be rotated about its axis by means of two gliding discs O
at the foot of the pillar; they may be clamped fast when desired.
In this way it is possible to bring the horizontal arm, bearing the
adjusting arrangements and the movable counter-weight / into any
desired azimuth, and to fix its position by means of the clamps at
O and the collar at 7. With the aid of a handle provided with a
vertical rack and pinion, this horizontal arm can be raised to any
height and fixed there with proper clamps. This arm can also be
moved horizontally, in order to vary its length. Moreover it appeared
to be necessary to prevent a slight bending of the pillar A7 under
ceriain circumstances, by means of three steel supports attached to
H and to the iron tripod *).

Just over #, it has at its end a rectangularly bent steel support,
to which are attached the spiraltubes G’, made of gas-tight aluminium-
tubes, nearly 3 millimeters wide, and also the similar tubes U, which
however consist of much wider spirals. The latter form the continu-
ation of the aluminiumtubes G, and their ends are firmly fastened
to the horizontal beam, which is fixed in the laboratory just above
the whole apparatus. The two sets of spiraltubes appeared to be
necessary to ensure the desired mobility of the apparatus with regard
to the manometer-connecting tubes, and also to render an effective
operation of the adjusting devices possible. The great sensitiveness
of the manometer makes it necessary, that all the connecting tubes
of the instrument, as well as the spirals Gand U, should be wrapped
with a thick layer of white flannel or asbestos, in order to avoid
the disturbing influence of slight oscillations of temperature.

!) In the construction of this apparatus the mechanics D. VonkK and A. VAN
DER MB®ULEN, and the amanuensis J. J. FoukeErs, all of Groningen, have aided ina

most practical and effective way.

Prof. Dr. F. M. JAEGER. The Temperature-coefficients of the free Surface-
energy of Liquids at Temperatures from —80° till 1650° C. I. Methods
and Apparates.

{
2 Poe

Fig. 2a.

Proceedings Royal Acad. Amsterdam. Vol XVII.

ae
eter

The adjusting device FR is
represented on a somewhat
larger scale, in fig. 26; it is
fixed in position over a
resistance-furnace, and con-
nected with the capillary
tube made of the platinum-
rhodium-alloy and the therro-
element #. In this drawing
the rectangular support with
the spirals G are also plainly
discernible, together with the
hollow water-sereen ./, in
which a current of cold water
is continually — circulating.
This adjusting device consists
of two semi-circular parts
about 40 em. in diameter.
One part is permanently
attached to the apparatus FR,
the other can be fitted to it
by means of pins and short
tubes. The latter part has a
circular elass- window, where
upon the totally reflecting and
movable (around a horizontal
axis) prism /7 is placed. By
means of this prism the be-
haviour of the liquid in the
furnace can be observed and
controlled at every moment. At
temperatures over 1000° C.,

coloured green glasses are

Fig. 20, inserted in front of the prism.

With the protection of the waterscreen / it proved possible, to use
the manometer even at temperatures of 1650° C., without any
disturbance from the heat-radiation of the furnace. The furnace 6
is a platinum- (or nichrome-) resistance furnace of the usual type ’);
it has an inside wound heating-coil, and can be heated with a
central tube of alundum inside, up to 1400° C., and without such a

; 1) F, M. JAEGER, Anleitung u.s.w. (1913). p. 36.

335

central tube, to about 1680° C. The platinum-erncible is borne upon a
movable support of burned magnesite. which can be fixed to the
iron support A at any elevation.

The construction and arrangement of the part # of the adjusting
device is elucidated more in detail in fig. 8a and 36, a giving the

a. Fig. 3. b.

external view from one side, / a section through it, in a plane,
perpendicular to that of fig. 2a.

The apparatus consists of two metal dises P, and P,, of which
the dise P, with the tube S attached to it, can be moved horizont-
ally round the hemi-spherical button Q, and by means of the screws
A, and A, can be brought to any inclined position with respect to

6:
B09

P,. Wf P, is turned in a horizontal direetion, the screws A, and A,,
as well as the springs /’, and F,, (fixed at one end only) will glide
along the upper dise P,, the whole upper part thus remaining in its
original position. It appeared to be necessary to use a third serew
B&B for the adjustment of the capillary tube. It is first completely
loosened from P,, then after ?, and P, have been brought into the
desired relative position, the screw / is turned so as to touch the
dise P, slightly: in this way the relative position of the two plates
is completely fixed. The tubes S and J}, (not shown in fig. 3a) are
bent rectangularly upwards, and fitted, to the spiral tubes G. By this
arrangement an undesirable motion of the apparatus (during the
adjustment of the capillary tube), due to the influence of the stress and
weight of the connecting-tubes, could be sufficienly prevented, while
the mierometerscrew J/ at the same time remained in working
condition. This serew J/, fitted with a drum WN and a seale D,
serves to move the discs ?, and P, together through a known ver-
tical distance. The serew has a pitch of 1 mm. exactly, the cireum-
ference being divided into one hundred equal parts, it thus permits a
vertical motion of 0,01 mm. to be measured at DY. This is more
than sufficient, because experience proves, that no adjustment of the
capillary tube in contact with the surface of the liquid, can be
made with greater accuracy than about 0,1 mm. During this vertical
motion the drum N and the micrometerscrew J/ remain in their
original positions, because they can only move in a horizontal direction
round the fixed part V of the apparatus. A vertical scale 7, provided
with divisions for about 30 mm., is moved at the same time with
the two dises P, and P,. In this way the number of revolutions of
N can be read directly. Concerning the adjustment of the capillary
tube with respect to the surface of the liquid, which can be made
either visually, or with the aid of the manometer-readings, the neces-
sary directions will be given below.

§ 6. It was soon found, that the adjustment of the slight diffe-
rences of pressure in the long connecting-tubes happened so slowly,
that considerable errors in the measurements must inevitably occur.
For this reason all the capillary tubes, with which the apparatus
was originally equipped, were replaced by 5 mm. gas-tight tubes.

These tubes were made in part of lead, in part of aluminium '

) and,

1) Also tubes of cellon, made by the Rheinisch-Westphdlische Sprengstoffe A.G.
in Céln a/Rh., and which may be bent in hot water, can be recommended for
such purposes. The material is gas-tight and fire-proof; however it is difficult to
obtain it from the plant in any desired shape.

340

where neeessary, were wrapped with a thick layer of asbestos.
A considerable time had to be spent, to get all connections
completely free from leakage ; but when this was accomplished the
indications of the manometer were so prompt as to be practically
instantaneous. After this no errors from this source needed to be
feared.

The connection of the tubes occurred in the usual way, as with
high-pressure apparatus; these connections appeared fo remain gas-
tight, even after a longer use.

§ 7. For the measurement of the maximum pressures to be observed,
originally a mercury-manometer of the type indicated by ScHEEL and
Heusk') was used. The instrument had been modified in some details ;
but it appeared not to be suitable for our work, because of the
necessity of always reading tivo menisci, which was very troublesome
with a pressure varying continually up to the moment, when the
maximum was reached.

This instrument therefore, which is very well adapted for static
measurements, was only employed for the calibration of the manometer
finally constructed. This second instrument was built on the principle
of the manometer with two liquids.

In the measurements of organic liquids, it was necessary to avoid
any contamination of the connecting-tubes with the vapour of the
manometer-liquids, so that only pure mercury could be used as one
of the liquids in the manometer. For the second liquid we chose
normal octane. This liquid is very thin, behaves very well in contact
with glass-walls, and, if completely dry, appeared not to blacken
the mercury-surface, even after long exposure. The vapourtension at
20° C. is only 10,45 mm., the viscosity at 238° C. is 0,0052 C.G.S.,
the surface-tension at 25° C. is 21,3 Erg. pro em?*., and the expansion-
coefficient is O0,00t18. After repeated fractional distillation, its boiling-
point was found to be 125° C. under 758 mm. pressure, and its
specific gravity at 25° C. was: dy = 0,6985, i.e. about 19,38 times
less than that of mercury at the same temperature. This last relation
operates in the following way :

Suppose the diameter of the wider tube (fig. 4) to be D, that of the
capillary tube d and the mercury-meniscus to the right to be @ m.m.
higher than to the left. Then the height of the octane-column to the left

1) ScugeL und Heuse, Ein heizbares Quecksilbermanometer fiir Drucke bis
100 m.M.; Mitt. aus d. Phys. Techn. Reichs-Anstalt, Zeits. f. Instr. 30, (2). 45,
(1910).

341

. / . at wri ] ind > 1 *
Side (c) 1s: — m.m., 1f e = ——- — 0.0516. Suppose 4p to be the increase
é 19,38

of pressure (in m.m. mercury), necessaryon the right side, to sink the

mercury-surface just 1 m.m. The mer-
aed cury-surface on the left side, will then
rise just 1 m.m., and the octane-
column from ¢ to c’ (=Ahmm.),

D
over ; m.m. The difference of level
ad

of the two mercury-surfaces is now:
(a—2) m.m., and the octane-column

: a D :
to the left =(-— 1+ i) mm. This
é C

corresponds to a mereury-column of:

a D Dé
—— {+ —)e={a—e+— |mm.
& d d

Therefore the necessary increase

fost?)

of pressure on the right side (= A p),
is evidently :

D
(« —e+ 7°) — (a—2) m.m. = 2 +

D
Fig. 4. +3 Ge 1) m.m., and thus :

€

or:

Soi

The reciprocal of the expression between }} will be seen to be
the “multiplication factor” /’ of the instrament. With small values of
é, (2—e) will differ little from 2; therefore it is necessary to reduce
d ‘ _ :
p* much as possible and to make F' as large as possible.

In our instrument these conditions were fulfilled in the following
way: preliminary experiment gave d = 2,406 m.m’, and D = 1257,36
d Bee
m.m’; thus p — 900191, and / becomes ea. 18. The reproducibility
of the same pressure appeared to be possible within a limit of
23

Proceedings Royal Acad. Amsterdam. Vol. XVII.

342

O,1 m.m. octane, which corresponds to 0,005 m.m. mercury-pressure.
The accuracy of the measurements was within the limits 0,05 and
O,1°/,; it was greater than necessary in comparison with the magni-
tude of the systematic errors of the method.

The final form of the manometer, as it was used in all the measu-
rements is shown in fig. 5. This final form resulted from a great
number of experiments and numerous changes. The tube A is made

from the best quality of hard-glass, and connects two bulbs B of
ca. 39,9 mm. diameter with a volume of about 1380 cubie centi-
meters ; they possess 1,2 mm. wall-thickness. The bulbs must carefully
be chosen, and be completely cylindrical throughout their full length.
As the height is about 110 mm., it is not easy to find tubes of the
desired quality. The capillary tube must have an internal diameter
of about 1,7 or 1,8 mm., and a wall-thiekness of about 2,5 mm.,
and must be suitable for precision-measurements and carefully

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343

calibrated. Its length is about 600 mm. Another tube D, of equai
length, but about 7 mm. in diameter, serves as a connection to
the gasapparatus. The capillary tube (bears at its top a silver
tube EH, overlapping the tube C; it communicates with C by means
of a silver capillary fube, and can eventually be easily removed.
The tube C' is widened at its top-end to about 10 mm.. and con-
nected with the silvertube in such a manner, that no dust of the
room can contaminate the capillary tube €, while at the other end
it communicates with a small reservoir &, partially filled with octane ; —
this for the purpose of preventing, as far as possible, the evapora-
tion of the liquid in C. For this reason F& is placed in the same
thermostat as the manometer-tube. The connection of R with the
atmosphere (or with the nitrogen) is made by means of an adjustable
glass tube G, which opens into a very wide connecting tube leading
to a large flask with three mouths, which is provided with dry
caleiumoxide, with a small manometer, a tube with drying materials
and with a connection to the nitrogen-holder. In the fig. 1 the octane-
reservoir is indicated by C, the silver capillary tube by |S, the three-
mouthed bottle by /. In the same way the manometer is indicated
by w, the drying-tube by z,, and the connecting tubes by Qand H.
The manometer is arranged in a glycerine-thermostat of the type
usual in dilatometer-thermostats (KOunLER), however its construction
has been varied in some particulars. The thermostats commonly sold are
quite unsuitable for this purpose, because they commonly show leakage
or will show it very soon; then they cannot be used for glycerine,
which was chosen because of its refractive index and low volatility,
because this liquid will dissolve the paste used in setting the glass-
windows, within a short time. Two rectangular frames were there-
fore made of brass, about 38 em. broad, and soldered to the thermo-
stat. These frames were smoothed as perfectly as possible and
possessed an inside furrow about 5 mm. deep and 1 em. broad, in
which a layer of very thin rubber paste, fixed by a solution of rubber
(in carbonbisulphide), held the two glasswindows fast. Then a second
layer of plastic rubber was applied, and the second brass-frame was
uniformly pressed against the former with some forty screws. The ther-
mostat holds 22 kilos of glycerine, but even after long use it shows no
leakage. By means of a toluene-regulator 7’ a spiral-stirrer J/ with
motor A, and a pair of small burners 4, and 6,, the instrument is
kept at 25°,1 C. +0°,1. Z is a thermometer, divided in 0°,1 C.
The support # is suspended from the lid H by means of four
movable rods /. The manometertube can then be brought into a
vertical position by means of the screws s,, s,, s; and s,. Within
23*

344

the thermostat and just behind the capillary tube C a glass-scale V
is introduced, which possesses a very accurate division in 0,2 mm.,
by means of very fine lines (38 microns) made by the Compagnie
Genevoise. The scale is read with a telescope and ocular-micrometer
by the same firm, and at a distance of about 2 Meters; the enlarge-
ment is about 25. During the readings the motor A’ must be stopped
for a moment, because even the slight vibrations are rather annoying.
The thermostat is wrapped with felt except for the narrow opening
needed for the readings. Behind the manometer a ground glass-plate
is applied, which is illuminated by two long, tube-straight-filament
incandescent-lamps, each of 50 candle power. Between the lamps and
the thermostat, a watertank with glasswindows, is introduced, to
prevent heat-radiation into the thermostat. With this mode of lighting
the fine divisions and the octane-surface are seen very distinctly,
without any observable parallax, against an illuminated background
and readings can be made with extreme accuracy, with the aid of
the movable cross-hair of the micrometer. However readings of less
than O,1 mm. appeared to be unnecessary, because of the fact, that
the mean oscillations in the successive determinations of H, were
about + 0,05 mm. octane, the total uncertainty therefore being about
0,1 mm. octane-pressure, or about 0,005 m.m. mercury-pressure.

§ 8. To bring the capillary tube into a vertical position, a mer-
curymirror was used: by means of the screws A, and A, (fig. 3d)
the position of the capillary tube is altered until its mirrorimage
will seem to be in a straight line with the tube; the position of P,
and P, is then fixed by means of the screw B. The capillary
tube itself was origimally made from purest, iridiumfree platinum ;
this however appeared to be too soft, and so an alloy with 10°/, or
20°/,

suitable capillary tubes for this purpose from the shops in trade.

of rhodium was used afierwards. It is impossible to get any

Therefore the rough capillary tube with its widened (ca. 6 mm.)
upper part, was purveyed by Herarvs; the lower end was then
carefully turned off on the lathe to a conical and sharp edge, which
Was once more whetted on an oil-stone, if necessary.

With some practice in this way the repairs of the damaged or
worn capillary tubes can be accomplished within a relatively short
time; and it proved to be possible to obtain a cross section of the
tube, which in several directions did not deviate more than about
0,002 m.m. from a pure circular shape, while the rim of the lower
end measured no more than 0,01 mun.

The cross section was determined by means of a_ horizontal

345

microscope, provided with a micrometer of the movable-cross-hairty pe
with divided ‘cylinder: the diameters were measured in ten or twelve
directions, the squares of these numbers added, the total amount
divided by the number of measured diameters, and the square root
from this value considered as the true value for 27. With regard
to the measurements to be made at extreme temperatures, and on
account of the fact, that a whetting of the capillary tubes appeared
to be necessary almost after every set of measurements, no tubes
with a radius of less than 0.040 ¢c.m. were used during these
investigations.

The platinum-rhodium-tube ends at its upperside in a carefully
smoothed, polished brass disc; the tube of the adjustment-apparatus
R possesses just such a smoothed circular brass-plate. As a washer
between the two discs, a very thin ring of mica is used ; the capillary
tube is screwed against the end of the apparatus #&, and both tubes
are then drawn together by the aid of two steel-keys, till the discs
are firmly pressed against each other: in this way an absolutely
gas-tight connection is obtained. This closure appears to be a very
perfect one, and if it is often controlled, no leakage needs to be
feared from this source.

§ 9. The temperature-measurements were made with our calibrated
thermo-couples and compensator-equipment, in the way always used
in this laboratory *). Originally it was planned to connect the platinum-
wire of the thermocouple directly to the end of the platinum-rhodium-
tube by means of the oxygen-flame; this tube then being considered
as the positive end of the thus obtained thermo-couple. However
the perfect isolation of the tube at very high temperatures appeared
to be a serious obstacle; so the idea was abandoned, and the usual
thermo-couples, provided with isolating Marquarpt-capillaries, was
fixed to the platinum-rhodium-tube by means of fine platinum-wires ;
at the other end they were connected with the ice-box J (fig. 2a).
The wires of the element are bare over a distance of about 5 e¢.m.
from the junction; this point lies in the same horizontal plane as the
lower end of the capillary tube, thus being in immediate vicinity
of its opening. Of course all platinum parts within the furnace
(crucibles, coils, ete.) need to be made from iridiumfree platinum,
to prevent contamination of the thermo-couples as much as possible.

§ 10. The adjustment of the capillary tube with respect to the

1) F. M. Jagger. Kine Anleitung u.s. w. (1913), vid. p. 16—24,

346

surface of the investigated liquid, can be made in the following way.
The surface of the liquid is strongly illuminated, and now attenti-
vely the moment is watched, when the capillary tube, while screwed
downwards, will just make contact with its mirror-image, seen in
the surface of the liquid. At temperatures above 500° C. ordinarily not,
and above 1000° C. never, a special illumination of the surface is
necessary: for the liquid radiates then sufficiently to make the obser-
vation of the moment of contact a very accurate one. If the tem-
perature however becomes 1400° or higher, it is often no longer
possible to discern the end of the capillary tube from the surround-
ings: in these cases the adjustment must be made by the aid of
the manometer, as is further below described in some details.

This visual method involves, even after sufficient practice an-
uncertainty of about O.1 mm. in the case of organie liquids, which
corresponds to ca. 0,006 to 0,008 mm. of mercury in the determi-
nation of the maximumpressure /7. The percentage error of the obser-
vation caused thereby, is about from 0,4 to 0,7°/,; this uncertainty
in the adjustment of the capillary tube on the surface of the liquid,
really appeared to be the chief source of the errors, as has been said,
and is hardly or not to be avoided. However just at higher tempera-
tures this and in the case of molten salts, where / is very great, the
accuracy of the method is only slightly affected by this uncertainty.

The other way of adjustment is this, that the capillary tube is
approached quite near to the surface of the liquid; then carefully
a flow of nitrogen is applied, and then, wlile the capillary tube is
slowly lowered by means of the micrometer-screw, by observation
of the manometer, just the moment is determined in which a sudden
rise of pressure, caused by the contact of the tube with the surface
of the liquid, is seey. In this way the proposed aim was also often
attained ; but the uncertainty appeared to be here of the same order
of magnitude, as in the case of the visual method. Furthermore it
is necessary to ascertain that the small column of liquid, which
often remains hanging in the capillary tube, if turned upwards,
has no misleading influence on this observation ; first this column of
liquid needs to be biown out by the aid of a sufficiently strong flow
of nitrogen, before the contact with the liquid is made in the way
just described.

§ 11. The manometer was originally calibrated by immediate
comparison with a mercury-manometer, which was read by means
of a cathetometer and a divided scale. The paralaxis appeared to
be extremely small; the accurate adjustment of the mercury-surfaces

was highly facilitated, by putting a half transparent and diffusely
illuminated sereen behind the manometertube, on which screen black
lines were drawn under an inclination of about 25° with the horizon
in such a way, that their mirror-images in the mercury-surfaces
were visible thereupon as a bundle of very fine and easily discern-
ible dark lines. After the application of a certain excessive pressure
to both manometers, two observers read siimultangously both instru-
ments; the manometers were connected with each other by a short,
very wide tube, sufficiently protected against temperature-oscillations.
As an example of this calibration, the following series of obser-
vations may be reproduced here in deta‘! :

Mercury manometer. Octane-manometer (25° C.)
Temperature: — Observed Pressure Rise of the octane column
pressure : 02 C m m.m.

12,°4 7,00 6,99 124.8
12,°6 10,23 10,21 181,8
12,°9 12,45 12,43 220,8
112.23 9,13 914 162,2
12,°6 13,14 13512 235,3
13,°0 13,78 13,75 245,0
13,°4 12,44 122) 219,9

A rise of the octane over 1 m.m. is therefore equivalent to an
excessive pressure of 0,0561 + 0,0003 m.m. mercury (=74,8+0,4
Dynes).

After it was found, that our measurements of the free surface-
-energy of purest water, were in so complete agreement with those ot
VoLKMANN, Brunner, Worry, among others, we afterwards repeated
this calibration in most cases by the accurate determination of x for
pure water, at three or more temperatures. The factor of enlargement
F of the manometer appeared after all to be only slowly variable :
in Octobre 1913 e.g. it was: 17,91 in February 1914: 17,86; in
June 1914: 18,10; ete.

§ 12. The molten salts to be studied were in most cases placed
into crucibles of iridium-free platinum; for the organic liquids we
used vessels of glass of the shape indicated in fig. 7. A eylindrical
glass tube P with rounded bottom possesses a narrower neck at
A; a wider glass cup A is fixed round it. A tube G, closed with
a stopper A, which is firmly fixed round the platinum capillary tube,
possesses a collateral tube 46, which ends into a drying tube G, which
communicates with the free atmosphere at Z, and which is filled with

odS

quick line. The vessel P is cleaned, care-
fully dried, and if possible several times washed
out with the vapours of the boiling liquid V;

—_
N

then it is filled again with a fresh quantity
of the liquid V’, while a layer of dry mereury
is poured into IW. The tube is placed into the
oil thermostat, and the capillary tube with
C the part GBC fixed to it, is lowered then,
till G makes contact with the surface of the
mercury. If V has reached a constant tempe-
rature, the capillary tube is further lowered
by screwing it so far downwards, as is necessary

Seok
SA

rr ye
ps3

to bring it just in contact with the surface
of the liquid. This enclosure by means of mer-
cury insures a sufficient freedom of motion,
while the Jiquid at the same time can be shut
off from the air’), and the small bubbles of
nitrogen, emerging from &, can freely escape
at Cand Z,. All communications with the free
atmosphere, which are present in the connect-

ing tubes of fig. 1, are provided with drying
apparatus, filled with dry caleium-oxide.

§ 18. All measurements now were made in such a way, that
always the zero-point was controlled anew accurately, before and
immediately after each reading of the manometer. One needs to
ascertain first, that all connecting tubes (fig. 6) are free from
leakage, and that a diminution of the speed of gas-flow has no
influence any longer on the value of the maximum pressure H.
After the highest point of the octane-column is reached the liquid
falls suddenly back to a point, which depends upon the speed of
gas-flow, and then it begins to rise again slowly ; ete. By experience
one learns to estimate the reliability of the measurements, by the
particular motion of the octane in the manometer ; finally the repro-
ducibility of the value of H needs to be considered as the decisive
criterion for answering the question, if the real pressure of equili-
brium in the gas-bubble has been measured. Even when the speed
of gas-flow is varied within certain limits, this value appears to be
reproducible quite exactly. The influence of the variation of the
depth of immersion 7 on the manometer-readings, can be found by

1) For if necessary, the air in the vessel P can be first substituted by a current
of pure nitrogen.

349

repeated lowering of tue capillary tube over known distances by
means of the micrometer-screw J (fig. da), and by repeating the
readings of the manometer in every case.

In all calculations we used the number 1383.2 Dynes as the
equivalent of 1 m.m. mercury-pressure at 0° C.; the surface-enerey
is expressed in Erg pro e.m.’. *)

§ 14. As an illustration of the general availability of the method
at all temperatures between — 80°C. and + 1650°C., we will give
here already some few instances, relating to: water, some colloidal
solutions, some organic liquids, and some molten salts. The specific
weights of the organic liquids were, after a pyenometrical control
at 25°C., calculated for other temperatures from the thermic expan-
sion-formulae, if they were already sufficiently and accurately
known in litterature.

In other eases the densities at 25°; 50°, and 75° C were pycnome-
tricaily determined, and a quadratic relation with three constants
was calculated from these observations ; this relation was used then
afterwards for the determination of the other specific weights. In
the case of the molten salts the specific weights must again be
- determined by means of a method to be described later. To use the
numbers for the densities with more than three decimals, has no
real significance, because the experimental errors are always of an
order so as to make the influence of more decimals of no importance.

§ 15.

The curve (fig. 8) is evidently concave with respect to the tempe-
rature-axis ; the temperature-coefficient of «is only small, and amounts
to from 0,9 to 1,05 Erg. per 1° C.

Furthermore in this diagram the corresponding curves are repro-
duced for a colloidal solution of tron-oxide and for a colloidal solution
of silicium-dioxride ; from both solutions the electrolytes were elimi-
nated as far as possible by longer continued dialysation.

It appears, that both curves are evidently situated somewhat above
that for the pure solvent, although the deviations for 7 from the
values for pure water are only very small. The temperature-coefti-
cients are analogous to those for the solvent itself; however in the
ease of the colloidal iron-oxyde it could be observed, that if
such a solution was heated toa higher temperature, and if afterwards
the determination of the surface-energy was repeated at the original

1) The result is after all the same, as when expressed in “Dynes pro c¢.m,”.

350

Ie
Water: H,0.
0) eee ee ee
Bo ese edad
ea Surface: Sneeitie rie:
HG — | | tension x in MERACe:
| &c jin mm. mer-| . iEre. procm?,) gravity d).| Cnerey “in
B~ Gat ere) Dynes | ea | is Erg. pro cm?.,
| PUN Ton SN ween OS Ese: 5) 2 |
0.4 | 2.593 3457 75.8.) 11.000. |) esaae
2 2.583 i 3444 13%) | 1.000 518.9
| 16.4 | 2.498 3330 | 73.0 0.999 502.1 °
| 18.4 2.488 3317 TPAST| 0.999 500.0
IP aay. 2.456 3275 TY 0.997 493.6
35 2.398 | 3197 70.0 0.994 483.1
37.8 | 2.383 | 3177 69.7 0.993 481.3
55 | 2.291 3055 66.9 0.986 464.3
74.2 | 2.178 | 2904 63.6 | 0.975 | 444.8
98.5 | 2.014 2688 58.9 0.960 415.8
99.9 | 2.004 2672 58.5 0.959 414.0

Molecular weight: 18.02. Radius of the Capillary tube: 0.04385 cm.
Depth: 0.1 mm.

The value of x at 20° C. is thus 72.6 Erg. pro cm.?; it is more
probable, than the often accepted value: 75.') The here mentioned
numbers are in full agreement with those of VOLKMANN 2) (1880),
BRUNNER 8) (1847) and Wor.ey *) (1914); they differ however consi-
derably from the values published by Ramsay and SHIELDS 5),

lower temperature, for x a value was found, somewhat different
from the formerly observed one with a fresh solution. Thus, although
the iron-oxide-solution remains ‘‘stable” until relatively higher
temperature and in general does not coagulate on heating, it seems
however yet to undergo some zrreversible change, which is manifested
by the somewhat changed value of the free surface-energy.

The described method is evidently also adapted for the investigation
of colloidal solutions of different nature; it is planned to determine
these values so highly important for the chemistry of the colloids
in the case of a more extended series of colloidal substances.

1) FREUNDLICH, Kapillarchemie (1909), p. 28.

2) VoLKMANN, Wied. Ann. 11, 177, (1880); 17, 353, (1882); 58, 633, 644,
(1894) ; 56, 457, (1895) ; 62, 507, (1897}; 66, 194, (1898). :

3) BRuNNER, Pogg. Ann. 70, 481, (1847).

+4) Wor.EY, Journ. Chem. Soc. 105, 266, (1914).

5) The other points mentioned in the diagram, have the following significance :

W=WenperG, Z. f. phys. Chem. 10, 34, (1892); S—=Sre, Diss. Berlin,
(1887); .R=RayweicH, Phil. Mag. (5), 30, 386, (1890); Ss = Senris, Ann. de
VUniv. Grenoble, 9, 1, (1887); H=PRocror Hatt, Phil. Mag. (5), 36. 385,
(1893); M—=Macin, Wied. Ann. 25, 421, (1885). These data were obtained by
very different methods; they are evidently appreciably deviating from each other.

351
§ 16. Aliphatic Derwatives.

II.

ETHYLALCOHOL: C,H;.OH.

o :
2} Maximum Pressure H Surface- ve, | Molecular
gO = eee es tension 7 Specific | Surface-
o We | rs
eae lent saan oes ee in Erg. pro | gravity d,,| energy ” in
S~ eae of 0° C. ae Dynes | cm?. pe pro cm?.,
— ———_ : — : : i =
—79° 1.066 1421.2 30.6 | 0.886 | 426.2
—24 | 0.881 1174.5 25.2 0.820 | 369.6
0.1 0.825 | 1086.5 23.3 OF SOT = 3 345.4
25 0.746 995.7 ZS 0.786 321.4
35 0.724 965.2 20.6 0.777 313.1
55 0.667 889.2 19.1 0.759 | 294.9
74.5) 0.617 822.6 17.6 0.741 276.1
| Molecular weight: 46.05. Radius of the capillary tube: 0.04385 em.

Depth: 01 mm.

The alcohol was completely anhydrous and was therefore preserved
in a bottle with drying-tube. At the boilingpoint (78°.4 C.) the |
value of z is 17.0 Erg. pro cm*. The mean temperature-coefficient of
» is only: 0.94 Erg.

Il.

Acetic Acip: CH,. COOH. |

: |

= Maximum Pressure H Surface- | ei | Molecular

s S |-— | tension x | ppecitic | Surface-

oOo || se | .

Sulla ate ae | in Erg. pro | gravity d,,| energy ” in

aco cury of 0° C. | in Dynes | em?. eal Erg. pro em?.

= | | | |
| * ) | : | =

26° | 0.943 | 1257.2 ON ele ate046 8) 400.7

34.6 0.914 | 1218.5 26.1 | 1.039 390.1

55 ORGA2 ile Sioa. eNO ed Oot 1/4 Ge aos

70 0.787 | 1049.3 22.4 | 1.010 | 341.2

98.5 | 0.691 | 921.3 19.7 0.987 | 304.7

Molecular weight: 60.03. Radius of the capillar tube: 0.04385 em.
Depth: 0.1 mm.

| By repeated freezing and distilling, the liquid was thoroughly
purified; its boilingpoint was 118°.1 C. The temperature-coefficient is
between 26° and 55° C.: 1.3 and preserves that value up to the boiling-
point. At the last temperature the value of x is: 17.7 Erg. pro cm2?.

352

Specific Surface-energy
in Ergs pro c.m2,

* Observat. of Vorkmann, and of BruNNER \ x
© Observations of Wor.ry (1914) d
© Observations of JancER (1913) és

* Observat. with SiQ,-, and Fes O3esol. (1914)

55 eee
10° 0° 10° 20° 30° 40° 50° 60° 70 80° 90° 100° Temperature.

Fig. 8. Surface-tensions of pure water and colloidal solutions
at different temperatures.

Although acetic acid doubtless is a gradually dissociating liquid,
and in accordance with this manifests only a small temperature
coefficient of uw, this last remains constant, contrary to the cases,
where the curves appear to be concave or convex.

z Maximum Pressure H Surface- Specifi | Molecular
g° ! ——| tension z EERE Surface-
oO . .
Beg |e ‘ Si ike in Erg. pro gravity d,, energy » in
s~ cury of 0° C. in Dynes em?. “| Erg pro cm?.)
—19.9| 1.237 1649.2 35.5 1.095 985.3
0.7} 1.167 | 1555.8 332) 1.075 941.2
8.5 1.142 H 1523.2 32.9 1.068 928.4
2oE2 1.077 1435.9 31.0 1.050 | 884.8
34.5 1.044 1391.9 30.0 1.041 861.2
50.1 0.994 1325.2 28.5 1.025 | 826.6
69.2 0.920 1226.8 26.3 1.005 | 712.9
102 9.804 1071.8 23.0 0.969 692.5
124.5 0.723 963.9 20.6 0.945 | 630.7
144 0.660 880.2 18.8 0.924 584.3
148.7 0.649 866.4 18.5 0.919 | Silla
171 0.571 761.6 16.2 0.896 | 513.9
= ale Ns eee Par
Molecular weight: 160.1. Radius of the capillar tube: 0.04385 em. |

Depth: 0.1 mm.

The compound boiled constantly at 1979.3 C.; at —50° C. it is
solidified. At the boilingpoint the value of ~ is about: 13.7 Erg pro |
em?,; the temperature-coefficient of » has as mean value: 2.52 Erg.

§ 17.

Aromatic Derivatives.

BENZENE: C,H.

= Maximum Pressure
gO ie :
Bo

a6 in mm. mer- Dv
@ |leury of 0°C.; ™ ~~ ynes
=

(o}

By | ASOT) 1436.7
9.5 1.055 | 1406.5
25.1 0.969 le ed2O1R9
35 0.920 1226.5
55 0.836 1114.6
74.6 0.757 1009.2

Molecular weight: 78.05.

Surface-
tension 7% in
Erg. pro cm?.

WNMNONMWW
=—-WOANOO
DwAW1W 0

Depth: 0.1 mm.

Although the mean value of the temperature-coefficient of » oscil-
lates round 2.0 Erg., the dependence of » and ¢ is not a linear one:
between 5° and 25° the coefficient is: 2.65; between 25° and 55° C.:
2.12; and between 55° and 75°: 1.95 Erg. At the boilingpoint (80.°5), |

e value of % is: 20.7 Erg.

Specific

895
.889
873
862
841
817

ooococoo

Radius of the Capillar tube: 0.04385 cm.

| gravity Ayo)

Molecular
Surface-
energy in
Erg. pro cm?.

607.7
596.6
553.8
530.3
487.8
451.4

ANISOL: CH,.O, C Hs.

| @o | |
Es Maxi ressur
aS | Maximum Pressure H Sirfake: Specific Molecular
30 Near, ; ———| tension y in aon
= jin mm. mer-| . Erg. proem2,) gravity d4o a eal
3" joury of 0°C. | me Dec | a 1 Erg. pro em?.
| | 1
] = = |
|—-21° hss Ai) WIEEER G7 4 39.3 1.029 874.8
| 0.4 1306) | elAliad 37.3 1.010 840.6
25 1210) ee eee OS cyl 34.6 0.987 UNS) |
45 1137) eal lo l6eo: 32.5 0.970 15255) 7)
74.4 12022 4 i 136225, 29.1 0.942 | 687.0
| 90.8 O2962) ey 1282/52 27.4 0.927 653.9
| 110 0.875 1167.3 24.9 0.907 | 602.9
| 134.7 O65: 4) 102022 21.7 | 0.882 | 535.3
151 0.700 |} 932.9 19.8 | 0.865 494.8 |
| |

| Molecular weight: 108.6. Radius of the Capillar tube: 0.04352 em.
Depth: 0.1 mm.

The boilingpoint was constant at 151.97 C.; at —50° the substance
crystallizes to a beautiful, hard aggregate of crystals. The tempera-
ture-coeflicient of » increases, just as in the case of water, with |
increasing temperature: between —21° and 45° C, itis: 1.88; between |
45° and 90°.8 C. it is: ca. 2.14; between 91° and 151° its mean value is: 2.63. |

VII.

PHBNETOL: C,H;.0O.C,H;.

|
5 _ | Maximum Pressure H | Surface- Molecular
re -| tension x Specitic Surface-
© | |e : B Rec
as iM er |} naDyhes ‘s aid se ae a's nae ‘A zs
2 eaty of O° CC. : ike Pe) PXORC MS
| | |
= 21° 1.289 1718.5 36.8 1.006 902.1
0.3) 1.213 1617.7 34.6 0.986 859.6
25.2! 1.117 | 1489:0 31.8 0.962 803.1
45 1 OSes el S8an3 29.5 0.943 755.0
74.3} 0.931 | 124038 26.4 0.914 689.9
90.6| 028715) i e lGie3 24.8 0.899 655.3
| 110 0.813 1084.6 23.0 0.889 | 612.3
184.7 0.734 | 979.0 20.7 0.855 565.6
150.1 0.687 915.9 19.3 0.849 529.8
160.5) 0.651 868.6 18.3 0.839 506.3

Molecular weight: 122.1. Radius of the Capillar tube: 0.04352 ecm. |
Depth: 0.1 mm. |

The boilingpoint is constant at 168°; the substance solidifies at
— 50° C. to an aggregate of long, colourless needles. The tempera-
ture-coefficient of » can be considered as constant, its mean value
being: 2.14 Erg.

355

ei We see ett a inl eee PS [ee LEE a
Molecular weight: 148.1. Radius of the Capillar tube: 0.04439 em.;
in the with * indicated observations, the |

radius was: 0.04352 em.
Depth: 0.1 mm.

The boilingpoint was constant at 230°.5 C.; the meltingpoint is: 2195 C.
Between 25° and 75° C. the temperature-coefficient of » is about: 2.53;
later on it becomes fairly constant: 2.25. At the boilingpoint the value
of ~ is: 1.68 Erg pro cm’.

GuasAcoL: CH,0.C 5H, . OH (1,2).

oO
5 Maximum Pressure H | :
Es : : Surface- | Specific | Molecular
$0 tension yin | | SEO
| Ss inmm.mer- . Erg. proem?.| gravity dy.) Cnerey “in |
| 5° leuy of o°¢,| i Dynes | jis | + Erg. pro em?.
| | |
| 26° 1.377 1°36.4 43.3 | 1.128 994.0
45.5 1.302 1736.4 40.9 1.109 049.6
66.5 1.224 1632.4 38.4 1.088 | 902.9
86 1.156 1540.7 36.2 1.058 861.8
106 1.087 | 1449.1 34.0 1.048 819.7
|125 1.024 1365.8 32.0 1.029 780.9
Hi4GmeeeeKOcose) SNP ri26500) | 12086 |) sl eitoos), I") "7394
166 0.874 | 1166.0 27.2 | 0.988 682.1
1184 0.803 1070.2 24.9 | 0.970 632.1
206) oF 1027189, MIGRL COS TT asp 10,2253 0.948 | 574.8
| |

| Molecular weight: 124.06. Radius of the Capillar tube: 0.04803 cm.
Depth: 0.1 mm.

The substance boils under 24 mm. pressure at 1069.5 C.; the melting-
point is 32° C. The temperature-coefficient of » is between 26° and
| 46° C.: 217; between 146° and 206° the curve is feebly convex to
| the f#axis and the mean value of the coefficient is therefore about:

2.66 Erg.

RESORCINE-MONOMETHYLETHER: C,H, (OH) . (OCHS) (1,3).

EI é Maximum Pressure / 45 Molecular
5 | Surface- Specific Saree
50 a — | tension x in :
= in mm. "| eravity d,.| energy in «
BF mercury of | in Dynes | Erg pro cm?. era ace Erg’pro cm?,
a
—— - = : =
—20° 2.622 | 3495.6 83.1 1.181 1850.1
OTF Pee lS6S6 een ee 211 el 51.6 1.161 1161.9
25.9] 1.462 1948.8 46.0 1.136 1051.0
45.9) 1.380 1840.5 43.4 1.119 1001.6
66.5) 1.318 1757.3 41.4 1.102 965.2
86.5 1.252 1669.7 39.3 1.082 927.5
107 1.196 1594.9 37.5 1.061 896.7
125 1.140 1519.9 35.7 1.044 862.9
146 1.075 1433.2 33.6 1.023 823.2
166 1.009 1345.0 31.5 1.003 782.0
184 0.956 1274.2 29.8 0.986 748.2
206 0.862 1149.4 26.8 0.965 682.6
|

Radius of the Capillary tube: 0.04803 cm.
Depth: 0.1 mm.

Molecular weight: 124.06.

Under 25mm. pressure, the compound has a boilingpoint of 144°C.

The observations over 180° C. relate to the substance already
slightly dissociated, as was seen from the brownish colour of the
liquid. At —79° C. it becomes glassy, without indication of crystal-
lisation. At 0° and — 20° ©. also, the viscosity of the liquid is still
enormous.

XI.

a OOK?

—22° 1.520 2026.5 44.3 1.104 1107.9

0 1.419 | 1892.3 41.3 1.084 1045.6

25 1.325 1766.2 38.6 1.064 989.4
45.3 1.250 1667.0 36.4 1.046 944.3
70.5) 1.166 1554.4 33.9 1.022 893.2
90.1 1.090 1453.2 31.7 1.004 844.6
116 1.007 1342.7 29.2 0.980 790.6
135.3 0.943 1257.0 27.3 0.963 TA7.9

*162.1 0.781 1041.0 24.4 0.939 679.8

*189.9| 0.700 932.8 21.8 0.914 618.4

*210 0.637 849.5 19.8 0.894 570.0

Molecular weight: 138.08. Radius of the Capillary tube: 0.04439 cm.;
in the with * indicated observations the
radius was: 0.04803 cm.

Depth: 0.1 mm.

The substance has a constant boilingpoint at 214°.5 C.; the liquid
can be undercooled to — 76° C., and solidifies to a crystal-aggregate,
wich melts at —52°C. At lower temperatures, as far as to 0° C., the
temperature-coefticient of » is rather large: 2.83 Erg; later it is fairly
constant, with the value: 2.25 Erg.

HypRocHINON-DIMETHYLETHER: CyH, (OCH), (1, 4).

g ; Maximum Pressure HH Surface-
a0 tension x
See in mm. in Erg
g= | mercury of | in Dynes pro em.
= 0° C.

66° 1.106 1474.5 34.7
86.5 1.031 1374.1 32.3
106 0.974 1299.2 30.5
126 0.909 1213.8 28.4
146 0.843 1124.4 26.4
166 0.775 1032.7 24.2
184 0.709 945.3 22a
206 0.628 837.0 19.5

Specific
gravity d 40

1.036
1.008
0.990
0.976
0.957
0.938
0.921
0.901

Molecular
Surface-
energy » in
Erg pro cm?,

905.4
858.3
820.3
dithle|
726.2
674.7
623.7
558.4

Molecular weight: 138.08. Radius of the Capillary tube: 0.04803 cm.
Depth: 0.1 mm.

The meltingpoint of the substance is at 56° C.; it boils under a
pressure of 20 mm., at 109° C. On cooling first a glass is obtained,
which gradually crystallizes in fine needles. Between 66° and 106°
the temperature-coefficient of » is about: 2.11; between 106° and 166°,
about: 2.46; and between 166° and 206° C., about: 2.88 Erg. The
relating curve is therefore concave to the f-axis,

§ 18. Heterocyche Derivatives.

XII.

PyRIDINE C;H,N.

g Maximum Pressure Surface- eas Molecular
ay tension Sa Surface-
Oo . . .
a, in mm. in Erg avity d,,| energy in
BF mercury of | in Dynes in em? ch eee Erg pro cm’,
= ONC:
—19 1.698 2263.8 48.9 1.078 827.8
—20.5 1.430 1906.5 41.1 1.018 722.9
0.1 1.329 1771.8 38.1 0.998 679.0
25 1.215 1619.8 34.9 0.975 631.8
35 Lol 1569.2 33.8 0.962 607.3
55 1.099 1465.2 31.5 0.942 583.4
14 1.022 1362.5 29.3 0.923 550s
92.5 0.960 1279.9 PACS: 0.904 523.5

Molecular weight: 75.09.

Depth: 0.1 mm.

The pyridine crystallizes readily at —52° C.; thus the measurements
at —-79° C. relate to a strongly undercooled liquid, The curve, giving
the dependence of » and ¢ is not quite regular. At the boilingpoint

Proceedings Royal Acad, Amsterd

am. Vol. XVII.

Radius of the Capillary tube: 0.04385 cm.

358

XIV.

o .
EES Maximum Pressure H Surface- BY ia Molecular
a tension , perie Surface-
ere inmm. | in Erg gravity Ayo energy #
| E er re of | in Dynes pro em?. in Erg
—70° eiey || Uleil - 47.4 1.036 950.8
—20.7| 1.246 1661.5 | 39.2 0.986 812511)
0 | 1.165 1553.2 | 36.6 0.965 7169.7
25.8] 1.074 1432240) SB lod 0.940 721.2
46 0.999 1332.5 31.3 0.920 679.6
66.5) 0.928 1236.9 29.0 0.900 638.9
86.5 0.846 1128.5 26.4 0.881 590.0
106 OFIST 2) a s104953. 4) 24.6 0.862 557.8
126 0.718 957.7 22.5 | 0.842 518.2

2-PICOLINE: C;H, (CH) N.

Molecular weight: 93.07. Radius of the Capillary tube: 0.04803.
Depth: 0.1 mm.

The liquid, which is boiling constantly at 1339.5 C., can be under-
cooled as far as —74° C.; it solidifies at — 64° C. and melts there
very rapidly. Between — 70° and — 21°, the temperature-coefficient
is about: 2.83; afterwards the mean value remains about: 2.02 Erg.

_CHINOLINE: CoH, - N. /3H3.

hee Maximum Pressure H L Surface- Molecular
€° | ee MELONS LOT Specific Surface-

| © | -
ie baer a | in Erg. pro gravity d,.| energy » in
a= ees of PO, in Dynes em?. = Erg. pro.cm*.
es

—21° 1.682 | 2242.4 49.1 | A124 | eGO RO

0 1.608 2143.8 47.0 | 1.108 1121.1

*24.8) 1.562 2082.5 | 44.7 | 1.089)- 9) 107826
*45.2) 1.486 1981.1 42.5 | 1.073 | 1035.6
*714.3 W319) 99 eel838 52 39.4 | 1.051 973.5
*94.7 1.303 1737.1 37.2 1.034 929.1
115 210) 3)" 61320) 9) 35.2 1.018 888.4
135.2 1.135 | 1513.8 | 33.0 1.002 841.7
160 1.047 | 1395.9 | 30.4 0.981 786.4
192.5 0.929 |} 1239.0 | 26.9 0.954 708.9
213 | 0:855, 113959 25.7 0.938 658.3
230 0.797 ° || 1063.3 = |) 23,0 0.924 619.2

Molecular weight: 129.07. Radius of the Capillary tube: 0.04439 em.;
in the with * indicated observations, the
radius was: 0.04352 em.

Depth: 0.1 mm.

The boilingpoint was constant at 233° C.; the liquid can be under-
cooled as far as —50°, and then crystallizes, melting readily at —25° C,
The temperature-coefficient of » increases with the temperature:
between —21° and 45° C. it is: 1.92; between 45° and 115° C.: 2.10;
between 115° and 230°: 2.33 Erg. At the boilingpoint the value of x
is: 22.7 Erg. pro cm’.

359

Molecular Surface- Fig. 9.
energy, in Erg pro c.m2.
7790

1160
7730
7100

7070

“80°-60°-40° -20° 0° 20° W* 60° 80° 100° 120° 140° 160° /S0° £00° 220° 240° Temperature

24*

Some of the curves, which relate to these organic liquids, are
reproduced here in the usual graphical way (fig. 9); the corresponding
critical temperatures of the liquids, so far as they are known, are

360

mentioned and written between () behind the names of the
substances investigated.
19. Salts of the Alkali-Metals.
XVI.
a ee
| POTASSIUMCHLORIDE: ACl,
lem eu eee
= &| Maximum Pressure Surface- Molecular
Ee ; Specitic
ae ico} a = tension x re Surface-
| a | {lure °
Be ° | in mm. mer- in Detieg fn re Pr | etevity idgo| PROTEUS
'5 £| cury of 0°C.| J em’, Erg pro em?.
ie ck | |
| 799:5| 3.015 4019 | 95.8 1.509 1290.0
| 827.1 2.957 | 3942 94.0 1.492 1275.3
861.5 2.873 3830 91.3 1.470 1251.0
| 885.1 2.819 3758 89.7 1.456 1237.0
908.5) 2.768 3690 88.0 1.442 1221.3
| 941 2.697 3595 85.8 1.421 1202.6
| 986 2.582 3442 82.2 1.396 1165.8
1029 2.484 3311 79.1 — =
1054 | 2.425 3233 iliez _ os
1087.5 2.361 3147 1522 — —
|1103.6 2.313 3083 USsa1l — —
11125 | Poel fe) 3033 72.5 — _
1167 2.182 2909 69.6 — —
Molecular weight: 74.56. Radius of the Capillary tube: 0.04736 em.

at 15°C. The expansion-coefficient is here
0.0000083.
Depth: 0.1 mm.

The salt melts sharply at 771° C.; after four hours heating between
900° and 1100°, it solidifies at 769°C. It evaporates rapidly at 980°,
at 1160° with great speed. Just as in the case of the other alkali-
salts, the vapours are doubtlessly acid, while the solidified mass gives
an alkaline reaction, if dissolved in water. The gradual dissociation
lowers the value of the maximum pressure more and more, as is
seen from repeated experiments after a longer heating 1100° C.

As some illustrations of the changes caused by the commenced
dissociation of the salt, the following measurements are given, which
were made after a heating at 850° and 1150° C. during full four hours:

| At 848° C. the maximumpressure was found to be 2.821 mm, mercury
| 904 2.720
| ” . ” ” ” ” ” » ” S = ” ”

” 941 ” ” ” ” ” ” ” ” 2.645 ” n

” 956.5 » » ” ” ” ” 5 a) 2.615 ” ”

” 1037 ” ” ” ” ” ” yn 7” 2.455 ” ”

All values are evidently lower than the previously observed ones,
and at the lower temperatures, at which the observations were made
after the longest heating of the salt, the decrease is most appreciable.

361

XVII.

POTASSIUMBROMIDE: (Br. |

Molecular weight 119.02.
Radius of the Capillary tube : 0.04728 cm. at 15°C.
Depth: 0.1 mm.

The dissociation and splitting off of hydrogen-
bromide and bromine is observed at 825° C. At
940° C. the evaporisation and dissociation of the
salt have become so rapid, that measurements |
at higher temperatures seemed to be without
any real significance.

XVIII.

POTASSIUM IODIDE: AV.

Temperat. Maximum Pressure H Surface-
mya Ce tension x
(corr. on in mm. in Erg
G. Th.) mercury of | in Dynes pro cm?,

0° C.
Sie ane meta nar a.
737 2.372 3162 15.2
164 2.274 3031 72.1
866 2.106 2807 66.8
873 2.097 2795 66.5

Molecular weight: 165.96.
Radius of the Capillary tube: 0.04728 cm. at 15°C.
Depth: 0.1—0.2 mm.

The salt melts at ca. 700° C. Already at 750° C.
it evaporates rather rapidly, and at 900° C. with
dissociation into hydrogen-iodide and iodine. Meas-
urements at higher temperatures can have hardly
any significance.

812 2.183 2910 69.2

362

XIX.

SoprumcuLoripn: NaCl.
o a
= E Maximum Pressure H Surface- bas me Molecular
gOS st ANS tension haa Surface-
o° : ;
Be |; Ula in Erg. pro gravity d energy ” in
ens aeee OG in Dynes em? 4 Erg. pro em?.
Bias E
802.6 3.580 4772 113.8 1.554 1275.9
810.5 3.572 4762 113.5 1.549 1275.4
820.8 | 3.552 4735 112.9 1.543 1270.8
832 3.520 4692 111.9 any 1262.6
859 | 3.457 4608 109.9 1.523 1247.7
883.2 | 3.401 4534 | 108.2 — —
907.5 3.345 4459 | 106.4 —
930.6 3.285 4379 104.5 — —
960.5 3.227 4302 102.7 —
995.5 3.132 4175 99.7 — _
1037 3.047 4062 97.0 —- —
1080 2.951 3934 94.0 — —
1122.3 2.864 3818 91.3 -— —
1171.8 2.761 3681 88.0 — =

Moleculair weight: 58.46. Radius of the Capillary tube: 0.04736 cm.
15°RC

Depth: 0.1 mm.

at
{

The pure salt melts at 801° C. At 1080° it evaporates already rapidly,

at 1150°C. very rapidly.

The temperature-coefficient of « calculated in

the few cases, where values of specific gravity were available, is very

small:

strong alkaline reaction;

about 0.57 Erg. The solidified mass gives in water a rather

reaction.

the vapours of the heated salt have an acid

SODIUMSULPHATE: Na,SO,.

2 a ‘ 55

2 SI Maximum Pressure H Saitate:

oe oS = :

Ey ° g tension yin

BS g |inmm mer | in Dynes | Bre procm

= 3
900 6.285 8379 194.8
945 6.247 8328 189.3
990 6.209 8278 188.2
1032 6.149 8197 186.5
1077 6.088 8116 184.7

Molecular weight: 142.07.
Radius of the Capillary tube: 0.04512 em.
Depth: 0.1 mm.

The pure salt melts at 884° C. If heated
to 1100° C. the solidified mass! gives in water
a rather strong alkaline reaction, indicating
a dissociation. Measurements at higher tempera-
tures than 1100° C. thus seemed to be useless.

XXI.
SopDIUMMOLYBDATE: Na,Mo0,.
|
Oo :
Bos Maximum Pressure H Satraee:
ra E | tension x in
S2)inmm.mer-| . i 2
5 cury of 0°C, | ™ Dyueaia pe rere eee
| eeu rie i
698.5 6.091 8122 214.0
| 728.5} 5.975 7967 | 210.0
Tl 5.921 7893 208.1
777 5.828 7770 204.9
| 818.8 5.757 7675 | 202.4
| 858.5 5.657 1542 199.0
; 903.8 5002 7401 | 195.4. |
| 948 5.436 7247 191.4
989.5 5.330 7106 187.7
1035 5.224 6966 184.1
1078.5) 5.141 6854 | 181.2
/1121.5 5.070 6760 178.8
1171.5 4.998 | 6654 176.1
1212 4.947 6595 174.6
=
Molecular weight: 206.
Radius of the Capillary tube: |
0.05240 cm.
Depth: 0.1 mm.
The compound melts at 687° C. to a |
_colourless liquid. =

XXII

| LITHIUMSULPHATE: Li,SO,.

\o
5 Maximum Pressure // Surface-
a H tension ,
|@29 6 ; .
}259} in mm. in Erg
a= mercury of | in Dynes pro em2,
a 0° C.
860° 6.361 8481 223.8
873.5 6.342 8455 223.1
897 6.303 8403 221.8
923 6.256 8341 220.2
962.5) 6°169 8224 217.4
| 976.8) 6.146 8194 216.4
|1001.2 6.099 8132 214.8
1038.5 6.027 8035 212.3
| 1057 5.987 7982 211.0
|1074 5.953 71936 209.8
|1089.5 5.923 7897 208.8
1112 5.879 7838 207.3
1156.5 5.791 77120 204.2
1167.5 5.766 71687 203.4
1183.5 5.737 7649 202.4
1192.2 5.718 71624 201.8
1214 5.675 7566 200.3
Molecular weight: 109.94.
Radius of the Capillary tube:
0.05240 em. at 16° C,
Depth: 0.1 mm.
The salt was prepared frompurest lithium-
carbonate and sulfuric acid, carefully dried
, and heated at 900° C.; it melts at 849° C.
After being heated to 1200° C., the substance,
shows an alkaline reaction with water. Also
here it is of little significance, to pursue the
measurements to higher temperatures.

XXII.

LITHIUMMETASILICATE: Li,SiO;.

5 : = Maximum Pressure 7 Surface-

EOS ee eS tension

oo | a .

a. 8 in mm. in Erg

8 sues mercury of | in Dynes pro em2.

a 2 O°RC:

al SSS SS Ee = SSS ee —_

1254° 11.82 15759 374.6
1380 11.29 15052 358.2
1421 Lee 14958 356.2
1479 11.11 14812 352.8
1550 10.97 14626 348.7
1601 10.90 14532 346.6

Molecular weight: 90.01.
Radius of the Capillary tube: 0.04706 cm.
Depth: 0.1—0,.2 mm.

The analysed metasilicate was perfectly pure. It
melts at 1201°C. The temperature-coefticient of » is
very small.

365

§ 20. In the case of Porassiumcunorate: ACUO,, the maximum
pressure HH was 3,573 mm. mercury at 413°.5 C; at 448°.5 C.
it was: 3,540 mm. The radius of the here used silver-capillary tube
being: — 0.03460 em., the free surface-energy is calculated :

At 413°.5 C. 7% = 82,4 Erg. pro cm’.
At 443°.5 C. ¥ = 8156 Erp. proven:

At the last mentioned temperature the salt commenced to decompose
already distinctly, while O, was split off; at higher temperatures
therefore the values of y appeared to increase gradually by the
generation of AC/O, and KC7.

It was not possible therefore to investigate the values of the
temperature-coéfficients at higher temperatures; in every case however
they seem to be rather small.

With Stnvernirrate: AgNO,, the value of x is about 164 Erg.
pro em*. at 280°C; at 410°C. it is about 153.8 Erg. In this case
the temperature-coefficient is also in the neighbourhood of 0.6 or 0.9,
— this being a rather small value too.

§ 21. It is not my intention, to discuss now already the here
mentioned data, nor to add the remarks, which are suggested thereby.
It is better to postpone that task, until the complete experimental
material now available will be published. The given instances may
however prove, that the question: how to measure the surface-tensions
of liquids with great accuracy within a temperature-interval, from
— 80° C. to 1650° C., may be considered now as completely solved.

Groningen, May 1914. Laboratory of Inorganic Chemistry
of the University.

Chemistry. — “The Temperature-coefficients of the free Surface-
energy of Liquids, at Temperatures from —80° to 1650° C”.
II. Measurements of Some Aliphatic Derivatives. By Prof.
Dr. F. M. Jagger and M. J. Suir. (Communicated by Prof.
P. v. Rompuren).

§ 1. In what follows the data are reviewed, which were obtained
by us in the study of a series of aliphatic derivatives after the
method formerly described by one of us‘).

With respect to the liquids here used, we can make the following
general remarks. No product of commerce, not even the purest ob-

366

tainable, can be esteemed suitable for this kind of measurements: the
small traces of humidity already, which even the best chemicals always
contain, are sufficient to make the results unreliable. Most of the orga-
nical liquids of commerce however seem to contain several admixtures,
in small quantities or even larger quantities of water. We often
obtained a first purification by distilling a small fraction from it,
whose boiling point remained constant between 1° or 2° C. In
several cases even this appeared not to be possible: in such case the
preparation was dried during some days by means of anhydrous
sodiumsulphate; then, if the special character of the substance did
not forbid this, it was dried again during a long time by means
of freshly sublimed phospherpentoxide, after which the fractional
distillation was tried again. Commonly it appeared to be possible, ’
to separate from it a fraction, whose boiling point remained constant
between 1° or 2° C. With some preparations we succeeded in drying
them by means of metallic sodium. After very dry fractions, boiling
within a few degrees, had been obtained in this way, they were once
more distilled with a small flame only, or on the water-bath, under
atmospheric or reduced (12—20 mm.) pressure; in this operation
only the fraction, boiling within an interval of 1 C°., was used
for further treatment. The liquid was then cooled during several
hours in a closed vessel, by means of a mixture of salt and ice,
or by a bath of, solid carbondioxide and alcohol. If it erystal-
lized, a further purification was often possible by repeated
freezing and decanting. Often a very thin layer of a solid substance
(eventually of ice) was deposed at the walls of the vessel, the rest
remaining liquid and transparent; the liquid portion was poured
into a dry, clean vessel then, and the said operation repeated,
till no solid layer any more appeared. [f however the phenomenon
continued to appear, the liquid was treated again at least during a
week with fresh phosphorpentoxide, and the freezing repeated again
and again. Finally the purified liquid was distilled once more under
atmospheric or reduced pressure; only the fraction, boiling within
half a degree was collected then for the measurements. It is hardly
necessary to mention, that hygroscopical liquids were preserved and
treated in a suitable manner. The thus obtained liquid was commonly
only a jvery small fraction (10°/, or 20°/,) of the original commer-
cial preparation; it must be remarked, that the observed boiling-
temperatures often differed appreciably from the data, given in the
literature, and in several cases appeared to be dower than those;
— which perhaps can be explained by the fact, that in the distil-
lations, described in the literature, the liquid was heated éoo rapidly.

In our experiments the speed of distillation often did not exceed
about six drops every minute. In some cases, e.g. with ¢olwene, it
was impossible to distil from the product of commerce a fraction,
fulfilling all conditions; in such cases the substance was prepared
in some other way, e.g. the mentioned toluene by dry distillation
of purified calciumphenylacetate; ete. In the series of compounds
described, several were taken from the collection of scientific prepa-
rations of this laboratory; from these also only the small, constantly
boiling fraction was used for our purpose.

§ 2. Notwithstanding the by no means negligible differences of
the boilingpoints observed, the specific gravities of the liquids in
most cases differed only slightly or not at all from the data, given

in the literature. If this was the case, — and we always controlled
this by some pycnometrical determinations at 25° C., — the specific

gravities at other temperatures were calculated from the expansion-
formulae eventually already determined. If the direct determination
of d=’ did not agree with the number, given in literature, or if the
expansion-formula was not known accurately enough, three specific
gravities, e.g. at 25°, 50°, and 75° C. or at a higher temperature,
were determined pycnometrically, and from these determinations an
empirical equation of the second degree with respect to ¢, was calcu-
lated. This is completely sufficient here, because the specific gravities
were all abbreviated with three decimals: an account of the densities
in more than three decimals, must be esteemed valueless here, with
respect to the obtained accuracy of the measurements. With most
liquids, the mean decrease of the specific weight for 1° C. does not
differ largely from 0,001. For temperatures of — 70° and above
100° C. it was often necessary to extrapolate by the aid of the
established empirical formulae ; although conscious of the uncertainties,
which are always connected with such extrapolations, we are of
opinion that we have not introduced here in this way errors of appre-
ciable amount, because for these values such an error could manifest
itself only in the third decimal place, and dilatation of the liquids
occurs ordinarily in so regular a way, that the probability of heavy
errors is thus highly diminished by this circumstance.

Moreover another way was not available at this moment, if not
with large sacrifice of time and labour.

§ 3. In the following the obtained results are collected in tables.
For the value of 1mm. mercury at 0°C., 1333,2 Dynes (45°), was
ealeulated, and this value was used in all further calculations; in the
tables all numbers for x and u are adjusted by the necessary corrections.

368

The graphical diagrams relate to the variation of the so-called
“molecular” surface-energy mu with the temperature; in the same
diagram analogous, homologous compounds or such, related by simple
substitutions, are put together; this will be of practical use for the
comparative considerations later to be given, and allows a rapid
review of the behaviour. For the construction of the diagrams, not
the numbers of the tables, but those following directly from Cantor’s
formula, are used; therefore the correction, necessary to derive the
absolute value of 4 from these readings by diminution, are indicated
on each curve in the diagrams.

§ 4. Aliphatic Derivatives.

This series of measurements relates to the following aliphatic

Molecular Surface
Energy in Erg. pro cm?*,

7000
«
990 =
~
940 x,
‘
9/0 os
Ne
SSO \
\\
\
G50 NS
‘
20 as
2 .
e
790 Saw
eR
ak
760 Ss
=2.
730 NG =
‘ °
700 YE
«
670 ee
XN
640 4 x
. «
610} , \
x .
bs \
I8O x Xe a.
.
5501. NS se
xy Xe NS \
5200, SO
RK Pee?
490 Hs eee
Sues co
ease Te Cp
460 AS: SS SoS “SOSo
See Sa ORS é
430 b. aS Stee SS “3556
Ss era! Ss, as Co. . ne
~ aa ’ 5 ,
400 SS a ne =<
; ne 2 eee
5 ASS SNS
370 ee 2) Sc atid
340 Se Se
[OSs SA -8
JII0 EE ote
(ae. SB
280 SLPS, =a
250

“50° -60°-40° -20° O° 20° 40° 60° 80° 00° 120° 740° 160° 780° 200° 220°247° Temperature

Fig. 1,

369

substances: norm. Propylalcohol; Isobutylalcohol; Diethylether ; Ethyl-
formiate; Ethylchloroformiate; Ethylacetate, Methyl-, Ethyl-, and

norm. Propyl-alcohol: C3H;. OH.

= Maximum Pressure Surface- Specifi Molecular
aS tension pecie Surface-
Es in mm. mer-) _ in Erg. per gravityd,, | energy v in
Bie cury of in Dynes: cm’. 4° | Erg. pro cm?,
& OOK:
~76 1.170 1559.8 33.4 0.881 557.4
—21 0.924 1245.4 © 26.6 0.837 459.3
0 0.875 1167.3 24.9 0.820 435.9
25.5 0.807 1075.4 22.9 0.800 407.5
45 0.755 1006.4 21.4 0.784 386.0
74.5 0.679 905.3 19.2 0.759 353.9
90.6 0.638 850.2 18.0 0.746 335.6
|
| Molecular weight: 60.06. Radius of the Capillary tube : 0.04352 cm.
Depth: : 0.1 mm.
The substance boils at 96°.7 C. constantly.

Isobutyl-alcohol: (CH3). CH .CH,OH.

v .
a Maximum Pressure Surface ee Molecular
so tension x Beeme Surface-
a” jin mm. mer- in Erg. pro ravity d,,| energy » in
EE | cury of in Dynes 2 Seat aes 2
2 he. y; cm’. Erg. pro cm’.
—11.5 1.149 1531.8 33.0 0.885 631.5
—12 0.890 1186.5 25.5 0.828 510.1
0.3 0.853 1137.2 24.4 0.817 492.5 |
10.4 0.825 1099.9 23.6 0.807 483.9 |
25.1 0.783 1044.5 22.4 0.794 | 460 9
35.1 0.756 1008.0 21.6 0.785 447.7
49.7 0.723 963.9 20.6 0.771 432.2
69.6 0.670 893.8 19.1 0.753 407.0
101 0.594 791.9 16.9 0.731 367.4

Molecular weight: 74,08. Radius of the Capillary tube: 0.04385 cm.
Depth: 0.1 mm.

The compound boils at 106°.8 C. constantly; at the boilingpoint y
has the value: ca. 16.5 Erg. pro cm’.

370

Tsobutyl-Isobutyrates; Acetone; Methylpropylcetone; Ethyl-Acetyloacetates
Methyl-Methylacetyloacetate; thyl-Propylacetyloacetate; Methyl-, Ethyl-,.

Diethylether: (CjH5)o O.

ql Maximum Pressure 7 Surface- 2 Molecular
SOP MAL. Be Et oes tension Specific Surface-
ao in mm. | inErg. pro | gravity d,. | energy in
ES mercury of in Dynes cm?. 4 Erg. pro cm?
| 0° C.
I-75" 0.990 1319.9 28.5 0.818 574.7
—20.5 0.748 997.2 21.5 0.758 456.2
0.2 0.670 893.8 19.2 0.735 415.8
10.9 0.628 837.2 17.9 0.723 392.0
2523 0.584 718.6 16.7 0.707 371.2
29.5 0.574 766.2 16.4 0.703 365.9

Molecular weight: 74.08. Radius of the Capillary tube: 0.04385 cm.
Depth: 0.1 mm.

The substance boils at 34.98 C. constantly; at the boilingpoint x is:
15.9 Erg. pro cm?

IV.

Acetone: CH;.CO.CH3.

iS Maximum Pressure 1 Surface- . Molecular
eS u a tension x Specific Surface-
2.0 in mm. in Erg. pro ity d energy » in
§-= | mercury of | in Dynes | . cm2, agree es Erg. pro cm”.
be OoRE
EY, le oles 1647.8 35.6 0.917 565.5
—19.5 0.971 1295.6 27.9 0.845 468.0
Oe) 0.886 1181.3 25.4 0.818 435.4
11.4} 0.838 1117.4 24.0 0.803 416.5
25.5 0.786 1047.9 22.5 0.785 396.4
35 0.740 085.6 Ake 0.772 375.9
50.1 0.695 926.6 19.8 0.757 357.4

Molecular weight: 58.05. Radius of the Capillar tube: 0.04385 cm.
Depth: 0.1 mm,

The boiliagpoint is 56° C.; the value of y is there: 19.4 Erg.
pro cm*.

Eye!

Propyl-, Butyl-, Tsobutyl-, and Amyl-Cyanoacetates; Tri-, and Tetra-
chloro-methane; and Isobutylbromide.

V.
—
Methylpropylcetone: CH3.CO.C,H;.
=
E ; Maximum Pressure | Surface- . Molecular
ey tension ~ Specific | Surface-
a. in mm. | in Erg. pro ity d,. | energy » in
5 P gravity
s* menu of | in Dynes | em2, | 4° Erg. pro ae
74-2 1.240 1653=2)00 35.4 | 0.936 721.4
—20.5, 0.996 el 32729 28.3 | 0.872 604.6
0.3) 0.913 1217.8 26.0 | 0.852 564.1
25.5} 0.831 1107.6 | 23.6 0.826 22
45 0.762 1015.7 21.6 0.806 486.3
74.3 0.672 896.1 19.0 0.777 438.3
90.8 0.613 818.1 | URS 0.761 404.7
99.6 0.589 785.8 | 16.6 0.753 391.1
| |
Molecular weight: 86.1. Radius of the Capillary tube: 0.04352 cm.
Depth: 0.1 mm.
The substance boils at 101.93 C. constantly.
= =|
VI.
Ethylformiate: HCO. O(C2H;).
v .
Ele Maximum Pressure H | Surface- acan Molecular
hes tension % peeitic Surface-
on in mm. : > in Erg. pro | gravity do energy » in
‘= | mercury o in Dynes em?. Erg. pro cm2.
2 ee | ee
1605) 12289 1661.2 | 37.8 1.032 502.7
*—16.2 0.945 1259.9 28.5 0.958 398.3
baer aad 0.864 1151.9 26.0 0.938 368.5
24.9 0.802 | 1069.2 22.9 0.910 331.2
Sone 0.757 1009.6 21.9 0.899 319.3
49.2 | 0.718 957.2 | 20.5 0.879 303.4
be a
Molecular weight: 50.0.5 Radius of the Capillary tube: 0.04408 cm.;

in the observations, indicated by *, this
radius was; R=0,04638 cm.
Depth: 0.1 mm.

After carefully drying, this ether boils at 54.93 C. constantly ; it
remains a relatively thin liquid as far as —79° C. At the boiling-
point , is 19.9 Erg. pro cm®*.

372

Molecular Surface-
ee ; Bs
Energy in Erg pro em?. Fig. 2.

80°-60°-40°-20° O° 20° 40° 60° 80° 700° 120° 740° 760°780° 200°22G° Temperature

VII.
Ethylchloroformiate: C/.CO.O(C:Hs).
vo °
iB , Maximum Pressure H | Surface Bane Molecular
See —EE -| tension pectic Surface
Be in mm. mer-) in Erg. pro | gravity d,,| energy win
ce cay ao in Dynes em? Erg. pro cm’.
— 15.5 1.353 1803.8 42.4 1.278 819.0
- 21 1.046 1395.0 32.6 1.186 661.9
0) 0.951 1269.2 29.6 1.160 609.9
25 0.847 1129.2 26.2 1.127 550.3
45.3 0.774 1031.8 23.9 1.095 Sila
70.2 0.692 922.6 Dili, 1.050 466.8
84.8 0.643 857.8 19.8 1.022 443.9

Molecular weight: 108.49. Radius of the Capillary tube: 0.04803 cm. |
Depth: 0.1 mm. |

The compound boils at 91.°5 C. constantly; at this temperature x
is 19.3 Erg. pro cm’.

VIII.
: Ethylacetate : CH,.CO.O(C)Hs).
rs ]
5 : Maximum Pressure 1 Surface- Specifi Molecular
e- tension z Beciuc Surface-
a. jin mm. mer-) | in Erg. pro | gravity d,.| energy # in |
a” ony ee | in Dynes cm?. Erg. pro cm’,)
|
S714 | 1.274 || “1698.5 36.6 1,016 716.8
—20 0.994 1325.2 28.4 | 0,949 582.1
0 0.892 1189.2 25.5 0,924 532.1
25.5 0.780 1039.9 22.2 | 0.893 473.8
34.7 0.744 992.5 21.2 0.881 | 456.6
55 0.679 897.2 19.1 0.856 419.3
70 0.623 838.5 17.8 0.829 399.2
Molecular weight: 88.06. Radius of the Capillary tube: 0.04385 em.
Depth: 0.1 mrh.
After very carefully drying and repeated distillation, this ether boils
at 77.°1 C. constantly. It remains a thin liquid as far as —80° C. At
the boilingpoint the value of z is: 17.2 Erg. pro cm’.

25
Proceedings Royal Acad. Amsterdam. Vol. XVII,

Molecular weight: 102.08.

The substance boils constantly at 91°.8 C.

Radius of the Capillary tube: 0.04352 cm.

Depth: 0.1 mm.

Ethyl-Isobutyrate: (CH3). CH.CO.O(C,Hs).

bol POs

eS)
ENE NS

Maximum Pressure Surface- : Molecular
ese ae we | tension x Specific Surface-
| in mm. mer- | in Erg. pro gravity Ayo energy » in
cury of in Dynes em?2, Erg. pro cm’,
a ay je —— —— — = = —
| 1.165 155352 i 33.3 0.976 805.4
0.940 1253.2 26.8 0.913 677.7
0.867 1155.9 24.6 0.891 632.3
0.779 1038.6 | 22.1 0.859 582.0
0.717 955.9 20.3 0.837 544.0
0.624 831.8 17.6 0.809 482.4
0.572 762.9 16.1 0.791 448.0
0.507 675.5 14.2 0.769 412.6

Molecular weight: 116.1.

Radius of the Capillary tube: 0.04352 cm.

Depth: 0.1 mm.

The substance boils at 110.°2 C. constantly. At —76 C. it is again
a thin liquid; it was only slightly turbid, probably by extremely fine

crys

tals.

375

XL.

Isobutyl-Isobutyrate: (CH3),CH.CO.O(CH) .(CH . (CH3),).

g ‘ Maximum Pressure Surface- +f Molecular
e* — tension x SUE Surface-
a. jin mm, mer-) in Erg. pro | gravity d energy in |
~ cary ot | in Dynes cm. =| 4° | Erg. pro cm’.
~16.5 1.182 1576.3 33.8 0.951 960.6
—21.3 0.927 1236.2 26.4 0.896 780.8
0 0.865 1S Sota 24.6 0.875 739.2
25.4 0.785 1047.8 | 22.3 0.850 683.1
45 0.731 974.3 20.7 0.830 644.2
74.7 0.638 850.2 18.0 0.801 573.6
91.1 0.596 795.0 16.8 0.784 543.1
109.2 0.545 726.1 15.3 0.766 502.3
134.5) 0.469 625.0 13.1 0.740 440.1

Molecular weight: 144.11. Radius of the Capillary tube: 0.04352 cm.

Depth : 0.1 mm.

The compound boils at 147.°2 C. constantly.

XIL.
Ethyl-Acetyloacetate: CH,;CO.CH,.CO.0O(C,Hs),
& Maximum Pressure H Surface- | S if Molecular
ES tension x | “Pectlic Surface-
te ‘in tim. mers) in Erg, pro | gravity dy. energy ” in
ce cary ct | in Dynes cm. | Et'g. pro cm’,
== = a — oa se SSS
—20°| 1.210 1612.8 3am) e070 900.7
1 1.133 1510.5 34.3 1.048 853.5
S25 ea ere Lets 1483.6 32.0 | 1.023 809.2
yaks) 1.069 1424.7 30.7 1.013 781.4
* 49.5, 1.024 | 1365.8 29.4 0.999 155.3
71 0.906 ae 201: Aten | 27.3 0.976 712.3
89 0.841 1121.2 25.3 0.958 668.4
e125 0.774 1031.9 211 0.923 587.7
MoS 0.675 900.2 18.9 0.896 522.1
=S1765") (05596 794.9 16.6 0.869 468.0
| =e Pale all 4
Molecular weight: 130.08. Radius of the Capillary tube: 0.04638 cm.;
in the observations indicated by *, it was
0.04408 cm.; in those by **: 0.04352 cm.

Depth: 0.1 mm.

The substance boils at 179.°6 C. constantly.

25*

Molecular Surface-
energy in Erg pro cm2.

720)

690 . §

660 y Sete
eS

Tempe-

-80°-60°-40° 20° O° 20° 40° 60° 80° 100° 120° 740° 160° 180° 200° 220° 240° 260" ature.

Molecular Surface-
energy in Erg pro cm’

7020

Fig. 4.

“80° -60°-40" -20° O° 20° 40° 60° 80° 100°120°740' 00180200

Temperature

377

XII
Methyl-Acetylomethylacetate: CH;CO.CH(CH3).CO. 0(CHs3).
a : Maximum Pressure | Surface- ie | Molecular
| Sie eee | tension x | Specific Surface-
are in mm. mer-| | | in Erg. pro | gravity d,,| energy “in
bi ue in Dynes | cm?, as pro cm’,
<1 | 1.477 | 1969.6 | 46.5 1.121 | 1106.2
—21 1.218 | 1623.8 | 38.3 1.071 939.3
0 1.137 1515s ees Bball 1.050 887.2
20e3 1.046 1395.0 32.8 1.024 828.9
45.5 0.985 1313.2 30.8 1.003 789.2
710.2 0.901 1201.2 28.1 0.977 | 732.7
85.2 0.856 1141.2 26.7 0.962 703.4
Lees OS 68 1024.4 23.9 | 0.930 | 644.0
138.2} 0.709 945.2 22.0 0.908 602.3
156 0.658 877.2 20.4 0.890 566.0
Molecular weight: 130.08. Radius of the Capillary tube: 0.04803 cm.
Depth :0.1 mm.
Under a pressure of 18 mm., the substance boils at 75.95 C.; in the
at —71°C. very viscous liquid, the growing of the gas-bubbles took
more than 60 seconds. The specific gravity at 25° C. is: Ayo = 1.0247;
at 50°C.: 0.9991; at 75° C.: 0.9732. At © C.: Ayo= 1.0500—0,001006¢

—0.00000024 #.
XIV.

Ethyl-Propylacetyloacetate : CH3CO.CH(C3H;)CO . O(C)Hs).

£ _ | Maximum Pressure H Sine | ato | Moteeular
eo tension x Recinie | Surface-
o - F y | ‘
Qa. jin mm. mer-| _ in Erg. pro | gravity d,,| energy “in
=o cury of | in Dynes 2 aS) 2
2 °C. cm | Erg. procm ‘|
° |
—76.2 1.430 | 1906.0 43.6 1.082 1280.1
—20 1.142 1522.2 34.8 1.007 1070.2
PAS) 1.058 | 1410.1 32.2 0.978 1011.3
i 2s) 1.018 | 1356.6 29.4 0.948 942.7
hs eta) 0.977 1302.2 | 28.2 | 0.934 913.2
™* 49 0.929 ~ | 1238.7 | 26.8 | 0.916 | 879.2
70 0.818 | 1091.0 24.8 | OFSS0Uy ea 88las
90.5 0.763 | 1017.7 23.1 0.866 786.8
*125 0.714 951.5 2022 0.833 706.0
*143 0.669 | 891.5 | 18.9 | 0.816 669.7
*152.9| 0.641 854.8 | 18.1 0.806 6465
lala 0.576 7167.5 16.2 | 0.785 589.1
*200.5 0.507 676.4 14.2 0.764 525.8

Molecular weight: 172.13. Radius of the Capillary tube: 0.04638 cm.; |
in the observations indicated by *, R |
was 0.04352 cm.; in those indicated by
** it was 0.04408 cm. Depth: 0.1 mm.

Under ordinary pressure the boiling point is 223.96 C. constantly ;

notwithstanding the great viscosity of the liquid at —76° C., it was

yet possible here to determine the value of z evidently very exactly,

if the time of grow ofthe bubbles was sufficiently long (ca. 40 seconds). |
a Ee ee eee

————

XV
Methyl-Cyanoacetate: CN.CH2.CO.O(CH,).

a |
3 : Maximum Pressure H Surface- : Molecular
sot eee at. | tension x Specific Surface-
Fe fe PRRs in Erg. gravity d,.| energy # in
& | mercury of | in Dynes pro cm’. Erg pro cm»
e 0° C.
6°| (2.424) | (3231.6) C41) ae 222 (1387.8)
16 pen tats 1923.2 43.9 1.140 861.2
1 1.362 1815.4 41.4 1.122 820.8
i= 25-5) 1.337 1783.0 38°6 1.096 me aitile!
50 | 1.184 1578).3' 14) 35.9 1.070 | 134.6
70.5) 1.116 1487.7 | 33.8 1.039 | 705.4
90 | 1.043 1390.8 | Set 1.028 666.2
* 124.5) 0.987 1315.8 28.0 0.994 601.8
* 153.1) 0.877 1169.2 24.8 0.965 543.7
* 176.5] 0.789 ae LOS 2ha Sy 22.3 0.942 496.8
Selo 0.713 Oo IRS Ira 20.1 0.921 454.6

Molecular weight: 99.05. Radius of the Capillary tube: 0.04638 cm.; in
the observations indicated by *, R was:
0.04352 cm., in those with “, it was:
0.04408 cm.
Depth: 0.1 mm.

The carefully dried ether boils constantly at 203° C.; at — 76? C.the
liquid is extremely viscous and gelatineous; although the time of
formation of the gasbubbles was about 100 seconds, the viscosity in
this case evidently diminishes the exactitude of the determinations of .
The specific gravity 40 was at 25° C.: 1.0962; at 50° C.: 1.0698; at

75° C.: 1.0438; at £°: 40 = 1,1231—0,001086 ¢ +- 0,0000004 ¢?,

XVI.

Ethyl-Cyanoacetate: CN. CH,.CO.O(CjHs).

ovo .
| 5 . | Maximum Pressure H Surface- ate Molecular

se = tension x Pecite Surface-
a inmm.mer- | | in Erg. pro | gravity d,, | energy » in

= cury of in Dynes cm? | Erg. pro cm?,
ol 0? ‘G
|-17° 1.313 1750.8 39.9 1.099 876.1

i) 1.245 1660.2 37.8 1.082 838.6

ieee) W222: 1628.8 35.2 1.056 7193.7
pareetaygs) 1.188 1583.5 34.2 1.046 776.1

49 1.083 1444.5 32.8 1.032 ible SD

71 1.016 1354.0 30.7 1.009 713.6
| 90 0.951 1267.8 28.7 0.990 675.6
mle 0.896 1194.8 25.4 0.955 612.4
P13 0.803 1070.8 ~ Bes 0.927 558.3
*176 0.727 969.7 20.5 0.904 512.7
* 201 | 0.651 868.6 18.3 0.879 466.3

Molecular weight: 113.07. Radius of the Capillary tube: 0.04638 cm.;
in the observations indicated by *, R
was 0.04352 cm.; in those by **, it was:
0.04408 cm.

Depth: 0.1 mm.

The compound boils at 206° C. constantly; at —76° C. it becomes
glassy and crystallizes very slowly on heating. The crystals melt at
about — 40° C. The specific gravity at 25° C. was: 1.0562; at 50°C:
1.0307; at 75° C.: 1.0052; at ¢-: A40 = 1.0817—0.00102 ¢, in general.

O79

XVII.
Propyl-Cyanoacetate: CN.CH,.CO.O(C3H)).
E ; Maximum Pressure H | Surface- | j Molecular |
So ae ee tension 7 Specific Surface- |
Be inmm., mer aa in Erg. pro | gravity do | energy / in
3 cury of | in Dynes a) Erg. 2,
2 0c. cm rg. pro cm
—16° 1.236 1647.3 37.5 | 1058; > 91259
0 1.184 | 1578.3 35.9 | 1.042 882.9
P25 1.164 1551.7 3350) 1.021 835.1
heels) 1.130 1506.5 | 32.5 1.011 815.5
hee 1.075 1433.8 | 31.0 0.996 786.0
ab! 0.961 1280.71, =} 29.1 0.976 747.6
| 114.5} 0.834 W225) 92522 0.933 667.1
2.5 0.858 | 1144.4 | 24.3 0.923 647.9
*152.5 0.780 1039.9 22.0 0.896 598.3
“176.1 0.701 934.6 | 19.7 0.872 546.0
*201 0.624 | 831.8 17.5 0.847 | 494.1
Molecular weight: 127.08. Radius of the Capillary tube: 0.04638 cm.;
in the observations, indicated by *, the
radius was: 0.04352 cm.; in those with
“it was: 0.04408 cm. Depth: 0.1 mm.
The substance boils at 216° C. constantly; at —79° it solidifies
slowly to a crystal-aggregate, which melts at about — 39° C. The
density d,. was at 25°C.: 1.0214; at 50° C.: 0.9973; at 75° C.: 0.9717.

| at AG: 40 = 1,0424 —0.000962 ¢-+- 0,0000012 &.

XVIII.
Butyl-Cyanoacetate: CV.CH2.CO.O(C4Hb).

vo .
ae Maximum Pressure Surface- ey Molecular
BY = — tension % Lo iay Surface-
a _ jin mm. mer- in Erg. pro | gravity d energy v in
E-= | cury of in Dynes 2 3 ce 2
2 0°'C. cm’. Erg. pro cm».
°
—21.3 1.213 1617.5 35.2 1.041 928.8
0 1.159 1545.2 33.6 1.020 898.7
psa 1.117 1489.0 31.7 0.998 | 860.3
if 45.2 1.055 1406.2 29.9 0.978 822.5
im 14.9 0.975 1300.6 Alot 0.952 715.8
* 94. 0.924 1231.6 26.2 0.934 743.2
114.5 0.852 1135.3 24.6 0.915 707.4
135 0.797 1063.3 23.0 0.895 671.2
161.1 0.729 971.9 21.0 0.870 626.3
192.1 0.662 883.1 | 19.0 0.840 | 578.4
213.1 0.615 820.0 17.6 } -0.820! || ° 544.5

Molecular weight: 141.1. Radius of the Capillary tube : 0.04439 cm.; i
in the observations indicated by * it was:
0.04352 cm. Depth: 0.1 mm.
The ether boils at 230°.5 C. constantly; it can be cooled as far as
—80° C., without crystallisation setting in. The specific gravity 40

is at 25° C.: 0,9978; at 50° C.: 0.9749; at 75° C.: 0.9518; at f° it is:
d 40 = 1.0204—0.000904 ¢ +- 0.00000016 &.

XIX.
lsobutyl-Cyanoacetate : CN.CHp. CO. O(CHp. CH. (CHs3)s).

uv .
E : Maximum Pressure 7 Surface- 3 Molecular
eS | Ae = tension Suen: Surface-
o. jin mm. mer- in Erg. pro ravity d energy » in
E= cury of in Dynes cm? 3 AS. Ete epro Gale
= 0° C. ae ;
°
—20.5 1.179 1572.4 34.2 1.033 907.1
0.3 1.122 1495.9 32.5 1.014 872.7
e225) 1.069 1424.6 30.3 0.990 826.7
pedo 1.013 1351.1 28a 0.971 793.3
* 74.8 0.934 1245.4 26.4 0.944 743.6
* 04.5 0.879 1174.6 24.9 0.925 710.9
| 115 0.811 1081.3 23.4 0.905 677.9
| 135.1 0.757 1009.2 21.8 0.886 640.5
161 0.686 914.6 19.7 0.862 589.5
191.8) 0.595 792.9 17.0 0.834 520.0
213 0.541 720.9 15.4 0.815 478.4

Molecular weight: 141.1. Radius of the Capillary tube: 0.04439 cm.;
in the observations indicated by *, Rwas:
0.04352 cm,
Depth: 0.1 mm.

The compound boils at 223° C. constantly; it can be undercooled
as far as —76° C,, and crystallizes then slowly into a crystalline
aggregate, melting at about -—26? C. The specific gravity at 25’ C.
was d,,. = 0.9903; at 50° C.: 0.9669; at 75° C.: 0.9441. At ¢° it is

generally : Ayo = 1,0138—0,.000952 ¢ + 0.00000032 @.

XX.
Amyl-Cyanoacetate: CN .CH,.CO.O(C;H\).
5 Maximum Pressure Surface- Pes Molecular
pho FS RE ae eee ad eet aa Specific Surface-
Go i energy
= en in Erg ravity d :
E-= | mercury of | in Dynes pro cm?, ier IS Sy 18
a 0° C. pro cm’.
a SSS SSS = — WSS SS ——————————————_SI ESSE
—17:5| 1.080 1440.3 32.7 1.017 933.5
IS 1.029 1371.3 SI 1.001 897.2
ee Zee 1.028 1370.2 29.5 0.976 865.5
aD) 1.000 1333.2 28.7 0.966 847.9
69 | 0.880 1172.9 26.5 0.939 797.8
89 | 0.831 1108.3 25.0 0.920 763.0
plas) 0.807 1075.4 Poel 0.891 107.7
153 0.744 992.6 21.0 0.864 668.3
0.689 919.1 19.4 0.843 627.6
201 0.634 845.6 17.8 0.821 586.1
|

Molecular weight: 155.11. Radius of the Capillary tube: 0.04638 cm.;
in the observations indicated by *, R was
0.04352 cm.; in those with * it was:
0.04408 cm.
Depth: 0.1 mm.

The compound boils at 240°.2C.; at —76°C. it is a jelly, but does
not crystallize. The specific gravity at 25° C. was: 40 = 0.9763 5
|) Yat 50>'G:: (0/9547; at 715° G2 O82, Ate itis: A4o = 1.0019—0.090061 z
+ 0.00000032 #.

Molecular Surface
Energy in Erg. pro cm’. Fig. 5.

4SO
-50°60"-40"-20° 0° 20° 4W° 60° 80° 100" 120° 14° 160° 180" 200.220 }eMperature

XXI.
| Trichloromethane: CHCl.

Maximum Pressure Surface-
tension x

| Temperature
iba © (CG,

OnE: | | pro em?2.

—22 1.142 | 1523.4 | 32.5 1.555 | 587.5
0 | 1.050 1394.3 29.7 1.519 545.3
25 | 0.927 1236.0 | 26.2 1.476 490.4
35 | 0.881 |) Lae S 24.8 1.459 467.8
55 | 0.798 1063.9 22.4 1.425 429 .2

Molecular weight: 119.51. Radius of the Capillary tube: 0.04385 cm.

| Depth; 0.1 mm.
The trichloromethane was prepared from purest chloral, carefully
| dried, at —79° C. several times frozen, and purified by repeated

distillation. It boils constantly at 61°.2 C.; at this temperature, the
value of x is: 21,8 Erg. pro cm?.

382

XXII.
Tetrachloromethane: CCl. |
|
£ | Maximum Pressure H | Surface- aa Molecular
go a = _____} tension x Becmc Surface-
a. in mm. mer- E in Erg. pro | gravity d,.| energy “in
| = | cury of | in Dynes cm?, 4° Erg. pro cm’,
= | OG.
—18° | 1.087 | 1450.4 | 30.9 1.659 633.0
0.1) 1.005 1340.9 28.5 1.632 590.2
25 | 0.899 1199.5 25.4 1.585 536.4
35 | 0.862 1149.4 | 24.3 1.560 518.6
55 0.793 1058.1 22.3 1.525 483.2
| 1 ie - ee. ase
Molecular weight: 153.80. Radius of the Capillary tube: 0.04385 cm.
Depth: 0.1 mm.
Under reduced pressure (ca. 90 mm.) it boils at 26° C., and solidifies
at — 60’ C. to a white crystalline mass. Under ordinary pressure, it
boils constantly at 76°.4 C. At this temperature the value of x is
about: 20.2 Erg. pro cm?*.
—4
Molecular Surface-Energy
in Erg pro em’. Fig. 6.
7020
990
960
aS
930 TAN
PAO
900 NESS
8 YO
a70 SEO RR
oh Na NG
; ‘Sa, NRG?
750 ~S ‘WS
720 SSE RY
a RES SENG
690 SS Oe Nah
660 GENS. SS
630 SNORE OS
\ SSS aN
600 FSS NS Ye
570 Ns We Se
500 Se x
> ? uN \’
510| tx CancacHiale® WO,
480 AS
450 : aot
SO OPI WO 20° YO” OF 80 100 120 M0 160 180 200 220° 200 260" “NPE

rature

383

XXIIL

Isobutylbromide: (CH3). CH . CH2B?).

= 4 Maximum Pressure H Surface- Specif Molecular
so : tension x | ~Pectlic Surface-
os in mm, mer-| . inErg. pro | gravity dg. energy “in
“ cury of in Dynes cm?. Eeonocotenall
= One: ot
= ] — =z = <== SS SSS SE —— = = = = = —
L95” 1.227 1636.5 38.4 1bS85 ma eeS2166
—19.5 0.949 1265.9 29.5 1.314 653.7
0 0.874 1166.0. | 27.1 1.291 607.6
25.4 0.790 1053.5 24.4 1.259 556.3
44.4, 0.728 970.2 22.4 | 1.236 By eie}
69.9, 0.646 861.9 19.8 1.205 464.8
85.3 0.600 799.5 18.3 | 1.186 439.2

Molecular weight: 137.07.

Radius of the Capillary tube : 0.04803 cm.

Depth: 0.1 mm.

The carefully dried compound boils very constantly at 90.°5 C.; at
this temperature x is about 17.9 Erg. pro cm?.

Molecular Surface-

Energy in Erg pro cM?.

Vig. 7,

-§0°-60°-40° 20° O° 20° 40° 60° 80°10"

Temperature

|
|
|

§ 5.

384

Temperature-coefjicients of w of the here studied substances.

norm. Propylalcohol. Isobutylalcohol.
Temperature-interval: re in Erg. Temperature-interval: = in Erg.
between —76° and —21° 1,78 between —71° and — 12° 2,3
—21° , +259 1,11 —12° ,, +101° 1,1
2 ap 91° 1,10
Diethylether. Ethylf ormiate.
between —75° and —20° 2,16 between —76°,5 and —16° 1,72
—— 2) ae 0? 1,94 —16° ,, +25° 1,62
O20 ay. 29° 1,70 Zoe ss 35° 1,29
Se 54° 1,12
Ethylchloroformiate. Ethylacetate.
between —75° and —21° 2,86 | between —74° and 0° 2,50
—21° , +25° 2,41 Og. 25° 2,37
Dock TOS 1,82 Dap 35° 1,86
WY 91° 1,70 GI? 5) 55° 1,78
55°u,. nis 1,30
Methyl-Isobutyrate. Ethyl-Isobutyrate.
between —73° and —219,5 3,0 between —78° and +109? 2,15
—21° , 25° 2,4 ;
Pao 45° 2,1
452), 91° 1,7
Isobutyl-Isobutyrate. Acetone.
between —76° and — 21° 3:2 between —73° and —19°,5 1,81
—21° ,, +135° 2,18 —19° 5, =e 1,66
Oy 54° 1,57
Methylpropylcetone. Ethyl-Acetyloacetate.
between —74° and 0° 2,13 between —20° and +-176° 2,19
2 5) g9° 1,73
Methyl-Methylacetyloacetate. Ethyl-Propylacetyloacetate.
between —71° and —21° 3,39 between —76° and —20° 3,74
Al 0° 2,47 —20°,, +20° 2,84
WH 70° 2,18 beer. 70° 2,36
TOR! Sf 156° 1,94 TPs ies 2,24
12525 eee OSS 2,11
Then an increase: 2,37 to 2,68, occurs
as a consequence of beginning dissociation.
Methyl-Cyanoacetate. Ethyl-Cyanoacetate.
between —76° and — 16? not measurable | between —-17° and +201° 1,88

independently of

viscosity.

—16° ,. +1979

1,90

Propyl-Cyanoacetate. | Butyl-Cyanoacetate.

ete Ou. . Ou.
Temperature-interval: ay in Erg. Temperature-interval: a in Erg.

between —16° and +152? 1,88 ‘between —21° and 4213° 1,62
Then an increase: 2.13, under dissoci-
ation and liberation of HCN.

Isobutyl-Cyanoacetate. | Amyl-Cyanoacetate.
between —20° and 0° 1,64 | between —17° and 4- 1° 2,0
Ps 1152 1,70 | 1 201° ca: 1,6

i taee 213° 2,0
Gradual decomposition, under liberation |

of HCN. |
Chloroform. Carbontetrachloride.
between —22° and --55° 2,06 between —18° and 0° 2,6
Ore; 25° 1,95
25° 55° 1,75
Isobutylbromide.
between —75° and —19° 3,0

alig2 9, -1-952 2,15
25°, = 699,9_—s—«2,08
70°, 90° 1,91

acy 0
Evidently only in some cases the coefficient 5, appears to be really

constant; in most cases it decreases doubtless with a rise of tempe-

rature. Where the inverse behaviour was stated, a decomposition of

Oo
the studied substance always seemed to occur. The value for -
t

is in the interval of ordinary temperatures relatively small for propyl-
and isobutyl-alcohol and for the cetones; however in these cases it
appears to be variable with the temperature in no higher degree

0
than in the cases, where the values of = do not differ largely from

2.0 Erg.
Groningen, June 1914. Laboratory for Inorganic Chemistry
of the University.

386

Chemistry. — “The Temperature-coefficients of the free Surface-
energy of Liquids, at Temperatures from —80° to 1650° C.
III. Measurements of some Aromatic Derivatives.” By Prof.
Dr. F. M. Jarcer and M. J. Surv. (Communicated by Prof.
P. vy. Rompuran).

§ 1. In continuation of our measurements of organic liquids, the
data obtained in the study of a series of aromatic compounds, are
reviewed here in tables, quite in the same way as in our former
communications’). This series of substances includes the following terms:

Nitrobenzene; ortho-Nitrotoluene ; Aniline; Dimethylaniline ; ortho-
Toluidine; Thymol; Methyl-, Ethyl-, and Benzyl-Benzoates ; Salicylic
Aldehyde ; Acetophenone, and the non-aromatic compound: e-Cam-
pholenic Acid.

With respect to the determination of the specific gravities and the
purification of the studied substances, we can refer to the preceding
communication; the diagrams also have the same significance, as
indicated there.

§ 2. Aromatic Derivatives.

Nitrobenzene: C,H;(NO,).

5 Maximum Pressure 1 | Surface- | Rae Molecular
| id | tension x | ~Pecic Surface-
| Sey he in Erg. pro | ity d energy “in
= in mm. mer-| ; | Sravity
=~ cury of 0?C.| '" Dynes cm? 4 Erg. pro cim?.
5 1.538 | 2050.5 | 44.4 1.215 064.7
26.6 1.473 | 1965.8 | 42.5 1.197 932.7
| 34.9 1.448 | 1930.5 41.7 1.190 918.7
55.3 Lon 1827.8 | 39.5 1.171 879.7
70.8 1.314 1751.8 37.8 1.156 849.0
100 1.198 1596.0 34.4 1.125 786.8
110 1.156 1541.6 33.2 1.115 _ 163.9
126 1.089 1459.8 31.4 1.097 730.4
145.5 1.014 1351.9 29.0 1.075 683.7
W225 0.903 1204.0 25.8 1.042 621.0

Molecular weight: 123.06. Radius of the Capillary tube: 0.04385 cm.
Depth: 0.1 mm.

The nitrobenzene was carefully dried, several times frozen, and
distilled; it boils at 209° C. constantly. At this temperature 7 = 21.2
Erg. pro cm? At O° C. it solidifies completely. The specific gravity
at 25° C. is: d4. = 1.1988.

1) F. M. Jaraer and M. J. Sarr, Preceding communication, (1914),

Il.

Ortho-Nitrotoluene: CH; .C ,H,. (N02).
(1) (2)

© } Maximum Pressure // Surface
30 = _ tension x
a | in mm. mer- in Erg. pro
Es cury of in Dynes eat
O2NG;
0.1 1.505 2006.8 43.3
9.6 1.465 1953.1 42.1
zo 1.416 1887.5 40.9
3438 1315 1833.1 39.7
* 49.3 1.257 1675.8 38.2
70 1.252 1669.4 35.8
101.6 1.132 1509.8 32.4
122.6 1.055 1406.5 30.1
144 0.971 1295.4 Qe
148.6 0.954 1272.4 27.2
170 0.864 1151.9 24.5

Molecular weight: 137.1.

The compound boils at 218° C. constantly; the meltingpoint is
— 4° C. At the boilingpoint, the value of x is about 18.1Erg. pro cm’.

0.04408 cm.;

0.04638 cm.
Depth: 0.1 mm.

Specific
gravity a4,

ee ee
_
—_

Radius of the Capillary tube: 0.04385 cm.;
in the observations, indicated by *, R was
in these with

Molecular
Surface-
energy » in
Erg. pro cm>,|

DOW bNWOWWH oo |

it was:

Il.

Aniline : CgH;(N H2).

E : Maximum Pressure H Surface-
a ———| tension ,
Yo : lire!

a in mm. | in Erg. pro
££ | mercury of in Dynes antl
fe O3E

(e)

0 1.573 2096.5 45.4

5.3 1.552 2069.8 44.8
26.2 1.473 1963.8 42.5
34.7 1.452 1935.8 41.8
54.8 1.371 1827.8 39.5
70 1.320 1759.8 38.0
100 1.190 1586.5 34.2
109.5 1.156 1541.6 382
126 1.089 1459.8 31.4
143 1.027 1369.2 29.4
148.8 0.998 1331.8 28.6
173.7 0.889 1185.8 25.4

Molecular weight: 93.04.

_The liquid boils at 184° C. constantly. It is colourless, and only at
higher temperatures it gets somewhat yellowish. At the boilingpoint,

x is: 24.3 Erg. pro cm?

Radius of the Capillary tube: 0.04385 cm.

Depth: 0.1 mm

Specific
gravity a4,

Molecular
Surface-
energy / in
Erg. pro cm’.

IV.

Dimethylaniline 5 CoHs 5 N(CH3)3.
| wo 7
(ees Maximum Pressure Surface- ; Molecular
HS) st sf | @tensionie Specific Surface-
oo : | = z 4 energy »
= eee in Erg. ravity d. :
== | mercury of | in Dynes pro cm?, SEE By Erg.
i= OPC, pro cm?.
26 | 1.165 1553.2 36.6 | 0.951 926.4
45.5 | 1.087 1449.1 34.1 0.935 873.0
| 66.5 1.018 S579) 31.9 0.917 827.3
| 86.5 | 0.959 | 1278.4 30.0 0.900 787.8
| 106 0.893 1190.8 271.9 0.884 741.5
125.8 0.831 1107.6 25.9 0.867 697.3
146 0.768 1024.4 23.9 0.850 652.0
166 9-709 945.3 22.0 0.832 608.8
184 0.650 866.1 20.1 0.817 | 563.0
Molecular weight: 421.11. i) Radius of the Capillary tube: 0.04803 cm.
Depth: 0.1 mm.
The liquid boils at 191° C. constantly; it solidifies easily and the
crystals melt then at 0°.5 C. The value of x at the boilingpoint is
about: 19.3 Erg. per cm?..

Molecular Surface-energy
in Erg pro em’. Fig. 1.
7170

450
“S§0°-60°- 40° 20° O° 20° 40° 60° 80° 100°/20° 740° 160° 150° 200° 220°

389

V.
Ortho-Toluidine: CH, .CgH,.(NH,) .
(1) (2) |
E ; Maximum Pressure 1 Surface- : Molecular
aU z= se tension x Specific Surface-
oe . . .
&_ jin mm. mer- in Erg. pro | gravity d energy in
Es cury of in Dynes ane. Se aa4e Erg. pro cm?
5 a: ‘
= ORNS |
—20° 1.573 2098 .0 | 45.4 1.027 1005.8
0.6 1.492 1989.1 43.0 1.013 961.4
9.3 1.465 1953.1 42.2 1.006 947.9
25 1.403 1870.5 40.4 0.992 | )ikeyGE) 5
34.6 1.375 1833.1 39.6 0.985 902.1 |
50.1 1.310 | 1765.8 Sileu 0.973 | 865.8 |
70.5 1.234 | 1645.2 39,0 0.957 | 824.4
101.4 ielS3 151025 S285 | 0.933 767.6
123.2 1.043 1391.0 29.9 0.916 714.9
144 0.957 1277.0 27.4 | 0.899 663.3
149.5) 0.937 1249.8 26.8 0.895 650.8
172 0.831 | 1108.2 Zoe 0.877 583.3

Molecular weight: 107.09. Radius of the Capillary tube: 0.04385 cm.
Depth: 0.1 mm.
The ortho-toluidine boils at 197.4 C. constantly. It is perfectly
colourless, but above 180° C. it gets gradually reddish brown. At
the boilingpoint 7 = 19.9 Erg pro cm’.

VI.

Thymol : (CH;),CH. CsH;. OH(CH3).

& Maximum Pressure H Surface- | eer Molecular |
EO) 5 || ea ok ees tension z% Wael te Surface- |
Vo 5 : :
a jin mm. mer- in Erg. pro itv d energy / in
5 . gravity |
E ¢ vary ot IPRS cm?, bk Erg. pro cm*:
g° 1.176 | 1567.9 34.2 0.986 975.1
25 1.109 1478.5 32.2 0.968 929.4
45.7 1.054 1405.7 30.6 0,952 893.1
710.7 0.991 1321.9 28.6 0.933 846.0 |
90.1 0.943 1257.0 27.3 0.920 815.2 |
115 0.875 1156.6 ZOE 0.901. 766.0
135.3 0.825 1099.3 23.8 0.887 728.2
“160 0.703 935.9 21.9 0.867 680.3
)* 190.1 0.628 837.0 19.5 | 0.845 616.2
er 0.578 770.3 17.9 0.829 572.9
Molecular weight: 150.11. Radius of the Capillary tube: 004439 cm. ;
in the determinations indicated by *, R
was: 0.04803 cm.

Depth: 0.1 mm.

The substance melts at 51°.5 C., and boils at 231.°5 C. constantly ;
it can be undercooled to a high degree. At the boilingpoint ~ is 16.6
Erg. The specific gravity at 24.°4 C. is 0.9639.

Ww
co

Proceedings Royal Acad. Amsterdam. Vol. XVII.

390

VII.

& Maximum Pressure
10)
D0 7
| ES in mm. mer- sa AGS
2 cury of 0° C. y
| |
le? 1.405 1873.1
S25r1 1.306 1741.2
| 245) e222 1629.2
tas: || 1.110 1479.8
*04.5| 1.034 1378.7
115.2 0.946 1261.2
135.3] 0.875 1166.9
(160 | 0.791 1054.6
192.5 | 0.686 914.6
I
| D

Methylbenzoate: C,H,;.CO. O(CH;).

Surface-

tension x
| in Erg. pro
cm*.

Specific
gravity ayo

Molecular
Surface-
energy “in
|Erg. pro cm2,

—KMNMMMWWwWwFt |
SCnanorhaA-
ADWRhREADWS,

epth: 0.1 mm.

Molecular weight: 136.06. Radius of the Capillary tube: 0.04439 cm.;
in the observations indicated by *, the
| radius was: 0.04352 cm.

The boilingpoint of the compound lies at 195.°2 C. The liquid can
be undercooled as far as —21° C.; then it crystallizes, and the crystals

melt at about —15 C. Atthe boilingpointthe value of , is: 19.4 Erg. pro cm’.

Specific
gravity Ayo

Molecular
Surface-
energy vin
Erg. pro cm:.

1.081
1.066
1.047
1.032
1.009
0.995
0.980
0.964
0.945
0.921
0.914

1045.7
1001.3
947.7
904.3
833.8
782.1
738.5
694.6
624.7
554.9
539.7

adius of the Capillary tube: 0.04439 cm. ;

in the observations indicated by * this

VIL.
| Ethylbenzoate: CyH;.CO. O(C:Hs).
E J | Maximum Pressure H Surface-
sos tension 7
Heese in Erg. per
| Se ht - :
| =.= jin mm. mer-| . f
& jcury of 0° C.| in Dynes cm’.
Pabete eat | | aw
550-51) Absssun| wuireses 39.0 |
0 | Lei) | 1694.1 | 37.0 |
be ay | 1.213 1617.6 34.6
* 45.1) 1.148 1530.4 S2ai
he ztey | 1.044 | 1392.4 29.7
* 04.4 0.972 | 1295.9 27.6
114.6 0.892 1189.4 25.8
| 135.4| 0.833 | 1110.6 24.0
160.2) 0.740 986.7 21e3
| 192.1] 0.649 | 865.0 18.6
| 200 0.628 | 838.0 18.0
—— — — = —< = | —
Molecular weight: 150.08. R
radius was: 0.04352 cm.
| The compound boils at 210.°8 C. It can be undercooled as far as

—79' C., and then slowly crystallizes to a white mass, which melts

at —57? C. At the boilingpoint, z is 17.4 Erg. pro cm*. The great
viscosity ofthe liquid at -70° C. makes accurate measurements impossible.

391

IX,
Benzylbenzoate: CoHs CO _O(CH . CzHs). a ae
8) .
ae Maximum Pressure 1 Surface- feline Molecular
Bo. a =| satensionyy peene Surface-
Be in mm. mer- | in Erg. pro | gravity d,, | energy ” in
= cury of in Dynes 2. Erg. pro cm’.
EB 0°C. Wee Be
51-8). 1.622 2162.4 | 47.4 1.153 1533.2
0 1.548 2063.5 45.2 1.136 1476.6
25 1.456 1941.9 42.5 oye) 1405.7
45 1.384 1851.8 | 40.5 1.099 135235
710.8 1.294 1725.8 37.6 1.078 1271.9
90.8 1.230 1640.0 35.8 1.062 Wn eli22se2
106.2 1.179 1572.4 34.3 1.042 1186.9
135.1 1.092 1455.2 Slei 1.027 1107.6
*159.9 0.949 1265.9 29.8 1.006 1055.6
“190 0.890 1186.7 27.9 0.982 1004.4
S215 0.849 1132.6 26.6 0.965 968.8

Molecular weight: 212.10. Radius of the Capillary tube: 0.04439 cm.;
in the observations indicated by *, this
radius was: 0.04803 cm.

Depth: 0.1 mm.

The substance boils constantly at 308°? C.; it can be undercooled
as far as — 70? C., and then crystallizes. The meltingpoint is some-
what higher than -++ 12° C. At the boilingpoint % is 22.6 Erg pro cm’.
The density at 25” C. is: Ayo = 1.1151; at 502 C.: 1.0940; at 75° C.:

1.0724; at PC: Ayo= 1.1357 — 0.000814 ¢.

Salicylic Aldehyde: C,H,.COH,

|
: p | Maximum Pressure H Surface- Specifi Molecular
hag = oa tension x Decne Surface-
| es in ae Wee ‘gras in eS pro | gravity dg. ety yn i
2 et cm? rg. pro cm*.
0 1.534 2045.5 44.8 1.176 989.4
25 1.443 | 1923.8 42.1 1.152 942.6
45.5 1.368 1823.8 39.9 1.132 903.9
70.7) 1.274 1698.6 STL 1.108 852.5
90.5 1.205 1606.5 35.0 1.090 813.1
116.2) 1.115 1486.8 32.4 1.066 764.0
135.4 1.053 1403.8 30.6 1.052 127.9
“160 0.896 1195.1 28.1 1.030 677.9
1909 0.796 1061.9 24.9 1.002 607.2

-- ——+-- a ——— ——— il — ——-~ = - —-—--— —~—— = —
Molecular weight: 122.05. Radius of the Capillary tube: 0.04439 cm. ;
in the with * indicated observations, this
radius was: 0.04803 cm. Depth: 0.1 mm.
The boilingpoint is constant at 192.°5 C.; the substance soon solidifies,
and melts at —7> C. At 25° C. the specific gravity is: dy. = 1.1525;
at 50 C.: 1.1282; at 75° C.: 1.1036. At ¢ in general: a4, = 1.1765—

0.000954 t—0.00000024 ¢?, At the boilingpoint, the value of x is: 25.4
Erg. pro cm?,

26*

392

in the observations indicated by *, the
radius was: 0.04803 cm.
Depth: 0.1 mm.

The compound boils constantly at 201. 5 C.; and becomes solid at
—20° C.; it melts at + 20°.5 C. At the boilingpoint the value of x is
22.6 Erg. pro cm*. The specific gravity at 25° C. is: ayo = 1.0236; at

| 502 C.: 1.0026.

XII.
| (CH,).:C.CH.CH, COOH.
| @-Campholenic Acid: |. >CHe
(CH,).C: CH
| . Nl al | oz 1 pa a . z
E : Maximum Pressure H | Surface- | ane Molecular
SS peste ie —| tension x peeilic Surface-
a. — |in mm. mer- in Erg. pro | gravity d, | energy # in
Wes eee Pe ate Os in Dynes cm’. Erg. pro cm’,
ie = ole eOSIC a | Lane
—19.8 (1.695) (2259.8) (52.6) | 1.030 (1598 .6)
1.177 1569.2 | 37.0 1.016 1114.1
25 1.077 1436.6 33.8 | 0.999 1029.4
45.4 1.019 1358.5 319 0.985 980.9
TOA Wscke |) 12D 29.8 | 0.969 926.6
85.3 0.915 1220.1 28.6 0.960 895.0
P| 0.846 | 1128.5 26 4 0.939 838.7
138.1} 0.805 1073-2 25.1 | 0.925 805.6
156 | 0.771 1027.9 | 24.0 | 0.913 771.5
2A 0:728 | 970.2 22.6 0.902 739.1
191.7 0.664 885.2 20.6 0.889 680.5
212 | 0.608 810.6 | 18.8 0.876 627.8
————— - ae . a No ee ee eee ee
Molecular weight: 168.13. Radius of the Capillary tube: 0.04803 cm.
Depth: 01 mm.

Under a pressure of 12 mm., the compound boils constantly at
153° C. Below 0° C. the liquid is extremely viscous; although the
growing of the gas-bubbles lasted about 50 seconds, the measurements
at —19°C. cannot be considered to be very reliable. The substance
| solidifies at —79 C.; above 160°C. it gets yellow by aslowly proceed-
| ing decomposition.

— —

Molecular Surface-energy
in Erg pro cm?
Fig. 2.

I00
40°-20° O° 20° 40° 60° SO° 700° 720°740°760° 180° 209° 220°

§ 3. Values of the Temperature-coefficients of the molecular
Surface-energy |.

394

Nitrobensene.

0 |
Temperature-interval: a in Erg:
t

between 5° and 35° 1,53
SOC aml 1,93
TAI able 2.16
WDD ee 2,25
145099, else 2,31
Aniline.
between 0°? and 35° 1,57
Sole OS 1,73
102 AS 2,16
o-Toluidine.
between —20° and +-101° 1,98
LOC 144° 2,44
14420 WP? 2.85

Above 1602 a graduél decomposition
with colouring of the liquid, sets in.

Methylbensoate.

between 0° and 25° 3,0

DOR MEADS 2,6

45° >= 192° 2,21
Bensylbenzoate.

between —22° and -+-135° 2,70

135omer 160° 2,08

160°, 211¢ 1,66
Acetophenone.

between 25° and 45° 2,99

RSD ee Ale 2,45

TEE, OS 2,19

90°, 160° 1,76

16025 7,7 #2002 1,61

o-Nitrotoluene.

Ou
Temperature-interval: va in Erg:
t
between 0°? and 25° 1,81
BRP 7 282 2,19
492 232 2,29
1232 8 4a 2,42
144° , 170° 2,82
Dimethylaniline.
between 26° and 46° 2,12
AGS fyi 2,23
Thymol.
between 0°? and 160° 1,83
16025 sez 2,09
Ethylbenszoate.
between —20° and +200° 2,29

Salicylic Aldehyde.

0° and 160°
160° , 190°

between 1,98

2,19

a-Campholenic Acid.
between —19°,8 cannot be determined

and 0° independently of
the viscosity
GF Aye 3,39
25°, «45° 2,42
45°, 85° 2,12
852 ele 1,76
117° ,:138° 1,59

Above 138° (decomposition) ca. 2,6

3esides some straight lines, there are found here several curves

for

the dependence of « and ¢, showing in contradistinction with

the formerly deseribed ones, the shape of that of wuater.

Groningen, June 1914.

Laboratory for Inorganic Chemistry

of the University.

- 395

Chemistry. — “The Temperature-coefficients of the free Surface-
energy of Liquids, at Temperatures from —80° to 1650° C.:
IV. Measurements of some Aliphatic and Aromatic Ethe:s.”
By Prof. F. M. Jagger and Jun. Kany. (Communicated by

Prof. P. van Rompurau.)

§ 1. In this communication the results obtained in the measure-
ments of the free surface-energy of a number of ethers, are recorded
by us. With respect to the purification-methods and the determina-
tion of the specific weights, we can refer to communication II of
this series); also the arrangement of the data and the significance
of the diagrams are completely the same as indicated before.
This series includes the following aliphatic terms:

Amylacetate ; Diethyl-Ovalate ; Diethylmalonate ; Diethylbromo-
malonate; Diethyl-Ethylbenzylmalonate; Dimethyl and Diaethyltartrates;
and the following aromatic substances :

ortho-Nitroanisol; Methyl-, Ethyl-, and Phenyl-Salicylates ; Methyl-
Cinnamylate.

| | |

I.
Amylacetate: CH3.CO.0O(C;H,;).
Semi, oe | Bir
ee Maximum Pressure H | Surface. | : Molecular
oe = tension x Specific | Surface-
reecennl in Erg. pro i | energy “in
in mm. mer-| .; : gravity d,. gy !
es cury of 0° C.| Ul TONES cm?. | : |Erg. pro cm?.
|
| | | : | a \ tie |
| | | ; a ;
SiN 1.099 1465.8 34.6 0.968 907.8
ir 4 0.915 1220.1 28.7 0.918 780.0
0 | 0.850 | 1132.6 26.6 0.896 734.9
25.8) 0.771 | 1028.6 24.1 | 0.869 679.5 |
46 | 0.712 | 949.4 22.2 | 0.847 636.8
66.5. 0.653 870.3 20.3 0.827 591.6 |
86.5) 0.600 | 799.5 18.6 0.808 550.5
106 0.549 7132.9 17.0 0.790 510.8
| 125 0.506 | 674.6 15.6 0.774 475.1
| 614.6 | 14.2 0.752 | 440.9
|

| Molecular weight: 130.11. | Radius of the Capillary tube: 0.04803 cm.
Depth: 0.1 mm.

The boilingpoint of the carefully dried compound lies at 148.94 C.;
| at this temperature x is 14.0 Erg. pro cm?®.

1) F. M. JAnGER and M. J. Suir, These Proc. (1914) p. 365.

396

II.

Diethyl-Oxalate: (C2H;) 0.CO.CO. O(C)Hs5).

| = | Maximum Pressure 1 Surface- , Molecular

—20.7| Nt rizt | 1569.9 37.0 1.139 941.0

Om ha OU 1482.5 34.9 1.110 903.0

26 | 1.025 | 1366.5 32.1 1.074 848.8

| 46 om52 | «(1278.4 «| = 30.0 1.050 805.5

| 66.7, 0.896 1195.1 | 28.0 1.025 764.0
86.5 0.818 1091.0 25.5 1.001 706.8
106 | 0.768 1024.4 23.9 0.977 673.3
125) 9 0.717 955.9 22.2 0.954 635.4
145.5 0.650 866.6 | 20.1 0.930 581.1
166 0.568 15des 17.6 0.905 521.8
184 | 0.478 637.3 14.6 0.883 440.0

Molecular weight: 146.08. Radius of the Capillary tube: 0.04803 cm.
Depth: 0.1 mm.

The substance boils at 99.°5 C. constantly, under a pressure of

about 12 mm. In solid carbondioxide and alcohol it soon solidifies,

and melts at —41.°5 C. Above 160? C. the ether seems to decompose
slowly.

Ill.

| Diethylmalonate: (C2H5) 0. CO.CH,.CO.O(C,Hs).

= _ | Maximum Pressure H Sur face- : Molecular
eS eee | at ensioney Specific Surface-
oD ie) . . .
a” |in mm. mer- _ in Erg. pro | gravity d energy » in
|} ££ | cury of in Dynes em? AS Ere nco
| 2 ole | ; g. pro cm’,
=
\—19.9) 1.237 1649.2 35.5 1.095 985.3
0.7 1.167 1555.8 | Oo, 1.075 941.2
8.5) 1.142 1523.2 32.9 1.068 928.4
| ayy 1.077 1435.9 31.0 1.050 884.8
| 34.5 1.044 1391.9 30.0 1.041 861.2
50.1) 0.994 132582) 28.5 1.025 826.6
| 69.2) 0.920 1226.8 26.3 1.005 7712.9
10204 0.804 1071.8 23.0 0.969 692.5
124.5 0.723 963.9 20.6 0.945 630.7
144 0.660 880.2 18.8 0.924 584.3
| 148.7) 0.649 866.4 18.5 0.919 571.1
tpl | 0.571 761.6 16.2 0.896 513.9

Molecular weight: 160.1.

Depth: 0.1 mm.

Radius of the Capillary tube: 0.04385 cm.

| The compound boils constantly at 197.°3 C.; after crystallisation,
it melts at — 50° C. At 25° C. the specific gravity was 1.0518; at 50° C.:
1.0254. At the boilingpoint the value of x is: 13.7 Erg pro cm*.

397

IV.

| Diethyl-Bromomalonate: (C2H;)O.CO.CHBr. CO. O(C2Hs).

| |

vu . |
= _ | Maximum Pressure /7 | Surface- | ; Molecular |
WO = —| tension x | SSE Surface- |
oe inmm,mer- | _ in Erg. pro | gravity d4o energy / in
ae cury of in Dynes | cm2, | \Erg. pro cm2,|
fe (HKG; |
—20.7 1.250 1666.5 | 39.1 1.464 1168.2 |
0 1.165 1553.2 36.4 1.436 | 1101.6
26 1.065 | 1419.9 33.2 | 1.401 1021.5
45.5 0.999 133259 Sel | © tess 968.9
66.6) 0.943 Zoe || 29.3 1.347 | 925.4 |
86.5 0.896 1195.1 27.8 1.320 890.0
106.5 0.853 1136.8 26.4 1.293 } 856.9
126 0.815 | 1086.8 25.3 1.266 | 832.8
| 146 OF780) Fa 103959 24.2 1240 807.7
i

Molecular weight: 239.09. Radius of the Capillary tube: 04803 cm.;
Depth: 0.1 mm.

Under reduced pressure (ca. 20 mm.) the substance boils constantly
at 121° C.; at —54> C. it becomes a jeily, but does not crystallize.
Above 150° C. it begins to be tinged brownish, apparently by beginning
deposition. The specific weight at 25°C. is: 1.4022; at 50° C.:: 1.3688;

ato? 1Gr 13359 Ata Gs: Ago = 1.4361—0.001366 ¢-+ 0.0000004 #2,

Diethyl-Ethylbenzylmalonate:
(C2H5)O . CO. C(CpHs) (C7H;). CO. O(CoHs).

EB Maximum Pressure 7 Surface- ; Molecular
a a = tension + Specific Surface-
° . | :
a. in mm. mer- in Erg. pro | gravity d energy v- in
se cury of in Dynes wae - 2
2 0-°C. i Erg. pro cm2,
fo} ]
—20.2 (2.174) (2898 . 4) (68.8) 1.086 (2775.0)
Ome 1.241 1654.5 | 39.0 1.072 | 1586.7
26 1.121 1494.9 35.2 1.052 1450.1
| 45.5) 1.050 1399.9 32.9 1.035 1370.2
66.6) 0.984 Sle 30.8 1.016 | 1298.7
86.7) 0.940 1253.4 | 29.4 | 1.001 1252.1
106 0.901 1201.2 28.1 | 0.986 1208.8
126 0.853 1136.8 | 26.6 | 0.971 | 1156.0
146 | 0.805 1073.2 2m } 0.956 1102.2
| 166 | 0.759 1011.9 23.6 0.941 1047.3
| 184 | 0.690 920.3 | 21.4 0.927 959.2
206.5) 0.637 849.5 | 19.7 0.911 893.3

Molecular weight: 278.18. | Radius of the Capillar tube: 0.04803 cm.
Depth: 0.1 mm.
Under 12 mm. pressure, the substance boils constantly at 189° C.;

at — 79° C. the liquid becomes a feebly opalescent glass. Already at
— 20° C. the viscosity is enormous, and at 0? C. again very great.
The grow of the gas-bubbles at 0° C. lasted about 40 seconds. The

specific gravity at 25°C. is: Ayo —HOpa ry at o0m Gor leOs22 ator Ges
1.0098. At ¢° C. in general: A4o = 1.0725 — 0.000746 t—0.0000012 ¢’.

VI.
Dimethyltartrate: (CH3)0.CO.CH(OH)CH(OH).CO.O(CH3).

45° 1.490 1986.6 43.2 1.306 1144.6
| 70.7 1.405 1873.1 40.7 1.281 1092.2

90.7) 1.340 1786.5 38.8 1.261 1052.2

116.2) 1.255 1673.2 36.3 1235 998.2
135.5 1.200 1599.5 34.7 1:216 964.1
159.6 1.046 1395.0 o2em Vai key 920.7
"190 | 0.974 1299.2 30.4 sila 876.1
| 210.3 0.929 1238.5 28.9 1.131 842.7

| Molecular weight: 178.08. Radius of the Capillary tube: 0.04439 cm.;
in the observations indicated with *, it was:
0.04803 cm.

Depth: 0.1 mm.

The compound boils under 12 mm. pressure, at 180° C. constantly ; at
—79°? C. it becomes a glass, which crystallizes with extreme slowness; |

the solid substance melts at + 48° C. Even at 25° C. the ether is so
viscous, that no reliable measurements were possible.

z VII.
Diethyltartrate : =
(C,Hs)O. CO. CH(OH). CH(OH). CO. O(C2Hs).
E f Maximum Pressure Surface- Specifi Molecular
ae |e ————e tension , Beane Surface-
ein mm. mer-| _ in Erg. pro | gravity d,, | energy » in
a cy | in Dynes cm?, Erg. pro cm?.
25° role 1755.5 37.6 1.210 1155.4
45.3 1.241 1654.4 35.4 1.191 1099.3
74.3) 1.134 1512.0 | aoe) 1.164 1018.5
91.1 1.082 | 1443.0 | 30.8 1.147 980.8
110.1) 1.024 I) 136429) 9) 29.1 1.129 936.5
134.7) 0.948 1263.8 26.9 1.105 878.2
| 150.1] 0.899 | 1199.4 | 25.5 1.091 839.6
| 160.3 0.872 | IG 24.7 1.081 818.2
| 192.7| 0.765 1019.9 22.0 1.050 743.1
212.7) 0.716 955.9 20.2 1.032 690.2
Molecular weight: 206.11. Radius of the Capillary tube: 0.04352 cm.
Depth: 0.1 mm.

Under circa 16 mm. pressure, the boilingpoint is 166.5 C. At —79°

the liquid becomes glassy, and crystallizes very slowly at —20° C.:

| only after 5 or 6 hours all has got crystalline. The meltingpoint is

15° C, At 0° and lower temperatures the liquid is too viscous, to
make reliable measurements possible.

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400

VIII.
ortho-Nitro-Anisol : Cs . . CgHy. re
(

al
| Ee | Maximum Pressure Surface- " Molecular
ae | aa es — tension x Specific Surface-
& | 01a
0? 1.613 | 2150.4 50.8 e273 1237.6
25.4 5S | 2048.8 48.4 1.247 | 1195.4
44.9) 1.480 1973.8 46.6 1.227 1165.1
70.1) 1.390 | 1853.0 43.7 1.202 1106.1
85.3 1.340 1786.4 42.1 1.187 1074.6
117 1.227 1635.8 38.4 1.156 997.6
138.2) 1.160 1546.5 36.3 1.135 947.3
| 156 1.109 | 1478.2 34.7 1.118 921.8
| 172 1.043 | 1390.8 | 32.6 1.102 874.4
191.5 0.968 1290.5 | 30.2 1.083 819.4
| A 0.850 S350 e ss) 26.5 | 1.062 728.8
—— a —- - -—— — = | — — — —
Molecular weight: 153.07. Radius of the Capillary tube: 0.04803 cm.
Depth: 0.1 mm.
The substance boils constantly at 272’ C.; at 20° it solidifies,

and melts at + 10° C. Above 165° C. a slow decomposition begins.
The specific weight at 25° C. is: Ayo — 124712" at o0Rn CG. al 22s mat

75° C:: 1.1970: at ¢ generally: A4o= 1.2732—0.001052 t-+ 0.00000048 #2.

IX.
Methylsalicylate: C,;H,(OH).CO.OCH3 .
ie ee (1) (2)
vo | 4
5 ' Maximum Pressure Surface- 4 Molecular
eg | = = tension Specific Surface-
Bs | in mm. mer- | in Erg. pro | gravity d,, | energy ” in
= cury of in Dynes cm?2. Erg. pro cm2.
(een SPP
—19:8| 1.518 2023.8 44.2 1.220 1102.9
0.3 1.436 1914.8 41.8 1.202 | 1053.4
gee Sie 1829.0 39.1 1.179 998.1
“45 1.303 1737.2 | Silo! 1.158 956.4
Rr aewll 1.193 1590.1 | 33.9 1.128 | 891.7
* 94 | 1.124 1498 2 31.9 1.110 | 848.3
114.5) 1.031 1374 2 29.8 1.092 | 801.2
13522 0.968 1290.5 27.9 1.073 758.4
| 160.5 0.867 1155.9 24.9 1.050 | 686.7
192.9 0.760 1013.7 21.8 1021-1) ) seieke
212.2 0.696 928.1 19.8 1.003 | 562.9

| Molecular weight: 152.06. Radius of the Capillary tube: 0.04439 cm.;
in the observations, indicated by *, it was
0.04352 cm.
Depth: 0.1 mm.

The substance boils at 217.°6 C. constantly; it can be undercooled
| as far as —50° C, and crystallizes to a solid mass, which melts at
| —16° C. At the boilingpoint z is: 19.3 Erg. pro cm?. The density at
| 25° C. is: dyo = 1.1787; at 50° C.: 1.1541; at 75° Ce l28opAtee Cr

Ayo = 1.2023—0.000924 ¢ —0.0000008 ¢.

401

Ethylsalicylate: C;H,(OH) .CO.O(C,Hs) .
(1) (2)

lars ; |
ety Maximum Pressure H | Surface- : _ Molecular
| BS tension | SITES Surface-
oe ‘in mm. mer-) | | in Erg. pro | gravity dao | energy » in
E-= | cury of | in Dynes | aa Erg. pro cm?.
| (1 (C, |
— ——st = — _ = — —
0° 1.346 1794.5 39.1 1.154
* 25 1.275 | 1700.4 36.3 180, Were
e451} 1.206 1608.5 34.3 1.110 | 966.7
|; a4. 1) 1.110 | 1479.8 SHES) 1.082 903.0
\* 94.3] 1.047 | 1395.9 29.7 1.063 | 861.6
} 115.1) 0.963 | 1284.1 27.8 1.043 816.7
135.2} 0.906 | 1207.4 26.1 1.024 716.2
159.8; 0.828 | 1103.8 23.8 1.001 118.6
193 OM7123)) |) © 96452") 2087 0.980 633.9
| 212.5 0.669 892.1 | 19.1 | 0.962 592.9
Molecular weight: 166.08. Radius of the Capillary tube: 0.0 ‘439 cm.
in the observations, indicated with * it was:
0.04352 cm.
Depth: 0.1 mm
The substance boils at 231.°2 C. constantly; at —20° C. it solidifies

and melts at ca. —10° C. At the boilingpoint y is 17.6 Erg pro cm?.
The specific weight at 25° C is: 1.1298; at 50? C. : 1.1053; at 75° C.:1.0806. |
At ¢@ it is calculated from: d4o = 1.1541—0.000968 ¢ -—0.00000016 7. |

XI.
Phenylsalicylate (Salol): C;H,;(OH) .CO.O(C Hs). |
(1
| = _ | Maximum Pressure Z | Surface- | } WeMolccnlartl|
hy —————— | tension z Specific | Surface- |
&. |in mm. mer-| | in Erg pro | gravity d,. | energy 4 in |
(ES cury of in Dynes 2 [aSean ey ac) 2 |
J 2, Erg. 4
oe oc | | cm | rg. pro cm
|—20-1| (2.613) (3482.8) | (76.5) 1.221 (2396.4) |
0 | 1.571 | 2095.1 45.7 | 1.202 1446.7 |
725) 1.485 1980.6 | 43.2 1.179 1385.2
| 45 1.419 S925 3 5 41.2 | 1.160 1305.1
TESS | 1035 EAT agk | 38.7 1.136 1272.0- |
fe O0st) "4.272 © "|| ¥ 1605.8 36:8: 9/1120 122th tee}
116 1.193 1590.4 34.5 1.098 1160.0
| 135 1.132 | 1509.3 | 32.7 1.078 1130.3
S16085) 0.971 | 1295.0 30.3 | 1.055 1046.3
*189.8} 0.890 HTSO=i ee 27.7 1.026 974.5
\*211.6 0.846 1128.5 | 26.3 1.006 637.5
Molecular weight: 214.08. Radius of the Capillary tube: 0.04439 cm.;
in the observations, indicated with * it was :
0.04803 cm |
Depth: 0.1 mm.

Under 12 mm. pressure, the salol boils at 173° C.; at —33° C. it
crystallizes spontaneously, and melts at +42? C. It can be under-
cooled to a very high degree, and possesses a small velocity of crys-
tallisation. At 35 C. the specific gravity is: 1 1697; at 50 C.: 1.1553;
ator 11330

402

Some other derivatives of aromatic phenoles: Anzsol, Phenetol,
Anethol, Guajacol, Resorcine-Mono-, and Dimethylethers; Hydrochinon-
Dimethylether have been described before by the first of us). The
temperature-coefficients of these compounds are however also reviewed
in the present communication, because they were not mentioned in
the one referred to. (Vid. also the preceding communications.)
Molecular Surface energy

in Erg pro cm?. Fig. 3.

7220
7190
1160

1130

530 oe
=20° O° 20° 40° 60° 80° 100° 120° 140°160" 180" 200° 220° Semperalure

1) F, M. Jarcer, These Proc., Comm. I. (1914) p. 354 seq.

403

XII,

Methyl-Cinnamylate: CjH/,.CH:CH.CO.O(CH,).

5 , Maximum Pressure H | Syurface- | - | Molecular
ise = 3 —_| tension x Specific Surface-
a jin mm. mer- in Erg. pro | gravity d,, energy » in
eo cury of in Dynes | em?, | : Erg. pro cm?.
Ee O2NE: | | |
45, HeS20r ee LIL S le | 38-1 AN | 7 1062 Ne anOs.2
71 1.230 1639.8 | 35.8 1.038 } 1038.1 |
90.6) 1.166 1554.5 | 33/69 | 1.020 | 994.5 |
116.2) 1.092 1455.2 Madi | 0.997 944.2
135.4) 1.024 136552555) 29.7 0.980 894.9 |

*159.7} 0.868 ) sea | Palle! 0.958 | 829.0 |

*190.5) 0.777 | 1035.9 | 24.2 | 0.930 | 155) )lenmn|

*210.9 0.712 949.4 | Doel | 0.911 | 699.1

Molecular weight : 162.08. Radius of the Capillary tube : 0.04439 cm.;
* in the observations, indicated by * it was:
0.04803 cm.
Depth: 0.1 mm.

point ~ is: 18.6 Erg. pro cm?. The specific gravity at 35°C. is:
@4o = 1.0700; at 50° C.: 1.0573 at 75° C.: 1.0340.

The ether boils at 253.°5 C., and melts at 36.°5 C. At the boiling- |
|

§ 3. Values of the Temperature-coefficients of the molecular
surface-energy & of the studied compounds.

Amylacetate. | Diethyl-Ozalate.
Oe. Ou .
Temperature-interval: ae in Erg: | Temperature-interval: ae in Erg:
i | at
between — 70°? and — 21° 2,59 | between — 20° and 0° 1,8
— 219 and -- 662 -2)14 0°? and 66° 2,02
66° and 106? 2,03 66° and 106° 2,2
106° and 148° 1,73 106° and 146°? 2,3
146° and 184° 3,6

| Above 146? a decomposition seems
slowly to set in.

Diethyvlmalonate. Diethylbromomalonate.

between — 20? and + 171° 2,52 | between — 21° and 0° 3,20
} 0°? and 26° 3,08

| 26° and 46° 2,67

| 46> and 67° 2,04

67° and 86° 1,75

86° and 106° 1,63

106° and 126° 1,35

126° and 146° 1,23

404

Diethyl-Ethylbensylmalonate.

Ou
Temperature-interval: - in Erg:
t

between —20° and 0° cannot be deter-

mined indepen-
dently of the vis-
cosity.
OO wae 5,2
AN oy (HO 3,7
66° ,, 106° 2,25
106gm,, 126° 2,6
1262" 5, 146° 2
1462 wl OGSe- 2,15
166° ,, 206° 3,85

Above 166° a slow decomposition begins |
to make itself perceptible.

o-Nitroanisol.

between 0° and 45°? 1,61
45°, 172°? 2,29 |
Wize loos 2,82
egy ee Pye) 4,45

Above 170°? a gradual decomposition |
sets in, which proceeds very slowly.

Ethylsalicylate.
between 0° and 212° 2,23
Methylcinnamylate.
between 45° and 210°,9 2,44
Phenetol. |
between —12° and 0° 2,0
0? , 74°,3 2,29
74°, 160° 2,13
The curve is almost a straight line, |
Om
with sama
Ot
Guajacol.
between 26° and 146° 2,17
1462, 2062 2,66

Dimethyltartrate.
Ou
Temperature-interval: x in Erg
t
between 45° and 117° 2,08
117°, 160° 1,71
160° ,, 210° 1,53
Diethyltartrate.
between 25° and 74°,3 2,15
pen Pile 2,35
Methylsalicylate.
2,30

between —19,°8 and 212°

Phenylsalicylate. (Salol).

| between —20° and 211°,6 2,43
Anisol.
| between —21° and -+45° 1,88
B52 91° 2,14
Co ole 2,63
Anethol.
between 24°,7 and 75°,1 2,53
15 eo 2,25

Resorcine-Monomethylether.
between —20° and O° cannot be deter-

mined indepen-
dently of the vis-
cosity.
QO 5 Base 4,3
26° OS 2,45
46° ,, 184° 1,82
184° ,, 206° 2,97
Above 184° a decomposition sets in

slowly.

405

Resorcine-Dimethylether. Hydrochinon-Dimethylether.
Ou Ou
Temperature-interval: va in Erg: | Temperature-interval: x in Erg:
t | OF
between —22° and U° 2,83 between 66° and 106° 2,11
D2 Vo Poe 2,2 | 106° ,, 166° 2,46
166° ,, 206° 2,88

Up to 166°, this -tcurve coincides
| practically with that of guajacol and of
resorcine-dimethylether.

Pyridine. | z-Picoline.
between —79° and —20° 1,79 between —70° and — 20°77 2,83
—20° , +25° 2,04 —20°,7 , +126° 2,02
25o re 92° 1,60
Chinoline. |
between —21° and +45°,2 1,92
45°, 115° 2,10
5 2302 2,33

§ 5. Also tor these substances one can state, that a decom-

position of the compound causes an extraordinarily rapid decrease
age Ou

of the values for x or « with inereasing temperature : a becomes
much larger in such eases with rising temperature. Furthermore it
can be seen from the cases of salo/, diethylbenzylmalonate, resorcine-
monomethylether, etc., that an extraordinarily great viscosity of the
liquid can appreciably diminish the accuracy of the measurements ;
however the case of dimethyltartrate on the contrary proves, that
sometimes reliable results can be obtained, even with very high
values of the internal friction.

Groningen, June 1914. Laboratory Inorganic Chemistry
of the University.

Chemistry. — “Vhe Temperature-coefficients of the free Surface-
energy of Liquids, at Temperatures from —80° to 1650° C.;
V. Measurements of homologous Aromatic Hydrocarbons and
some of their Halogenderivatives’. By Prof. Dr. F. M. Janerr.
(Communicated by Prof. P. van RompBvurGu.)

§ 1. In order to answer also the question of an eventual depend-
ence between the chemical constitution of liqnids and the values
of their free surface-energy and of its temperature-coefficient, in

Proceedings Royal Acad. Amsterdam. Vol. XVII.

406

this communication the results of the measurements are recorded,
made with a series of homologous hydrocarbons and some of their
halogen-derivatives. With respect to the methods of purification, the
determination of the specific gravities, and the significance of the
diagrams, we can refer to the previous communications.

This series includes the following terms :

Benzene; Toluene; para-Xylene; Mesitylene; Pseudocumene; Tri-
i y

phenylmethane; Chlorobenzene; Bromobenzene ; meta-Dichlorobenzene ;

yara-Eluorobromobenzene; meta-Eliorotoluene; and para-Chlorotoluene.

For the purpose of comparison with benzene, also Cyclohevane
was taken into account here; the data relating to benzene were’
already published in a former paper‘), but are repeated here once
more for comparison with the other hydrocarbons. The obtained
results are put together in tables, in the ordinary way.

§ 2. Aromatic Hydrocarbons and some Halogenderivatives.

it
Cyclohexane: CgHjo.

= ; Maximum Pressure H Surface- ee Molecular |

a = _ tension % pecific Surface- |

40 0.682 909.2 23m 0.768 BPA Pa = |
| 58 0.601 | 801.2 20.3 0.744 474.6 |
| 70 0.548 730.6 18.4 0.732 434.9 |
| 80 0.504 | 671.6 16.9 0.723 402.7

Molecular weight: 84.1. Radius of the Capillary tube: 0.05240 cm.
Depth: 0.1 mm.

The liquid boils constantly at 80.°7 C.; at this temperature the value
of x is: 167 Erg. pro cm®. Jt solidifies at 10 C.; the crystals melt at
+8 C. The specific gravity at 25° C. is. 0.7733; at 35° C.: 0.7645; " |
at 502707515 At tame, d4> = 0.7958—0.000913 ¢ + 0.00000053 #7, |

1!) FB. M. Jaccer and M. J. Smit; F. M. Jazarr and J. Kann; F. M. JAEGER,
these Proc., Gemm. I, II, IV. (1914;

407

II.

Benzene: CoHg.

| E Maximum Pressure Z | Surface- idee Molccula®. |
SS — _| tension x peeie Surface-

|. jin mm. mer-) _ in Erg. pro | gravity d,, | energy » in

ao CaS | in Dynes | cm?. | Erg. pro cm?.

=a ———————— = = = =
5.4 1.077 1436.7 30.9 0.895 607.7
9.5 1.055 1406.5 30.2 0.889 596.6
owl 0.969 1291.9 | 27.7 | 0.873 553.8
35 0.920 1226.5 26.3 0.862 530.3
55 0.836 1114.6 |} 23.8 0.841 487.8
714.6 0.757 1009.2 21.6 0.817 451.4

Molecular weight: 78.05. Radius of the Capillary tube: 0.04385 cm.
Depth: 0.1 mm.

The compound was already formerly described !), and is here only
mentioned for purpose of comparison. The boilingpoint is 80.5 C.;
at this us ty DoE x is: 20.7 Erg. pro cm?.

1) JAEGER, These Proceedings, Comm. I. (1914).

Tin

Toluene: CH,. C,H;.

5 : Maximum Pressure /1 _ Surface- eee Molecular |
oe = tension 7 Preemie Surface- |
vo =) .
a jin mm. mer- in Erg. pro | gravity d,, | energy # in |
ES cury of in Dynes | em2 Ao 2 |
& 0°C. Erg. pro cm?
| |
I—71 | 1.385 1946.5 | 43.7 | 0.956 918.1
—21 | 1.090 Ip 45325 7 34.3 0.905 | 747.6 |
Om 1.006 1340.8 31.6 0.884 | 699.5 |
26 0.906 1207.16) 5} 28.4 0.860 640.3
46 0.831 1107.6 26.0 0.841 595.0 |
66.6 0.756 | 1007.7 | 23.6 0.823 547.9
| 86.5 0.693 924.4 21.6 0.803 509.7
| 106 0.637 849.5 19.8 0.783 475.2
| |

INoteeurar Weishe: 92. 06. Radius of the Capillary tube: 0.04803 cm.
Depth: 0.1 mm.

The commercial toluene appeared always to manifest a turbidity
of the liquid at — 22° and —79° C.; a solid substance in little quan-
tities separated at the walls of the tube. The here used toluene there-
fore was especially prepared by distillation of sodium phenylacetate;
it was dried by means of phosphorpentoxide, and boils at 109.°4 C,
Down to —20°C. it remains perfectly clear; at — 79° C. it shows, as
e.g other hydrocarbons (pseudocumene) do, a slight turbidity, At ‘the
peer z is ee es pro cm?,

PHT fi

para-Xylene: (CH,) .CgH,.
(1)

(CH3) .
(4)

E 7 | Maximum Pressure /I Surface-
go tension
a. in mm. mer- ' in Erg. pro |
e cury of in Dynes cm?2.
= OFIG:

a_|
Zoe 0.928 1236.7 29.1
45.9 0.853 1137.2 26.7
66 0.774 1031.9 24.2
86.5 0.709 945.2 22.1
106 0.648 863.9 20.1
126 | 0.597 7194.6 18.5

Molecular weight: 106.08. Radius

Depth: 0.1 mm.

The substance boils at 136.°2 C.
point z is about 181 Erg. pro cm?,

Specific

gravity d4o

Molecular
Surface-
energy » in
Erg. pro cm’,

of the Capillary tube: 0.04803 em.

and melts at 15°C. Atthe boiling
At 20° the density is Ayo = 0.8611.

V.
Mesitylene: (C/Z,);.CgH,. (1-3-5-).
= ‘ Maximum Pressure JI Surface- : Molecular
we tension ~ Specific Surface-
a in ua. mee ve | in Erg. Pro | gravity d4o energy in
Thien y o in Dynes em?, Erg. pro cm?.
coal | DXC. |
= | — . — = ————— ee
20-8 1.141 ! 1521.1 32.6 0.897 | 853.2
hy OL. | 1.061 1415.4 30.3 | 0.880 803.2
25.5 0.972 1296.0 iles| 0.859 746.2
45.2| 0.907 1208.7 25.8 0.843 703.8
140i 0.807 1075.4 | 22.9 0.818 637.3
91.3 0.755 1006.4 21.4 0.804 602.5
110 0.700 933.0 19.8 0.788 565.0
134.5 0.631 841.0 17.8 0.768 516.7
150.5 0.585 Ula. | 16.5 0.754 484.8
160.5, 0.562 749.3 | 15.8 0.741 469.7
|

Molecular weight: 120.1.
Depth: 01 mm.

The compound boils at 162.°8 C. constantly. At —46° C. it soli-

difies to an aggregate of long, silky needles.

Radius of the Capillary tube: 0.04352 cm.

VL.
Pseudocumene: (C//3), . CgH; (1-2-4-).
lia l Tr i z
| 5 _| Maximum Pressure H | Surface- | cee le Molecular
ig — —_ = | tension x pecilic | Surface- |
rae ‘in mm. mer-) | in Erg. pro gravity d, | energy in |
e= cury of in Dynes | cm. ‘ Erg. pro cm?.
= 0G: | |
= — 1 = = — ———— = SS SSS =
Bo ee ag) aa 0.910 | 883.9
| 0 1.031 | Is74eiy |) 3274 0.893 850.5
26 0.953 1270.1 29.9 0.871 798 .0
46 | 0.890 1186.4 27.9 0.855 153.9
66.5 0.828 1103.5 25.9 0.839 708.8
86.5, 0.768 1024.4 24.0 0.823 665.2
105 0.725 966.1 | 22.6 0.807 634.7
125 0.656 | 874.5 20.4 0.792 | 580.1
145.9, 0.600 799.5 18.6 0.776 536.2
; 166 0.525 699.6 | 16.2 0.760 473.5

Molecular weight: 120.1. Radius of the Capillary tube : 0.04803 cm.
Depth: 0.1 mm.

The substance boils at 168.°5 C. constantly. It solidifies at —79° C.;
the meltingpoint is about —60° C. At the boilingpoint the value of
z is 15.8 Erg. pro cm?.

Molecular Surface-
energy in Erg pro c m2.
960

450
-S0°-60°-Y0°-20° O° 20° 40° 60° 80° 700° 720° 140° 760° 780°

Fig. 1.

Temperature.

Triphenylmethane: CH (C,H;);.

2) |

5 4 | Maximum Pressure /I Surface-

ae _—_— | tension x

| ae in mm. met : | in Erg. pro
E--= | cury of in Dynes cm2,

[ec | 0°C.

—— = = SSS = SSS a

| 138.4] 1.074 145254 pl) ones

| 156 1.044 1391.9 32.8

| 7p 0.999 | 1332.5 31.3

; ee Wesia) 1211.9 28.4

0.833 1110.5 26.0

Specifi Molecular
peeric Surface- |
gravity d45 energy » in |
Erg. pro cm?
0.984 1330.5
0.971 1302.6
0.959 1257.1
0.942 1154.4
0.928 1067.4

, Molecular weight: 244.11. Radium of the Capillary tube’: 0.04803 cm.
Depth: 0.1 mm.

The meltingpoint of the compound is 92° C.; it is hardly possible
to keep it in undercooled condition. Above 165° C. a slow decom-
position begins; finally the liquid is coloured brown. The specific
gravity 40 is at 95° C.: 1,017; at 100°: 1,013; at 125° C.: 0,994; at

150° C.: 0,975; it was determined by means of the hydrostatic balance.
Ate ayo = 1,013 — 0,00076 (¢ — 100).

VIII.

Chlorobenzene: C,H, Cl.

E Maximum Pressure H
aU |
So, | See
a. jin mm. mer-
Es cury of in Dynes
om Ov
o}
—16 1.252 1668.8
0 1.184 1578.3
25 1.143 1524.5
rao 1.099 1465.5
| 50 | 0.980 1306.6
70.5) 0.893 1190.2
| 90 | 0.805 1079.0
\*102 0.807 | 1075.4
Stas 0.751 1001.8
= 12255 0.717 955.9

Surface-

| tension x
in Erg. pro

cm?,

Specific
gravity d 40

Molecular

Surface-
energy in
Erg. pro cm?,

es
| Palio

So
HUW CAMCCO

is)
oO

144
128
101
090
-078
051
029
O16
-003
-995

as ee a

completely crystallized.

The compound boils at 131? C.

Molecular weight: 112.5). Radius of the Capillary
with the observations, indicated by *, R
was 0.04352 cm.; with those: **, it was:
0.04408 cm.
Depth: 0.1 mm.

tube: 0.04638 cm.;

constantly; at — 34.°5 C. it is

41]

Ix.

Bromobenzene: C,H, Br.

= : Maximum Pressure | Surface- |
aS — : tension i |
26 in mm. alee | in Erg
‘= | mercury 0 in Dynes ro cm?.
& | One: ae
° |
—17.5 1.394 | 1858.6 42.2
ee 1.309 |) 1746-4 | 39.6
~25 1.267 | 1698.5 | 36.5
*35.6 1.229 | 1638.5 | SHge
*49.8 1.172 156255 33.5
71.5 1.032 ISTEEO || 31.0
90.5) 0.953 | 1270.5 28.5
125.5) (0.875 1167.3 24.5
pal53 0.758 LOWER) 21.1

Depth : 0.1 mm.
The compound boils constantly at 154° C.

Molecular weight: 156.96. Radius of the Capillary tube: 0.04638 cm.; in
the observations, indicated by * R was:
0.04408; in those by **, it was: 0.04352 cm.

meta-Dichlorobenzene: C,H, Cl, (1-3-).

The boilingpoint is at 172.55 C. constant; the liquid can be under-
At

cooled to a high degree, but once solidified, it melts at —19° C.

the boilingpoint ~ is: 22.2Erg pro cm?. The specific gravity at 25°C.
is: 1.2824; at 50°C.: 1.2543; at 75° C.: 1.2253; at f C.: 1.3096—0.00107 ¢

| —0.00000072 f.

Molecular |
Surface- |
energy »
in Erg
pro cm?.

}

Molecular Surface-

energy in Erg per c.m?*.

412

450 2 — Temperature.
-40°20° 6° 20° 4b° 60° EI? 100° 120° 440° 60" 18D”
Fig. 2.
XI.
| para-Fluorobromobenzene: C,H,. /. Br (1-4-).
_——S ee ES : : ey
£ | Maximum Pressure H | Surface- Molecular
| ee ian Specific Surface-
| &. jin mm. mer- | in Erg. pro | gravity d@,,| energy v in
ears cury of in Dynes cm2, | Erg. pro cm?.
= OG: |
eines 1707.8 398 | 1.654 890.2
0 1.198 1597.2 37.2 1.626 841.5
25.5 1.106 1474.1 34.3 1.590 787.6
45.3 1.031 1374.1 31.9 1561 741.6
710 0.953 1270.1 29.4 1522 695.1
84.7| 0.906 1207.6 27.9 1.504 663.8
Hedi 0.810 1079.9 24.8 1.460 602.8
| 138 | 0.734 978.6 22.4 1.436 550.5
Molecular weight: 174.95. Radius of the Capillary tube: 0.04803 cm.
Depth 0.1 mm.

The boilingpoint is constant at 150° C.; the value of x there is:
21.2 Erg. pro cm’. The specific gravity at 25° C. is: Ayo = 1.5998;

| tat 50Gs 15538; atwiocn Ga M5147) eAb eaiteis. @4o = 1.6257 —0.00135
| t—0.00000168 #2.

oats 9

413
XU.
meta-Fluorotoluene: CH,.Cs,H,.F . |
(3) |
; : i Rests |
— Maximum Pressure | Surface- Fal Molecular
ig = 2 | tension ~ Specific | Surface-
| &e jin mm. mer-| — | in Erg. pro | gravity d A energy / in
| & | cury of in Dynes | cm?. oat Erg. pro cm2.,
is eed | |
Ae oe as _ aE en |
ie || Bessy 1782.5 42 | 1.097 909.0
—20.5 1.090 1453.3 34.2 1.041 764.7
0 1.006 1340.9 31.5 1.021 TNS:
25.4 0,906 1207.9 28.3 0,994 652.6
, 45.3 0.839 1118.5 26.2 0.973 612.8
| 70.2 0.760 1021.2 23.8 | 0.947 566.8
84.9 0.721 961.9 22.4 | 0.932 539.2

Erg. pro cm?

Molecular weight: 110.06.

Dept

h: 0.1 mm.

Radius of the Capillary tube: 0.04803 cm.

The boilingpoint of the substance is 114°.5 C.; 7 is there: 20.2
The density at 25° C. is:

d4> 1059942 o0P G:

0.9680; at 75°C.: 0.9420. At © it is calculated from: d4o= 1.0206—
—0,00106 ¢ + 0.00000016 ?.

Molecular weight: 126.51.

Radius of the Capillary tube: 0.04439 cm.;

in the observation, indicated by *, it was:
0.04803 c.m.
Depth: 0.1 mm.

The substance boils constantly at 162.5 C.; it solidifies at —22°C.,
| and melts at +7.°5 C. At the boilingpoint z is 20.1 Erg. pro cm?.

414

Molecular Surface-energy
in Erg pro cm?.

7020
290
960
930
200

S70

450
-80°60-40"-20° O° 20° 40° 60° 80° 100° 120 ryo'réo' 760" ‘Temperature

Fig. 3.

§ 8. Values of the Temperature-coefficients of the molecular Sur-
Fface-energie & of the liquids here studied.

Cyclohexane. | Benzene.
; Ou. . Ou.
Temperature-interval: a in Erg: Temperature-interval: ae in Erg:
Ot
between 9 and 80° Be between 5°,4 and 25°,1 2,73
This value is remarkably great; the 25 » 0D 2,20
curve is almost a straight line however. 55 » 14,6 1,85
Toluene. para-Xylene.
between —71°? and —21° 3,40 between 25°,5 and 45° 2,53
Ve 2 GAS 2,27 45286 2,43
Gili 86,5 1,90 86 » 106 2,21
86,5 , 109 1,76 106 7 126 1,71

415

Mesitylene. Pseudocumene.
Temperature-interval: a in Erg: Temperature-interval: = in Erg:
between —20°,8 and 0° 2,40 between —21° and 0° 1,60

0 lO 2,20 QO 2 2,00
15 » 110 2,06 20h an LAG 2,18
110 POO 1,97 146, «166 3,0
Triphenylmethane. Chlorobensene.
between 138°,4 and 156°? 1.59 between —16° and +25° 2,20
156 = algal 3.03 2 50 2,42
gil ney! 4.46 SOE e122 2,60
194 » iz 4.83
Bromobengene. meta-Dichlorobengene.
between —17,°5 and +125,°5 =.2,38 between —22° and 09° 2,79
1:25)50n,, 153 2,53 O) =) 224) 2,23
25 yo Anti
Ol se 1,88
WG si SS 1,64
136, 160 1,51
para-Fluorobromobenzene. meta-Fluorotoluene.
between —21° and 0°? 2,41 between —71° and —20°,5 2,85
OF} j 45 2,09 —20,5 , 0 2,49
ey py Lily 1.97 On, 25,4 2,38
lily EO) 2,49 25,45 45,3 1,99
45,3 84,9 1,85
para-Chlorotoluene.
between 25° and 45° 2,33
45 ay HL 2,23
Tie wallG Lor |
L1G, 160 1,49

|
Especially the last mentioned four cases prove once more very

Ou
strikingly the fact, that re cannot be considered as a constant, but
r t
that it is itself a function of temperature: in most cases in such a
way, that it will decrease with increasing temperature. With ch/oro-
and bromobenzene however evidently just the reverse happens. In the
same way benzene, toluene, p-vrylene and mesitylene belong to the first
group of substances, while the isomeric psewdocwmene manifests on
A Caen a
the contrary an increase of — with rising temperature. The devia-
tions of the linear decline are so great and in most cases so system-
atical, that they can by no means be accounted for by experimental
ae MOBY Fas
errors; the variability of F with the temperature must therefore
° t
be considered as an essential fact.
Groningen, June 1914. Laboratory of Inorganic Chenustry
of the University.

416

Chemistry. — “The Temperature-coéfficients of the free Surface-
eneryy of Liquids, at Temperatures from — 80° to 1650°C:
VI. General Remarks”. By Prof. Dr. F. M. Janexr. (Commu-
nicated by Prof P. RompBuren).

§ 1. If we wish to use the results up to now obtained in the
study of these more than seventy organic and about ten inorganic
liquids, to draw some more general conclusions, the following remarks
in this respect may find a place here.

In the first place it is proved once more, that the free surface-
also in the peculiar case of the electrolytically
conducting, molten salts studied at very high temperatures, — always
decreases with increasing temperature. This fact, an exception to
which also within the temperature-interval hitherto investigated —
has never been stated, must be esteemed in every respect quite in
concordance with the views about the origin of such surface-
tensions. It is immediately connected with the other fact, that
a decrease of the molecular surface-layer must be accompanied
by a heat-evolution, an increase of that layer however with a heat-

energy of liquids,

absorption, if the temperature is to remain constant. Furthermore
this gradual diminution of % with increasing temperature is in full
agreement with the continual levelling of the differences in properties
between the liquid phase and its coexistent vapour, when the
temperature is gradually rising: at the critical temperature the value
of y must have become zero’).

Of more importance for our purposes however are the following
results :

I. A linear dependence of y and ¢ appears in general noé to exist.
1] The observations prove the possibility
; of all the three imaginable principal spe-
cies of y-é-curves: the type 1, with a
concave shape towards the temperature-
axis; the type 3 with a shape convex to
that axis; and the rectilinear type 2.
Besides there are found some rare cases
of combinations of these three principal
types. Characteristic for type N°. 1 is,
that oh will inerease with rising tempe-

rature, while it decreases under those

oO t

circumstances on the curves of type 3;

1) The critical temperatures of the studied liquids, are as far as known, in the
diagrams indicated between ( ), behind the names of the different substances.

417

only in the case N°. 2 this quotient remains really constant. It is
now of importance to draw attention to the faet, that in contradiction
with the hitherto prevailing views, the presence of type 2 on one
side, and of types 1 and 3 on the other side, appears to be in no

: s : : du é
clear connection with the absolute value of the quotient a nor with
the absolute values of x or w themselves.

Il. In agreement with the results of previous investigators, it
appears to be possible, although only in some arbitrary way, to
divide the studied liquids into fo principal groups, with respect to

the value of —. In the first group A belong all liquids, whose
at :

, du
quotients = really are very near to Eérvés’ “constant”: 2,27 Erg
a
pro every degree Celsius. However it must be said here, that only
a F.
a mean value of = evidently can be considered in these cases, and

only over a sparely extended temperature-interval; for, just as we
already mentioned sub I, these liquids will by no means always
show a linear dependence of y and ¢, corresponding to the type
2, and therefore such a linear dependence may be supposed in most
eases only for rather short parts of the curves in question.

To this group A we can bring e.g.: a number of ethers, like
Ethyl-Isobutyrate (2,15); Tsobutyl-Isobutyrate (2,18); Diethyl-Ovalate
(2,26); Diethylmalonate (2,52); Diethyltartrate (2,35); Ethyl-Acety/o-
acetate (2,19); further: Chloroform (2,06); Dimethylaniline (2,23);
Phenetol (2,14); Anethol (2,25); Methylbenzoate (2,21); Ethylbenzoate
(2,29); Methylsalicylate (2,30); Ethylsalicylate (2,23); Methylcinna-
mylate (2,43); a-Picoline (2,02); ete.

With most of these and analogous substances however, we can
state a considerable increase of at /ower temperatures (type 3), and

at
for many of them a value in the vicinity of 2,27 may be accepted
only within a very narrow range of temperatures, e.g. between
25° and 80° C.
45 ; du

To the group £6 all liquids belong, whose quotients = show
values appreciably lower than 2,27 Erg pro 1°C. To this group the
following substances can be brought: Water (1,04); Ethylalcohol
(0,94); Propylalcohol (1,10); Tsobutylaleohol (1,10); Acetone (1,6) ;
Acetic Acid (1,3); Pyridine (1,6); ete. However with several of these

418

du,
liquids the value ot ; increases much at the lower temperatures,
at

while to the other side many liquids of group A, which e. g. between
Oe
25° and 80°C. show rather normal values of vo will have abnor-
mally low values for it at the higher temperatures. As far as the
not numerous determinations of the specific gravities make a con-
clusion possible in this respect, to this group 4 can be brought also
the molten salts of the alkali-metals: Sodzmehloride (0,6), Potrssium-
chloride (0,64); ete. Furthermore the hitherto observed dependence
of x and ¢ for: Sodiumsulfate, Sodiummolybdate, Sodiumtungstate,
Sodiumphosphate ; Potassiumbromide, Potassiumiodide, Potassium- .
phosphate, -molybdate, -tungstate ; Lithiumsulphate, Lithiummetaborate,
Lithiummethasilicate ; ete. ete., -—— seems to prove, that also with

Oe:
these salts the values of 5 will appear to be remarkably small.
Ot =

§ 2. The prevailable opinion is, that the liquids of the group B
must differ from those of group A in this respect that they would
be associated, while the liquids of group A would be normal ones.
Regarding those liquids, which show an almost linear dependence
of y% and ¢ (type 2), the “association-coefficient” x is then calculated

3
: 2,2 |2
from the expression: «= \—

Ow
I(r)
a linear dependence can not be supposed, several other formulae are
proposed"). After what has been said, however, it can hardly be quite
sure, that such a calculation of the degree of association can be
thought of as a step in the good direction. For among the substances
of group A the greater number are of a kind, whose «-t-curves
belong to types 1 or 3; type 3 can be thought moreover again to
be in so far in agreement with the postulations of the theory, that

- while in the cases, where such

here at least exists the possibility that the curve will approach
to the axis asymptotically in the vicinity of the critical temperature.
If now however the supposition were right, that a decrease of

1) After vAN Der WAALS (Z. f. phys. 18. 716. (1894)) e. g., a relation of the

: T \B

form: wt = A{ 1 — —] , — in which B at the critical temperature should
ot Vr

have the value: 3/o, but im praxi appears to be: about 1,23, — would reproduce

in many cases the dependence of y and / to a rather sufficient degree.

419

Ou
the values for va indicated an augmenting degree of association, it

would be very difficult to imagine, why the larger number of

liquids just show u-teurves of the type 3: for from the gradual
Ola suse :
decrease of a with increasing temperature in these cases, we must
; 2

conclude, that the association of the liquid would increase for most
liquids with a rise of temperature. But because by far the most
dissociations are accompanied by a heat-absorption, the mentioned
conclusion could surely be hardly put in concordance with the laws
of the mobile equilibrium. With liquids, which will dissociate to a
higher degree at higher temperatures, one had to expect on the
contrary the progress of type L: water e.g. is such a liquid, showing
a gradual dissociation of complex molecules into simpler ones at
increasing temperatures, and the «-tcurve here really possesses ')
the expected type 1. In the same way we observed some organic
liquids (Diethyl-Ovalate; Ethyl-Propylacetyloacetate; Propyl-, and
Isobutyl-Cyanoacetates ; — 0-Toluidine; Resorcine- Monomethylether ;
Hydrochinondimethylether ; a-Campholenic Acid; ete.), for which
a gradual dissociation or decomposition at higher temperatures
could be stated, and for those we found also a faster increase of

Oye a
a than before, as soon as the temperature of beginning decomposition
t

was surpassed. In opposition therewith is the case of acetic acid, where
a gradually proceeding depolymerisation with increasing temperature
has been quite doubtlessly proved, and where notwithstanding

0
this fact, the value of va remains constant within very wide limits

of temperature. *)
These facts seem after my opinion to make it very dubious, if

Ou
the increase or decrease of a with varying temperature can be esteemed
: ying

mot: ‘ , : {
1) From E6éryés’ observations one can deduce already immediately Pek
t

will increase with rising temperature in the case of water: he observes between
3° C. and 40°C. a coefficient: 1,59; between 40°C. and 100° C.: 1,80; between
100° ©. and 150° C.; 2,28; and between 150° and 210° C.; 227.

®) Also this fact can be already de jiuced from Eérvés’ observations: between

l
91° and 107° GC. he finds for —:; 1,52; between 107° and 160° GC. also: 1,82;

Ot
between 160° and 280° C.; 1,38.

420
any longer to be connected directly with the degree of association
of liquids?
Son ae , On :; Mee
§ 3. The variations of 5 must in the first instance be dependent
t

on the way, in which the specific heat ¢ of a liquid, is connected
with the magnitude S of the bordering layer of it. In general we

0c 077 . i
shall have a relation: so Tas , from which follows, that x can
Ox °

only be a linear function of 7’ in the case, when c is mdependent
of |S. From our measurements however we must doubtlessly con-

that therefore ¢ must really be dependent upon S. This fact proves

clude, that generally can not be supposed equal to zero, and.

at the same time, that the specijic heat of the surface-layer must
have another value than for the remaining part of the liquid. The
surface-energy therefore cannot be completely of a potential nature,
but partially it must be considered as being of kinetic origin. In
what manner however it will vary with the state of proceeding
polymerisation or depolymerisation of the liquid, we cannot tell in
advance; and the same is the case mtatis mutandis with the depend-
ence of g upon ¢.

At the same time it is not superfluous in this connection to fix
the attention upon the fact, that it cannot be permitted to make
any definitive. statement") concerning a high degree of association

in the case of molten salts, because the observed values of a are
very small, and the w-teurves seem to approach in these cases much
better to the rectilinear type 2. For the whole theoretical exposition
of Eérvés cannot be applied to cases like the present one, where
nobody can know a priori, if the law of corresponding states will
be valid. It is just the question, if the measurements still to be
made will permit us to draw general conclusions upon an analogous
connection between the temperature-coefficients of the molecular
surface-energy and the degree of association of such electrolytes?
Such conclusions could only be esteemed sufficiently justified, if
certain analogies in the behaviour of molten salts and of the organic
liquids should be found; at this moment we are still far distant from
the time, when we shall be able to give any definitive judgment
upon this matter.

1) Vide e.g. the relating views of Watpen, Bull. of the Academy of Petrograde
loco cit.

421

§ 4. The rather appreciable differences of our results with respect
to the variations of w and xy with the temperature, with those of
other investigators, who bave principally worked after the method
of capillary ascensions, have suggested to us to investigate in detail, if
perhaps in our way of working certain factors could be present,
which may cause systematical errors in any direction ?

First it was noted, that besides the particular shape of the mentioned
curves, also the absolute values of y, determined by us and already
by Feusten, were generally somewhat higher, than those obtained
with the same liquids by other experimenters and by other methods.
Of course it is very well possible, that e.g. the lower values published
by Ramsay and Suieips, and obtained by them by means of the
method of capillary ascension, are caused by the fact, that the
moistening of the glass-walls in their capillary tubes has been not
so complete, as is supposed in the theory of the phenomenon. In that
case the angle of contact gy will play again a role; and because the
height of ascension ceteris paribus is proportional to the cosinus of
the supplementary angle of y, there could thus really be found a
cause, which would make their results appear smaller, than those
obtained in our work.

But moreover we were able to prove on the other side, that our
values for z, calculated after Cantor’s theory, must surely appear
somewhat higher, than they really are, because in praxi_ the
conditions are not completely fulfilled, on which is based the
deduction of the jinal formula between H, d; and 7 in Canror’s
theory.

Let us start with the somewhat more summary deduction of his
formula by Frusre.’). From this deduction as it is found in the
paper of this author, it can be seen, that the formula of Canror
ean have only validity in the special case that the angle 6, which
the tangent in every point of the sharp edge of the capillary tube
drawn in any azimuth to the rotation-surface of the small gasbubble,
makes with the horizontal surface of the liquid, — differs only slightly
from 90°; in that case 6 = 90° —s, wherein « bas a very small
value. Some years ago prof. Lorentz was so kind as to draw my
attention to the fact, that this limiting supposition can be avoided, if
one makes a few simple substitutions in the two formulae of FrusrTut ;

2x 1

—cosA0=r.d,

ti ; i COs Oy

and

1) R. Feusret, Ann. d. Phys. loe. cit.

Proceedings Royal Acad. Amsterdam. Vol. XVII.

ote d; . sin 6 y. di 2
H = —_____—_ + ——_— | ¢9s 9 + ———_—_},
cos G (1 — cos 6)? 3 sin @ 1 — cos A

2) él
by putting: ¢g = — 3 and) —— Fe Where » is the radius of the
rT . ht r.cdt

capillary tube, and y and // are the known symbols.
The mentioned formulae can by this substitution be changed into:

1 1 1

(= en p=gsn@ + ct 48 ie
4 cos 6 sin* (9/,) ; : 3 © sin O sin® (’/3)

Table of Corresponding Values of

0, q and p

0 q p
0° ea) (co)
10 4399.4 793,94
20 292,60 100,080
30 61,717 30,86
40 23,850 15,33
45 16,458 15,21
50 12,192 12,06
55 9 588 9,995
60 8,000 8,660
65 7,098 7,862
70 6,753 7,546
710 31/43” 6,750 7,542
715 7,033 7,814
80 8,433 9,183
85 13,770 14,479
86 16,567 17,269
87 21,277 21,960
88 30,764 31,448
89 59,35 60.027
89°4 63,44 64,12
90 oe) co

Now it is possible to calculate for a complete series of values of
6, the numbers p and g, and to plot them against each other with
respect to rectangular coordinate-axes. If /7 is measured, and 7 and
d, are known, p can be caleulated for every experiment, and from
the diagram the corresponding value of qg (and therefore also of x) can
be immediately found. The following table gives a survey of the
corresponding values of p and q, for a series of angles 6 between
OprandeoO 2s.

From this table it is seen, that » and qg reach simultaneously a
mininiun tor 6= 70° 31'43", and that Canror’s formula is properly
only valid without appreciable error for values of ¢ between O° and

423

0°55'. The corresponding curve generally deviates only a little from
a straight line; however we found that this deviation is yet sufficient,
to make a correction necessary for all numbers, caleulated from
Cantor’s formula.

§ 5. From a special case we can now see easily, that the cal-
culation of the results in this way and from Cantor’s formula, w7//
never cause an appreciable change in the general shape of the p-t-

. . Ou

curves, and therefore neither in the deduced values of =f the deviat-
at
ion of a linear relation between p and q is between 6= 70 31'43"
and 90° only so slight, that a somewhat important deformation of
the mentioned curves cannot be the result of this difference in com-
putation. However there will be caused a parallellous shift of every
curve, which will dininish the absolute values of % and w with a
small amount. That this influence is not at all without importance
in the cases hitherto investigated, may be proved in the following
way. We choose for this purpose two extreme cases of the here
studied liquids: diethylether, because the observed values of H are
here the smallest, and e.g. a substance as resorcine-monomethylether,
whose values for // belong to the rather great ones. The caleulation
is made as follows: HZ in m.m. of mercury (O| C.) is multiplied by
the specific weight of mercury, and this number divided by the
product r.d,, (r being expressed in mm.). With the obtained value
for p, the corresponding value of g is found from the table or the
diagram; this divided by 2 and multiplied by the product 7? .d,,
gives y% in mG. pro m.m; the number is reduced to Erg pro cm?,
by multiplication with 9,806,

Diethylether.
yinErg. yinErg. winErg. win Erg.

Us p J em. em.-?(Cantor) em.-2 em.-? (Cantor)
MOL MOOLOD Ao, 28,9 574,7 582.8
=20°.5 30,60 29,89 21,5 PLS) 456,2 464,7
OF Deets) Da ats! AIG 19,6 415,8 424,5
1 SSR WOW ally) 18,4 392,0 402,9
EP DESI DSO0) AUT viel 3 74,2 380,0
292.6 25.30 2470 A6y4 16,8 365,9 374,8

The whole y-tcurve is thus parallellously shifted to an amount
of — 0,4 Erg.
28*

424

Resorcine- Monomethylether.

yin Ere. yin Erg. win Erg. win Ere.

be P gq ems? em.?(Cantor) em.? cem.-?(Cantor)
== 20° 62785 62520) -83; 83,9 1850,1 1867,9
OS Sees) SOB) = bul 52,4 1161,9 ORS
46° 34,91 34,30 43,4 44,2 1001,6 1020,1
NMOS aileils sil no) eC) 38,3 896,7 915,8
166° 2848 27,80 31,5 32,3 782,0 801,8
206° 25,29 24,60 26,8 27,6 682,6 703,0

Here is the y-d-ecurve shifted totally to an amount of —0O,8 Erg.

This is the correction to be applied, and which was already
indicated in our first communication’); it has been taken into account
since in every case in all the tables. It may here be repeated once more,
that although the absolute values of the surface-energy really have
approached closer by it to the values formerly published, however
the shape of the y-¢, or u-f-curves is not altered by it with respect
to any particular feature.

§ 6. Another question to be answered with respect to the obtained
experimental results, is this, if it may be considered as possible to
determine the right values of 4, without being embarrassed there-
with by the influence of the viscosity of the studied liquid? For
just because the internal friction of liquids always increases rapidly
at lower temperatures, and an extreme viscosity of the liquid, — even
if the bubbling of the gas is executed with extreme slowness, —
will cause, as we have seen, the maximum pressure /7 to appear
too great from all kinds of disturbing effects, — the influence
of this viscosity could perhaps be advanced as a cause of such a
deformation of the y--curves, that they just would manifest a steeper
temperature-gradient at the lower temperatures than at the higher.
Therewith an explanation of the curves of type 3 would be given;
but it must be here remarked already in advance, that such a cause
could hardly be adopted for the presence of the curves of type 1,
just because all viscosity-curves have themselves the shape of type 3.
However there seem to be many reasons, not to attribute too higha
value to this explanation of the curvature of the «-¢-lines, even not
in the case of type 3.

In the first place it must be remarked, that the curvature of the

1) I’. M, Jarcer, these Proc., Comm. I, (1914).

425

said curves does not run parallel to the variations of the viscosity
with temperature. Most strikingly this can be seen in those substances
where the curvature is so slight, that the curves can be considered
to be straight lines: with ethylbenzoate, whose viscosity at 10° is
about six times that of acetone, and in a temperature-interval of
50° decreases to two or three times that value, the y--curve is a straight
line; with the tsobutylbromide, whose y-t-curve between O° and 85°
ean be considered as a straight line, the viscosity decreases to less
than half its original value (from 0,008 C.G.S. to 0,008 C.G.S.) ;
etc. Neither does the curvature of the y-¢-lines seem to be inmediately
connected with the absolute value of the viscosity : with acete acid,
whose viscosity is about three times, with salicylic aldehyde, whose
viscosity is four times, with pyridine, whose viscosity is about twice,
with pheneto/, where it is circa three times as large as that of
ethylalecohol, — in all these cases the curvature of the z-écurves is
less than for the last mentioned liquid, because they are almost
straight lines; and with the amine and nitrobenzene, whose viscosity
is about eight or ten times as great, as that e.g. of the edhylformiate,
the z-t-curves are even slightly convex. In many cases the y-¢-curves
will show a more rapid and steeper curvature at the higher tempe-
ratures, where the viscosity becomes smaller; and the part of the y-¢
curve between — 79° and O° is often almost a straight line. With
.the ethylalcohol the viscosity is about three times as great as in the
ease of ethylacetate or eihylformiate, but notwithstanding that, the
y-t-curves show in all three cases about the same curvature.

To be sure, we have met during our measurements numerous
cases, where very clearly the impossibility was shown, to determine
the surface-energy dependently of the viscosity. But this we
observed only, where the viscosity reached such enormous magnitude,
that the liquid became glassy or gelatineous, and did not or hardly
move on reversing the vessel. Such cases we found in: methy/-
cyanoacetate, methyl-methylacetyloacetate, diethylbromomalonate, cie-
thylbenzylethylmalonate ; in undercooled dimethyl-, and diethyltartrate
and a-campholenic acid, and very strikingly with salo/ and resorcine-
monomethyl-, or dimethylethers.

Even in these unfavourable cases we succeeded sometimes in
making some good measurements ; but in most cases this appears to
be impossible, which is shown by the fact, that even with so small
a velocity of formation of the gas-bubbles as 50 to more than 209
seconds, it proved to be impossible to find a maximum pressure
fl, which really is independent of the speed of the nitrogen-
flow.

426

The behaviour of such extremely viscous liquids with respect to
the gas-bubbles produced in them, is very variable and often very
peculiar: in this ease the bubbles are hardly loosened from the
capillary tube, in that case one observes a periodic increase and
decrease of the gas-pressure, without a bursting of the bubbles
occurring ; in another case a very large bubble is produced, which
suddenly explodes into a great number of very small bubbles ; but
in no case a maximum pressure can be measured, which is really
independent of the speed of the gas-flow, proving that it corresponds
to a real state of equilibrium of the gas-bubble. And this last men-
tioned fact is so characteristic for all our other measurements :
within rather wide limits one can vary the speed of nitrogen-jlow, when
working with ordinary liquids, without a measurable change in the
determined pressure H_ being observed. On the contrary we studied
a long series of very thin liquids: e.g. ethylalcohol, diethylether, ethyl-
formiate, ethylchloroformiate, acetone, methylpropylcetone, chloroform,
ete., cooled to —-80°C., which notwithstanding the low temperatures
gave very reliable values of //7; the occasional fact that the temperature
is so low, can therefore neither be considered of high importanee
for the abnormally high values of y and w observed. However it
must be said in this connection, that E6rvés’ relation can no longer
be considered as valid at temperatures, lower than about half the
absolute critical temperature of the studied liquids.

In this connection it is not superfluous to remark, that with liquids
whose volatility is very great, and which therefore possess at higher
temperatures a very considerable vapour-tension, there is often some
difficulty in obtaining reliable values for 7, this maximum-pressure
being apparently somewhat increased. However the right value can
be deduced in such cases by often repeating the adjustment of the
capillary tube, until a really reproducible value will be found. The
influence of these abnormally high vapour-tensions cannot be of
essential significance, if the measurements are controlled accurately
and often carefully repeated.

All arguments taken together, we think it really very improbable,
that the changes in viscosity of the studied liquids could be argued
as the chief cause of the observed curvature of the y-¢- or u-t-curves.
But in cases of abnormally great values of the viscosity, the deter-
mination seems doubtlessly no longer possible after this method in
any exact way; however with liquids, whose viscosity comes e.g.
very near to that of glycerine, or is even somewhat greater, such
measurements are already quite reliable if only the formation
of the gasbubbles takes place ewtremely slowly: in this way for

427

instance we found again reliable values with: déethylimalonate (—20
and butyl-, or tsobutyl-cyanoacetates (—22°).

Therefore we think it right to draw the conclusion, that the non-
linear dependence of 7 on the temperature, must be connected with
the very nature of the surface-energy itself, and that it will manifest
itself always, as soon the studied temperature-interval is only wide
enough.

We can also mention here the fact, that in the ease of
molten salts, even at very high temperatures and with very small
viscosities of these liquids, we observed just the same three types of
y-t-curves: so with potassiwmiodide the type 3, with potassium-
metaphosphate the type 1, with many others the rectilinear type 2,
— without it being possible to indicate an immediate reason for it.
Finally we can draw the attention to the fact, that notwithstanding
the fact that these determinations range over a much smaller tem-
perature-interval, some y-écurves of other experimenters (vide e.g.
Guye and his collaborators) show, on better consideration, also clearly
a deviation from the rectilinear type; for water this has moreover
already been mentioned before.

§ 7. Finally it is bere the place to discuss some points connected
with the relations between the magnitude of w and the chemical
constituents of the studied liquids, in so far as we may draw con-
clusions about it already with respect to the sparing experimental
data. Moreover the investigations relating to this subject will be
continued in this laboratory in a quite systemaucal way, because a
great number of problems have risen in this respect, which only by
collecting a more extended experimental material can be answered
by generally acceptable views. The facts hitherto gathered are
principally adapted, to bring the values of u in qualitative connect-
ion with the homology of some analogous compounds, and with the
substitution-relations between some organic derivatives. This can be
executed best by comparison of the a-¢-diagrams, which were published
in the successive communications.

A. Homology.
Of homologous series we can mention the following:
Ethylalcohol. Bthylformiate. Ethylacetate.

1.) n.-Propylalcohol. *) Ethylacetate - *) Amylacet ate.
Isobutylalcoho!.

428

Methylisobutyrate. Acetone. 6 Bthylacetyloacetate.
4.) Ethylisobutyrate. ’) Methylpropylcetone. *) Eiirylpropyloacetate.
Tsobutylisobulyrate.
Tsobuty!cyanoacetate. \ Diethyloxalate. Dimethyltartrate.
Amylcyanoacetate. ae | Diethylmatonate. , | Diethyliartrate.
Dutyleyanoacetate.
*\ Propylcyanoacetate.
| Ethylcyanoacetate.
| Methyleyanoacetate.
10 | Trichloromethane. | Benzene. o \ Nitrobenzene. Aniline.
"| Tetrachloromethane. Toluene. ~) 0-Nitrotoluene. ~” ) o-Toluidine.
ll. p-Xylene.
Mesitylene.
| Pseudocumene.
Anisol Resorcinemonomethylether. Methylbenzo ate.
: | Phenetol. é | Resorcinedimethylether. 16. { Hthylbenzoate.

Benzylbenzoate.

Methylsalicylate. Pyridine.
17.) Ethylsalicylate. ‘) a-Picoline
Phenylsalicylate.

By such a comparison of the results obtained we can now derive
the evidently general fact, that the values of the molecular surface
energy at the same temperature increase in homologous series, if we come
to terms of higher hydrocarbon-radicals. Although quantitative relations
do not so. strikingly come to the foreground, it seems however to
be clear, that the influence of the same increase in this respect,
becomes smaller within the series, if the molecular weight of the
compound increases; a fact, that must be thought also completely
comprehensible. In most cases these rules hold, as the following
instances may prove: The value of w is at the same temperature
greater for isobutyl-alcohol, than for normal propylalcohol, and here
again greater than with ethylalcohol; just so with ethylacetate greater
than with ethylformiate, with amylacetate greater than with the
corresponding ehylether; it is greater for isobuthyl-isobutyrate than
for the ethylether, and here again greater than for methylisobutyrate ;
with ethyl-propylacetyloacetate greater than for ethyl-acetyloacetate.
In the series of the six cyanoacetates, the value of «is greatest with
the amyl-ether, and decreases here regularly within the series till
the methylether is reached, while the temperature-coefticients remain
almost the same; the zsohuty/-ether however has another value for

Ou
- and values for uw, which are only partially greater than for the

429

propyl-ether: in this also a manifestation must be seen of the differ-
ences between normal and ramified carbon-chains. In the same way
the molecular surface-energy of diethyltartrate appears to be greater
than of dimethyltartrate. In the series of aromatic hydrocarbons, the
curves for pseudocumene and the isomeric mesitylene are situated
highest; then follow successively: p-xylene, toluene, and benzene; in
the same mw is greater for o-toluidine than for aniline, for o-nitrotoluene
greater than for nitrobenzene; just so for phenetol greater than for
anisol, for dimethylaniline greater than for aniline, and for a-picoline
greater than for pyridine. The only exception to this rule hitherto
found, is presented by the resorcine-monomethylether, which possesses a
ereater molecular surface-energy than the corresponding dimethylether.

The substitution by means of members of the aromatic series has an
analogousinjluence as by those of the aliphatic series, but it is much more
intensive: in the series of the benzoates, the value of u for the ethy/-ether is
indeed, greater than for the methyl-derivative, but for the corresponding
benzyl-ether it is excessively much greater; in the same way it is
the case with methyl-, and ethylsalicylates and salol, and with methyl-
propylcetone on one side, and acetophenone on the other.

B. Relations of Substitution-derivatives.

The conclusions, which in this respect can be drawn hitherto,
can be summed up shortly in the following rules:

1. The substitution of H by halogens is accompanied by an inten-
sive increase of the molecular surface-energy at the same temperatures;
the injluence increases evidently with augmenting atomic weight of the
halogen.

So u for chlorotoluene is greater than for slorotolwene*), and here
much greater than for todwene itself; for bromobenzene ai is greater
than for chlorubenzene, and appreciably greater than for benzene;
with the m-dich/lorobenzene it is greater than for /lworobromobenzene,
showing that the specific influence of fluorine seems to be less than
the difference between bromine and chlorine. In the same way the
ralue for diethylbromomalonate is appreciably greater than for dietyl-
malonate; for tetrachloromethane just so greater than for chloroform.

2. Vhe substitution of N-atoms for C-atoms, or of that of negative
nitrogen containing radreals for a H-atom, is followed by a relatively
great increase of the molecular surface-energy at the same temperatures.

+) The relatively small differences caused by the structural isomerism of these
compounds, is here neglected for the present; generally the pava-substitution seems
to be of the highest, the meta-substitution of the smallest influence in this respect.
We will discuss this peculavity afterwards by considering the results of a special
set of measurements.

430

So yt is appreciably greater for o-nétroanisol, than for anisol; for
o-nitrotoluene much greater than for ¢olwene; for nitrobenzene much
greater than for benzene; for aniline and o-toluidine, much greater
than for benzene ov toluene. Just so for pyridine appreciably greater
than for benzene; ete.

3. The substitution of aromatic hydrocarbon-radicals instead of
H-atoms makes the values of the molecular surface-energy also con-
siderably greater.

So the values for sa/o/ ave much greater than for the other
salicylates; of benzylbenzoate it is much greater than of both the
other benzoates; of acetophenone much greater than of démethylcetone
or methylpropylcetone; of diethyl-benzyethylmalonate much greater than
of diethylmalonate itself; ete.

Only continued investigations in this direction can however, as
has already been said, prove with more certainty, if these rules may
be considered as general ones. Researches of this kind will be
started in this laboratory within a short time.

Laboratory for Inorganic Chemistry
of the University.
Groningen, June 1914.

Mineralogy. —* On the real Symmetry of Cordierite and Apophyllte”.
By Prof. H. Haca and Prof. F. M. Janerr.

§ 1. In continuation of our investigations!) on the symmetry of
erystals, which can be discerned as mimetic or pseudosymmetrical,
we will give in the following a review of the results obtained in
our experiments relating to the cordierite (tolite; dichroite) and to the
apophyllite (albine; ichthyophtalm). Of both kinds of silicates specimens
of dijferent localities were at our disposal, — a fact, which hardly
can be over-estimated in the study of ROnreEN-patterns, as will be
proved below. We will describe in the following pages successively
our observations with: a) Cordierite; b) Apophyllite.

§ 2. «a. Investigations on the true symmetry of Cordierite.

Cordierite, asilicate of the chemical composition: H,( Mg, Fe), Al,Sz, ,0,,.
belongs to those minerals, which lke the arragonite, imitate the
habitus of hexagonal crystals by means of particular polysynthetical
twinformations. In literature it is only mentioned, that it is “rhombic”

1) Haga and F. M. Jagcer, these Proceedings, XVI. p. 792. (1914).

431

(a: b:¢ =0,5871 :1:0,5585), but it is evidently unknown, to which
symimetry-class of the three possible ones it belongs. Its pseudohexagonal
habitus is obtained in two ways: a. by twin formation parallel
to {110}, consisting in an intergrowing of ¢hree individuals in such a
manner, that the faces of {110} will function as the apparent prism-
faces of the pseudohexagonal combination; 4. by a twinning parallel
to {130}, in which three_ individuals form either a threefold twin
by contact, or a threefold one by imtergrowth, the faces of {110}
being turned outward (fig. 1a). In crystals of the structure, described
sub a, a plate cut perpendicularly to jOOL{, will appear to be divided
into six sectors, of which every one is optically biaxial, the planes
of the optical axes being situated in three successive sectors under 60°
one to the other, while they are of course equally directed in every two
diametrically opposite sectors. In crystals of the type 4 there will
be either three sectors, in which the axial planes are orientated
along the larger diagonal of the kite-shaped sectors (fig. 16,); or
there appear six sectors, in which the axial planes are orientated
perpendicularly to a diameter of the rhomboidal boundary of the whole
complex (fig. 16,); in this last mentioned case the axial planes in
two diametrically situated sectors will appear, as in the case sub a,
orientated in the same direction. The considered possibilities are
elucidated by some schematical drawings in fig. 1.

(ii {ft) 10)’ 010) (iio) (iio) cs
=f ane s™~ 5 oo) 9
(730) coe (130) f Sp (Seca | 2 |
“ ev « | < y "
(070) (20:) (e10) (o10)| e--0 >< e-e-@ | (0 (110)} % P \(ilo ’ | be EY
4 22 | Sal y e cc3o |
(130) y /(190) (10 Atel SS eae , L POC ‘iio (0) ane (110)'
(110) ——— “( 110) Sales SIL ~Y
(100) 7
Single Cristal re £ b,
Vig. 1.

In most cases the boundaries of the sectors are not distinet; the
different individuals on the contrary, will penetrate each other
partially. The cleavage occurs parallel to {O10}, but it is not very
distinctly pronounced. The optical axial plane is parallel to {LOO};
the c-axis is first biseetrix, and the dispersion is only weak: o<v.
Cordierite is one of the most striking instances of polyehroitic minerals
(dichroite); the here used crystals also showed this phenomenon in

a very marked degree.

§ 3. In our experiments we could use cordierites of the following
three places: a colourless cordierite of Madagascar; a pale blue

cordierite of Bodenmais; and a pink cordierite of Jount Ibity on
Madagascar.
a. From a magnificent, almost colourless, homogeneous and single

crystal of cordierite, after its label from J/adagascar, three plane-
a parallel plates about 1 or 1,2 mm. thick,

i) . . 5 5
'Snkensive Were carefully cut, and the following optical
| Viele properties of them determined (fig. 2); the

aa eT | arrows indicate the direction of the luminous
dight Lac

(001) |
|
|
|
|

vibrations, for whieh the mentioned colours
were observed in the crystals; obviously
thus the absorption-scheme with respect to
the crystal-axes is: a@ >>b>>c. The axial -
plane was parallel to {100}; the c-axis was

| del low White

4 (100) first biseetrix (a). The birefringence is about
_ | 62 =. 05008, and of negative characters @treqes
Dery Sight Lilac | IntensVutey of these plates we obtained a R6ONTGEN-pat-

Fig. 2. tern, after they had been carefully orientated
in the way formerly described by us.'). The distance of the photographic
plate and the erystal was 45 mm., while the time of exposure varied
between 1*/, and 2°/, hours respectively. In connection with the question
of the orientation, attention must be drawn here once more to the fact,
that deviations of the theoretically right orientation, even so slight

that they cannot be controlled any more by means of optical test,
will however always manifest themselves by a slight dissymmetry in
the R6OnrGEN-pattern. For instance, the image obtained by radiation
through {O01} in several experiments, appeared to be always un-
syminetrical to a more or less degree, while by the optical test in
any of these cases no appreciable deviation of the optical image
and of the right orientation of the first bisectrix could be proved.
Thus even the greatest attainable degree of precision in this orien-
tation can never exclude the necessity, to acknowledge certain
imperfectibilities of the expected symmetry of the obtained
RONTGEN-patterns as of only secondary importance in the com-
parison of these images. and to neglect them presently in drawing
conclusions from the photographs. This point must always be con-
sidered in all following discussions of the obtained results; without
this restriction it simply appears absolutely impossible to draw any
valuable conclusion from the results obtained by experiment. At the
same occasion we wish further to remark, that the use of a phos-
phorescent screen (species “Eresco”) behind the photographic plate

1) H. Haga and F. M. Jagaer, these Proc., loc. cit. (1914).

TABLE I: Cordierite.

433

evidently often causes disturbances in two possible ways: (st. by
increasing appreciably the dimensions of the central spot, because
of the diffuse light-emission of the sereen; which fact may render
some of the spots situated in the immediate vicinity’ of the central
part invisible in the reproductions; and 2". because the impossi-
bility of pressing the phosphorescent screen over its whole surface
quite equally against the photographic plate, eventually will cause
some differences in the intensities of the black spots, which apparently
create an accidental dissymmetry in the obtained photograph. Also
both these disturbing effects must be taken into account together with
the above given arguments, to explain the inevitable imperfection of
the ROnrGEN-radiograms, thus prepared.

The R6énreen-patterns, which now are reproduced ‘in fig. 3, 4, and
9 of plate I, can teach us the following facts: A somewhat more
accurate study of these photographs will immediately show, that
the images obtained by radiation through the erystalplates {100} and
{010}, possess only a dilaterc] symmetry: the molecular arrangement
of the crystal, seen in the two directions perpendicular to these
faces, can thus possess only one single plane of symmetry, in the
first case perpendicular to {100}, in the last one perpendicular to {O10}
and passing through the c-axis; by both images however it is proved
indubitably, that axes of binary symmetry are completely absent. The
image, obtained by radiation through the erystal in a direction perpen-
dicular to {001} however, must be considered doubtlessly to be symme-
trical with respect toa set of two symmetry-planes, perpendicular to each
other ; of course the intersection of these two planes, being the c-axis,
needs to be an aais of binary symmetry too. On Table / we have repro-
duced a RonTGenogram of this ease, which shows some dissy mmetries
by a very small error in the normal orientation; the distribution
of spots of equal intensity however, etc., suggests the symme-
trical nature of this radiogram with respect to the mentioned planes
without any doubt. Of this same crystalplate we obtained some
more radiograms, which were however not sufficiently intense for
reproduction; they were somewhat more symmetrical than the pho-
tograph reproduced here, which fact apparently was caused by a
somewhat better adjustment of the crystalplate with respect to the
Ronreen-tube. But an optical investigation of the crystal-plates in quite
the same position as in which they were during the experiment, allowed
no distinction of the orientation in the several cases: it must there-
fore be considered a fact of mere chance, if one gets accidentally
the right position of the plate, necessary to obtain a pattern, whose
symmetry approaches the pure one with more or less perfection ;

434

and furthermore, as we already mentioned, the accidental situation
of the phosphorescent screen will play in this question also a more

or less important role.

§ 4. The obtained results were so surprising, that we thought it
necessary to repeat the experiments of radiation through the plates
parallel to {100} and {O10}, also with cordierites of other localities.

6. From a beautiful, pink eordierite of J/ount Lhity, Madagascar,
which had no geometrically definite boundaries, two planeparallel
plates were cut after {100} and {010} and about 1 m.m. thick. The
plate parallel to {O10} was distinetly dichroitic : for vibrations in
the directions of the axial plane it was lilaec-white, for those perpen-
dicular to it intensively pink. On {100} the colour for vibrations:
perpendicular to the c-axis was pink; for those parallel to it, the
plate was almost white.

In the same way two such plates were cut from a single, short.
prismatic, chaleopyrite-covered cordierite-crystal of Bodenmais ; it was
fixed upon an aggregate of chalcopyrite and sphalerite. The mentioned

fo)

plates were from 1,0 to 1,1 m.m. thick, and showed no distinet di-
chroism: the plate parallel to }100} showed hardly any difference of
colour for two perpendicular directions ; that parallel to {010} was for
vibrations parallel to the c-axis yellowish-white, for those perpen-
dicular te it however pink coloured.

In a quite analogous way as described before, ROnrarNograms of
these four crystal-plates were obtained. The fig. 6 and 7 give the photo-
graphs for the erystal from Lodenmais, the figures 8 and 9 those
for the crystal of Mount lbity *).

From these ROnTGEN-patterns it can in the first instance immedia-
tely be seen, that also with these crystalplates all radiograms are
only symmetrical with respect to one single vertical plane, and
that in these minerals also binary axes perpendicular to {100} or {010}
appear to be absent. In connection with the results obtained with
the other cordierite-plates, it is hardly possible to give any other
explanation of this, than that the absence of both horizontal binary

1) The cordierites of /bity are somewhat richer in SiO;, Al,03, and MgO, than
those of Bodenmais, but their content of iron-oxides is less ; the followimg analysis
may give some idea of this:

Ibity : 49.05 9/9 SiO, ; 33.08 /) Al,Og; 11.04 °/) MgO; 5.2%) FeO + Fe,Os ;
1.649/, HO.

Bodenmais : 48.58 °/, SiQ,; 31.47%) Al,O3; 10.68°/) MgO; 4.90) FeO;
1,85/, FeO, ; 0.09 %/) CaO; 1.96%/, H,0.

Vide also: Wutrine and Oppenueimer, Silz. B Heidelb. Akad. d. Wiss. Abt. A.
N°. 10. (1914).

435

aves and of the horizontal symmetry-plane, is really characteristic of
the molecular arrangement of the silicate. Founding our statement on
these experiments, we must therefore draw the conclusion, that
cordierite is an hemimorphic mineral, belonging to the rhombic-pyra-
midal class (rhombic-hemimorphie class) of the rhombic system, just
like calamine and struvite, ete. The threefold twinning-aggregations
of the cordierite must thus be considered to be real pseudo-hevagonal,
and no pseudo-trigonal mimetic forms.

Because all possible space-lattices of the rhombic system, as deduced
by Bravals, possess vertical and horizontal planes of symmetry, the
molecular arrangement of cordierite can therefore by no means
correspond to such a Bravats’ space-lattice. However the pseudo-
hexagonal symmetry of the mineral, just as its prismatic twinforma-
tions, seem to indicate with strong emphasis a structure-unit, which
must be considered derived from the rectangular prism with rhombic
base, whose angles will differ only slightly (ca. 25’) from 60° or
120°. The choice between the possible structures is hardly to be
expected: after SCHOENFLIES’ theory e.g., there will be no less than
22 arrangements, which correspond to the hemimorphy of the rhombic
system. (SCHOENFLIES, Krystallsysteme und Krystallstruktur, 1891,
Sk ZSR)E

j) 5. A second peculiarity of the obtained R6nrGEN-patterns is this,
that notwithstanding their agreement with respect to their general
symmetry, yet appreciable differences in the distribution of the black
spots show themselves, if analogous crystalplates, but of different
localities are compared. Even a superficial comparison of the figures
3, 6, and 8 of plate I to the one side, and of fig. 4, 7, and 9 to
the other side, is able to manifest the great differences immediately.
Doubtless all analogous images show a number of common spots ;
but in every radiogram there are moreover new ones, while even
homologous spots in the different photographs appear with such
different relative intensities, that the total aspect of the figure becomes
a quite different one by it.

As these photographs were made all under precisely the same
circumstances, we must conclude from this, that the symmetry of
a species of minerals being evidently always the same, the number
and the arrangement of its molecular reticular planes, just as their
molecular densities, are however variab/e with the special conditions,
which were prevailing during the formation of the crystals. With
respect to the erterni/ form of the crystals, this is a fact which has
long been known, and which can moreover readily be explained

436

by the different influences of the factors accompanying the formation
of the crystals. But from our experiments it follows moreover, that
the ¢nternal arrangement also, the molecular structure itself, must be
considered as being variable with those evternal factors; thus to the
different localities, where minerals are found not only the especial
differences in habitus of the erystals must correspond, but also some
variations of its internal structure. With respect to the great signi-
ficance of this conclusion for the question about the constancy of
mineral-species in general and about the velations between the
external forces during the crystallisationprocess and the internal
crystalline structure, — we must remark, that the correctness of
our view will be established only — satisfactorily by a great
number of such experiments, to be made with minerals of very
different origin and accurately known chemical composition. For
especially of many silicates, and also of cordierite, it is known, that
they can be altered under the influence of chemical reagents’); and
it is very well explicable, if such differences in internal structure,
as we have stated here, were dependent upon such differences in
chemical composition, instead of being attributed to the Variation of
physical factors, whieh may have had a variation of the external
forms as a consequence, however in the case of cordiriete, these
variations in chemical composition are only small. Only numerous
experiments in the direction indicated above, will enable us to decide
in the alternative.

§ 6. We have tried to prove the hemimorphy of the cordierite,
just as it follows doubtless from the described experiments, by
verifying it again by means of the now usual physical methods.

In the first instance we tried*) to reach our purpose by the aid
of the wellknown method of corrosion-figures. The plates of cordierite,
having been carefully cleaned by benzene, afterwards by alechol
and ether, were submitted during a short moment to the action of
a very dilute solution of hydrotlhuoric acid; later we made again
such experiments by means of gaseous hydrofluoric acid and with
dilute potassiumhydrate-sclutions. In the last mentioned ease, we
were unable to get any well-shaped corrosion-figures; in the expe-
riments with hydrofluoric acid however, we always got, even after
‘) Vide in this respect the paper of WuLrinG and OPPENHEIMER, just published
in: Sitz. B. Heidelb. Akad. d. Wiss., Abt. A. N°. 10. (1914), p. 5 and 6;
l,, OPPENHEIMER, Inaug. Diss. Heidelberg, 1914.

*) In these experiments Dr. A. Siwek has willingly given us his esteemed assist-
ance.

437

the shortest possible action and by means of very dilute solutions
of the acid, a great number of corrosion-figures, which appeared to
be elevations, instead of impressions in by far the most cases. They
generally (fig. 10a, 6, c) did not have any well definiable shape,
and were moreover quite irregularly distributed over the surface of the
erystalplates*), only on {O01{ we succeeded sometimes in getting
some extended rectangular forms, proving the presence of a binary
axis and of two perpendicularly intersecting symmetry-planes. The
corrosion-figures on {100} and {010}, and also on the prism {110}
of the crystals from /bity and Bodenmais, proved clearly in every
ease the absence of a horizontal plane of symmetry; they were
however furthermore so abnormally shaped, that they could hardly
he used for the control of the above deduced symmetry of the
crystals. This case proves once more, that the method of corrosion-
figures used, eventually can give unreliable results, either by the
production of abnormal etching-figures or by a shape of the corrosion-
figures, which cannot sufficiently exactly be defined.

A second trial to determine the physical symmetry in this case,
was based upon the idea, that because the principal axis c was of
polar nature, it would be possible, that its ends would manifest
opposite electrical changes on mechanical deformation or on heating.
Although we are strongly convinced of the truth that a negative
result can hardly be considered to be a decisive argument in this
question, we have nevertheless spent a considerable time in en-
deavouring to prove the polarity of the c-axis by means of Kunpt’s
method of dust-figures. Although we were able to obtain on this
oceasion e.g. the alternative red and yellow powdering of the vertical
edges of prismatic quartz-crystals in a very satisfactory way, however
all our numerous tentatives with plates of cordierite, as well with
the pinacoidal as with the prismatic plates, remained without a
positive result. In every case, if present, this piezo-, or pyro-electrical
polarity of the c-axis appears to be only so feeble, that it seems
‘impossible to prove its existence in the described way with any
certainty.

It is a quite remarkable fact, which strongly corroborates the
value of the new method that even where all crystallographic methods
to find the smaller physical symmetry-differences of crystals used up
to this date, are failing, the new method however appears to be quite
able to elucidate the finer feature of symmetry of such crystals in
so complete and persuading a way. Therefore an indubitable place

1) In these photographs, the crossed hairs in the field are parallel to the
directions of optical extinction of the plates.
29

Proceedings Royal Acad, Amsterdam. Vol. XVII.

438

needs to be reserved in future to the method of RONtGENograms
among all other crystallographical methods. At the same time however
it is proved by the results obtained with minerals of different
localities, how strictly necessary it properly must be considered, to
build up the whole systematical mineralogy starting from this new
point of view, and what surprising results are surely to be expected
therefrom.

We will now deseribe here the analogous experiments, made
with apophyllite.

§ 7. Investigations relating to the Symmetry of Apophyllite.

For our investigations of the symmetry of apophyllite, we had
material at our disposal from the following localities: a. from .
Paterson (U.S. A.); from Bergen Hill, Erie Railroad N.J.; ¢. from
(ruanajato, in Mexico; d. trom Berufjord in Iceland. The apophyl-
lites of American origin we will place opposite to that of Iceland
as a typical group, because they manifest, as will seen below, some
peculiarities in their molecular structure, which are not present in
the /celand-mineral, and are substituted in it by other qualities.

Apophyllite, a mineral with the chemical composition :

KH,Ca,Si,O,, +45 H,O
belongs to the important group of the remarkable zeo/ithic silicates ;
they all contain water, and as was proved for many of them already,
their vapourtension at constant temperature appears to be continually
variable with their momentaneous content of water, — a behaviour
quite opposite to that of hydrated salts in general. The explanation
of this pbenomenon is commonly given in this way, — which is
confirmed completely moreover by the physical properties of these
silicates, — that the water is not combined with the silicate like
the water of crystallisation, but that it is present, at least partially,
either in solid solution or hold in the silicate-skeleton by absorption.

Apophyllite is a typical representative of an optically anomalous
or mimetic crystal: Brewster in 1819 already discovered the partition
of the crystal-sections in numerous fields, and since that time the
pseudo-tetragonal crystals of this mineral have often been the subject
of research. For the explanation of this anomalous behaviour, two
theories have been started: in 1877 by Matriarp, who supposed the
erysials of apophyllite to be polysynthetic twinnings of perpendicularly
crossed and penetrating monosymmetric lamellae, — the dimensions
of the monosymmetric molecular-arrangement differing only slightly
from those ofa tetragonal structure. The second- view, chiefly defended
by ©. Kiri, explains the optical abnormalities as caused by internal

439

stresses, which in their turn are caused by an isomorphous mixture
of optically positive and negative material '). The supposition of the
existence of such positive and negative apophyllite-substances which
is really confirmed in some cases by direct observation, must serve
at the same time for the explanation of the very weak birefringence,
and the so-called lewhocyclite-, and chromocyclite-phenomena. We will
demonstrate in the following pages, that, — waiving tbe question, how
far the last mentioned phenomena need to be explained by this
intergrowth of optically positive and negative substances, -— in every
case the method of the R6nrepn-radiation decides the alternative
between the two views indubitably in favour of MALiLarD’s hypothesis.

§ 8. The American apophyllites used were all transparent, pearl-
coloured crystals; they have a layer-strueture parallel to {001!, to
which form also the direction of perfect cleavage is parallel.

Without exception all these apophyllites are optically biaxial in
convergent polarised light, with positive character of the birefringence.
The apparent axial angle is only small, with a dispersion: 0 < v.
By means of a gypsumplate giving the red colour of 1s* order, one
sees, that numerous blue-, and orange-tinged, rectangularly bounded,
very small fields are in juxta-, and superposition to each other, as
in a mosaic; the crystal makes the impression of consisting of an
innumerable quantity of perpendicularly very small lamellae, which
evidently are distributed and superposed in very unequal number
and in a rather irregular way.

All these preparations give, if the ROnrarnrays are directed per-
pendicularly to {O01}, the radiograms, which in Table // are repro-
duced in the figures 1, 2, 3" and 4. Of all these radiograms it is
again characteristic, that they possess a single plane of symmetry as
unique symimetry-element ; it is placed in a vertical situation in all
reproduced figures, and corresponds, as was found later, to a direction
perpendicular to the axial plane of the optically biaxial individuals.
The direction of this plane of symmetry can always rather easily
be fixed on the original negatives by the particular aggregation of
spots at the upper side of the image, which has the shape of a
double pinnacle between the two very distinct circular garlands of
spots there; and also by the facet, that it cuts symmetrically the
group of the five very intense black spots, which in fig. 1, 8' and 4
are visible just beneath the centre: in fig. 2 these spots are invisible

1) The optical phenomena in basal sections of the optically positive apophyllites
are (after Kooke) exactly analogous to those which would be produced in the
originally uniaxial crystals, by stresses, working parallel to the edges (O01); (110).

29*

440

on the reproduetion, by the strong radiation of the phosphorescent
screen and the enlargement of the central spot caused by it, but
they were distinct on the original photographs.

It is therefore doubtless, that these photographs can be considered
to have brought the proof of the fact, that the pseudotetragonal c-axis
of the apophyllite-crystals, is not even a binary axis; but that at
best it can be compared with the vertical axis of a monosymmetric
molecular arrangement: the original molecular structure of apophyllite
is not of tetragonal, but of monoclinic symmetry.

We once more emphasize in this connection the existence of the
group of five intensive spots, just beneath the centre of the image.
Indeed this garland of five spots, which correspond to five molecular
planes, seems to be typical for all apophyllites of American origin ;
it plays evidently in these silicates a preponderant role. As in
literature there can be found some data, relating to the fact, that
a heating to 270° C. would be able to expel a part of the water
and to make the crystal tetragonal in reality, — we have studied
ihe effect of such a heating at 270° to 300° C. by means of the
heating-apparatus formerly described by us. And now it was found,
that all spots disappear, but that the mentioned five intense spots
are elongated like the fingers of a hand (tig. 36 on plate II). This
fact could be explained by the supposition that the original sets of
parallel molecular planes, by which the five intensive spots were
produced, are changed during the deshydratation and heating gradually
into the same number of now divergent molecular planes lying in
five zones respectively. This would be possible, if the molecular
planes, which are situated nearer to the crystal-surface, will lose
their watermolecules sooner and more easily than those situated
nearer the inner part of the crystal: the expelling of the water
takes place namely very slowly and gradually, while the planes are
rotating round their zone-axes continually during this deshydratation.
It is possible, that an analogous, but far more irregular distortion
of the positions of the molecular planes will be the cause of a gra-
dually getting vaguer and finally of a disappearing of all other points
and spots; if not the other explanation, namely that all these points
correspond to the action of the zafermolecules alone, can be accepted.
It will be only possible to give some stronger affirmation of this view,
if more zeolithic silicate will be investigated in an analogous way.
The fig. 34 is made, after the heated crystal being cooled down
to the roomtemperature; it appears to be completely identical however
with the image obtained at 300° C. within the furnace, and it is
only reproduced here instead of the other, because the last mentioned

441

photograph was too pale. The resulting state of the heated apophy llite
remains thus absolutely fixed on cooling; after the data given in
literature, the water expelled at 260° C. will be only resorbed after
about 3600 hours from an atmosphere of water vapour. Anticipating
on our experiments with the apophyllite of Jceland, we can remark
in this connection, that with this mineral, which did not show the
five mentioned spots, there remained nothing at all on the photo-
graphic plate, after the crystal was heated, except some feeble action
on the places of the most intensive spots of the original image;
they only proved, that the transformation by the heating was not
yet completely finished. In no case we have therefore succeeded in
proving, as before was done with the boracite, that the pseudotetra-
gonal aggregation of monosymmetric material, above a certain tem-
perature can be changed into the really higher symmetrical form :
instead of such inversion, a change in the silicate-skeleton is pro-
duced, which at least during the short interval of the experiment
can be considered to be zrreversible, and which has nothing or not
directly to do with the real transformation into a true tetragonal
form.

§ 9. In opposition to these American crystals, the used apophyllite
of Leeland must be discerned as a most beautiful, glassy, and perfectly
clear crystal, which was determined to be a combination of sharp
pyramid {111} and basal pinacoid {OO1{. The angles of the pyramid
and of pyramid and basal pinacoid were variable within rather
wide limits; they deviated from the angles commonly mentioned in
literature by an amount of cirea 30' to 1°; yet the reflected images
were splendid and quite sharp, this phenomenon too leading to the
supposition, that the tetragonal symmetry could only be a mimetic
one:

{O01} : {t11} = 59°24’ to 60°13; in literature : 60°32’.
144} : {4171} ao : ‘5 : 58°56'
Shea): fe == 74°38! to. 75°39" 3 BO add

“rather oscillating’’.

From this crystal two planparallel plates were cut, the one
parallel to {OOL}, the other to {100}.

The plate parallel to {O01} between crossed nicols appeared
to be not completely isotropous, but to possess an extremely weak
birefringence, with the principal optical sections orientated perpen-
dicularly to the edges (110) : (OO1).

By means of a gypsum-lamella, giving the red of 1% order, it
appeared to be divided into four sections, of which the diametrically

442

Opposed ones were tinged blue, while the other ones were orange.
Every sector is optically biarial, with positive character; the axial
plane is in every sector perpendicularly orientated upon the corre-
sponding edge (110):(O0O1). The four quadrants were limited in the
centre of the basal section by straight borders, corresponding with
the edges of the psendo-tetragonal pyramid; in every sector the
direction parallel to the corresponding edge (110): (O01) is that of
smaller optical elasticity.

The plate, which was cut parallel to {100}, showed on very
strong enlargement and by the aid of a gypsum-plate with the red
of Ist order, a very fine lamellar structure: the lamellae are super-
posed parallel to the faces of the pyramidal, apparently tetragonal
limiting forms, while also locally smaller or more extended fields
can be discerned, in which the optical orientation appears to be
different and in an orientation, evidently perpendicular with respect
to each other.

Of these plates the RONrGEN-patterns were obtained in the usual
way: the fig. 5a, plate II represents the image, if the plate parallel
to }OOL} is radiated through; it corresponds to the centre of the
basal sections, where the four sections are tangent to each other;
fig. 6 was obtained by radiation through one single sector, and
fig. 56 represents the RON?rGENogram, correspondiug to a radiation
through the plate, cut parallel to {100}.

Although fig. 5@ appears to be approaching to a much higher
degree to real tetragonal symmetry, it is easy to recognize in it the
perpendicularly crossed partial figures of the photographs fig. 1—4,
but without the formerly mentioned intensive five spots near the
centre; and fig. 54 shows a symmetry with respect to two planes
of symmetry, perpendicular to each other, and a binary axis. In
fig. 6 it would again be possible to doubt this approach to tetragonal
symmetry; however it seems to be present, and the figure allows,
e.g. by direct comparison with fig. 4, to prove that in the radiograms
of the /celand-apopliyllite doubtlessly several elements of the mono-
symmetric American structures are present. From all these peculiarities
it seems that we may conclude, that the image of the apophyllite
from Iceland approaches only therefore more that of a real tetragonal
crystal, because the intergrowth of the monoclinic lamellae is in this
case much finer and more regular than in the American species;
and with this doubtlessly the other facet is connected, that the
Iceland-mineral looks so much clearer and within larger sectors
more homogeneous, than the turbid-looking and opaque American
apophy llites.

445

Finally we can here also fix the attention to the fact, that the
RontGenograms of the apophyllites of different localities differ yet
in their finer features, although they possess the same general
symmetry.

§ 10. In our opinion these investigations have decided ‘without
any doubt between the two prevailing theories for the explanation
of the optical anomalies of apophyllite, i favour of MaLiarn’s
hypothesis: not the tetragonal molecular structure, disturbed later by
internal stresses, must be considered as the primary state of the
mineral; but this state corresponds to an originally monoclinic
molecular arrangement, which approaches very closely to a tetragonal
one, and which reaches its pseudo-tetragonal character by the
crossing and intergrowth of two such monosymmetric structures,
by means of polysynthetic lamellar twinning, and a mutual penetration
in directions, which make an angle of 90° with each other.

POSTSCRIPT.

Finally we will use this opportunity, to add here again a con-

@
fe) ®
®
Q ®
(o)
® Q
e 2
@
Oo
2
— + — —— — —— @Q— ——&) —
®
(e}
e
= ®
@
S e
e ®
®
® @
@

Boracite at 300°. C.

444

struction-figure, relating {0 our paper on the symmetry of boracite ‘);
this figure will reproduce the changes observed by us with this
mineral before and after heating, in a ciearer way, than the not
very satisfactory photographical reproductions given in that paper.
In constructing this stereographical projection, Dr. L. S. Ornsrpin
has given us again his kind assistance, for which we thank him here
also once more. The change of the binary axis into the quaternary
one, is proved by this figure again in a very striking manner, and
it is easy to see, which reticular planes of the molecular structure
have disappeared at higher temperature.

At the same time we will correct some errors in the former
paper, where on p. 797 the words “right” and “left” need to be
interchanged several times, because the photographs are unhappily
placed in reversed position, so that on comparison of the text and the
figures, there is a confusion of right side, left side, and of horizontal and

Boracite at room-temperature.

') H. Haca and I’, M. Jan@er, these Proc. loco cit. 798 (1914).

445

vertical directions. The new figure in this paper has been adjusted in
such a position, that it will correspond to the text of p. 797, if only the
words vertical and horizontal (line 9 and 10 from beneath) are inter-
changed on reading.

Groningen, June 1914.
Laboratories for Physics and for Inorganic
Chemistry of the University.

Physics. — “FRESNEL’s coefficient for light of different colours.”
(First part). By Prof. P. Zeeman.

One of the empirical foundations of the electrodynamics of moving
bodies in the domain of optics is Fiznau’s celebrated experiment on
the carrying along of the light waves by the motion of water. Let
w be the velocity of water relative to an observer, then for him
the velocity of light propagated in the water wauld be

-
CG. === sB07
u

if the dynamical laws for the addition of velocities were perfectly
general.

In this equation a designs the index of refraction of water, c the
velocity of light in vacuo, and we must take the upper or the lower
sign, according as the light goes with or against the stream. Fiznau

demonstrated that not the entire velocity w but only a fraction of
it comes into action. This particular fraction appeared to be approxi-

1
mately equal to 1 — —, Frusnew’s coefficient. Hence we must write
3 ae
in place of the above given formula:
= c
Cr SS SSC Joh is Joo antes Me ape (al)
where
1
Sieelettee iii gd callie oy
we

For water ¢ is equal to seven-sixteenths.

The extremely important role which the formulae (1) and (2) have
had in the theory of aberration, in the development of Lorenrz’s
electronic theory needs not to be exposed here, and it is hardly
necessary to state that equation (1) is now regarded as a simple
confirmation of Einsrrin’s theorem concerning the addition of velocities.

I may be permitted however to point out the smallness of the

446

second term of formula (1). The velocity which we are able to
obtain in a column of water transmitting light is of the order of
magnitude of 5 metres per second. We have thus to find a difference

; 3108 :
of velocity of 5 metres in 13 m., i.e. Of one part in fifty millions.

This was done by Fizeav ') in one of the most ingenious experi-
ments of the whole domain of physics. Fiznau divided a beam of
light issuing from a line of light in the focus of an object-glass
into two parallel beams. After traversing two parallel tubes these
beams pass through a second lens, in the focus of which a silvered
mirror is placed. After reflection the rays are returned to the object
glass, interchanging their paths. Each ray thus passes through the
two tubes. A system of interference fringes is formed in the focus
of the first lens. If water is flowing in opposite directions in the
two tubes, one of the interfering beams is always travelling with the
current and the other against it. When the water is put in motion
a shift of the central white band is observed: by reversing the
direction of the current the shift is doubled.

The ingenuity of the arrangement lies in the possibility of securing
that the two beams traverse identical ways in opposite directions.
Every change due for example to a variation of density or of tem-
perature of the moving medium equally influences the two beams
and is therefore automatically compensated.

One can be sure that a shift of the system of interference fringes,
observed when- reversing the direction of the current must be due
to a change of the velocity of propagation of the light.

The tubes used by Fizeau had a length of about 1,5 metres and
an internal diameter of 5,3 m.m., whereas the velocity of the water
was estimated at 7 metres. With white light the shift of the central
band of the system of interference fringes observed by reversing the
direction of flow was found from 19 rather concordant observations
equal to 0,46 of the distance of two fringes; the value calculated
with FRESNEL’s coefficient is 0,404. :

The result is favourable to the theory of Fresnen. The amount
of the shift is less than would correspond to the full velocity of

‘ ? ei: 1
the water and also agrees numerically with a coefficient 1——, if-
ul
the uncertainty of the observations is taken into account.

) H. Fizeau. Sur les hypotheses relatives a |’éther lumineux et sur une expérience
qui parait démontrer que le mouvement des corps change la vitesse avec laquelle
la lumiére se propage dans leur intérieur. Ann. de Chim. et de Phys. (3) 57
385, 1859.

447

Fiznau’s experiments, though made by a method which is theore-
tically as simple as it is perfect, left some doubts as to their accu-
racy, partly by reason of the remarkable conclusions as to relative
motion of ether and matter to which they gave rise, and these
doubts could only be removed by new experiments.

35 years after Fiznau’s first communication ') to the Académie
des Sciences, Micuenson and Moriny*) repeated the experiment.
They intended to remove some difticulties inherent to Fizeau’s method
of observation and also, if possible, to measure accurately the fraction
to be applied to the velocity of the water. Micurnson uses the prin-
ciple of his interferometer and produces tmterference fringes of con-
siderable width without reducing at the same time the intensity of
the light. The arrangement is further the same as that used by
Fizwau but performed with the considerable means, which American
scientists have at their disposal for important scientific questions.
The internal diameter of the tubes in the experiment of Michrtson
and Moriey was 28 m.m. and in a first series the fotw/*) length of
the tubes was 3 metres, in a second series a little more than 6 metres.

From three series of experiments with awhile light Micuuson found
results which if reduced to what they would be if the tube were
2 5 metres Jong and the velocity 1 metre per second, would be
as follows:

“Series 4A = double displacement
if 0,1858
2 0,1838
3 0.1800”

“The final weighted value of A for all the observations is 4 =0,1840.
From this by substitution in the formula, we get «= 0,454 with a
possible error of + 0,02”.

For light of the wavelength of the D-lines we calculate 1

1 at
— —, = 0,437. This agreement between theory and observation is

u
extremely satisfactory.

A new formula for ¢ was given by Lorentz *) in 1895 viz.:

1) Comptes rendus 53, 349, 1851.

2) A. A. Micuetson and E. W. Mortey, Influence of motion of the medium on
the velocity of light. Am. Journ. of Science (3) 31, 377, 1886.

8) Viz. the sum of the lengths of the ways in the moving medium, traversed
by each of the interfering beams, or approximately twice the length of one of the
tubes.

4) H. A. Lorentz Versuch einer Theorie dev electrischen und optischen Erschei-
nungen in bewegten Kérpern, p. 101, 1895. See also Theory of Electrons p. 2¥0,

1 gn

=1-- —-——4 Wome AEN oe © sale
j uw uda (3)

For the wavelength of the sodium lines this becomes:
0.451.

We see, therefore, that the value deduced by formula (3) deviates
more from the result of the observations than the value given by
the simple formula (2).

“Sollte es gelingen, was zwar schwierig, aber nicht unméglich scheint,
experimentell zwischen den Gleichungen (8) und (2) zu entscheiden,
und sollte sich dabei die erstere bewahren, so hatte man gleichsam die
Dorrrer’sche Veranderung der Schwingungsdauer fiir eine kiinstlich
erzeugte Geschwindigkeit beobachtet. Es ist ja nur unter Beriick-
sichtigung dieser Veranderung, dass wir die Gleichung (3) abgeleitet
haben’. 7)

It seemed of some importance to repeat with light of different
colours Fizeav’s experiment, now that the correspondence between
theory and observation had become less brilliant, and in view of
the fundamental importance of the experiment for the optics of
moving bodies.

From the point of view of the theory of relativity the formula (3)
is easily proved, as has been pointed ont by Lave’), neglecting
terms of the order sh Recently, however, again some doubt as to

;
the exactness of Lorentz’s term has been expressed. I may refer
here to a remark by Max B. Weinsrein*) in a recent publication
and to a paper by G. Jaumann *). The last mentioned physicist gives
an expression for the coefficient ¢, which for water does not differ
much, but in other cases deviates very considerably from FREsNEL’s
coefficient.

The interference fringes were produced by the method of Micuerson.
The method of observation introduced will be described later on.
The incident ray s /a meets a slightly silvered plate at a. Here it
divides into a reflected and a transmitted part. The reflected ray
follows the path abcdea f, the transmitted one the path
aedcbha f. These rays meeting in the focal plane of 7 have

1) Lorentz. Versuch u. s. w., 102.

2) M. Lauvs. Die Mitfiihrung des Lichtes durch bewegte Kérper nach dem Re-
lativititsprinzip. Ann. d. Phys. 28, 989. 1907.

5) Max B. Wernsrery. Die Physik der bewegten Materie und die Relativitits-
theorie. Leipzig. 1913, see note on p. 227 of his publication.

) G. Jaumann. Elektromagnetische Theorie. Sitzungsber. d. Kaiserl. Ak. der
Wiss. Wien. mathem. naturw. Kl. 117, 379. 1908, especially p. 459.

449

pursued identical, not only equivalent, paths, at least inis is the
case for that part of the system of interference fringes which in
white light forms the centre of the central band.

Fig. 1.

In order to verify the formula (3) it is necessary that the light
be monochromatic. Further it seems of immense advantage to have
a water current which remains constant during a considerable time.

For observations with violet light this even becomes strictly neces-
sary, because visual observations are impossible with the violet
mercury line (4358) used. MicueLson obtained a flow of water by
filling a tank, connected with the apparatus; by means of large
valves the current was made to flow in either direction through the
tubes. “The flow lasted about three minutes, which gave time for
a number of obseryations with the flow in alternating directions”.
In view of my experiments the municipal authorities of Amsterdam
permitted the connection of a pipe of 7.5 em. internal diameter to
the main water conduit. There was no difficulty now photographing
the violet system of interference fringes, though the time of expo-
sition with one direction of flow was between 5 and 7 minutes.
The pressure of the water proved to be very constant during a
series of observations; the maximum velocity in the axis of the
tubes, of 40 m.m. internal diameter and of a total length of 6
metres, was about 5,5 metres. :

Before recording some details of my experiments, | may be per-

450
mitted to communicate the general result that for water there eaists
a dispersion of Fresxwi’s coefficient and that formula (3) and there-
fore the third term of Loruntz ts essentially correct.

I wish to record here my thanks to Mr. W. pn Groot phil. nat.
eand. and assistant in the physical laboratory for his assistance
during my experiments with the final apparatus.

The difficulties encountered in these experiments were only sur-
mounted after two reconstructions of the apparatus. Great annoyance
gave the inconstancy of the interference fringes, when the pressure
of the water or the direction of flow were changed. Then not only
the width of the interfereice bands, but the inclination of the fringes
were undergoing uncontrollable variations. All these defects were
perfectly eliminated by the use of wide tubes and by arranging the
end plates in the manner indicated in Fig. 3.

I am indebted to Mr. J. vAN Dpr Zwaat, instrumentmaker in the
laboratory for his carefully carrying out my instructions and designs
in the mechanical construction of the apparatus.

In fig. 2A a side aspect, and in Fig. 2B a horizontal projection
of the arrangement on a scale of about ‘/,," is given (see Plate).

The interferometer is at the right side, at the left the rectangular
prism is placed.

The mounting of this prism is only sketched and was in reality
more stable than might be inferred from the drawing.

451

Prism and interferometer were mounted on the piers cemented
to the large brick pier of the laboratory. The tubes are entirely
disconnected from the interferometer and mounted on a large iron
[ girder; this girder is placed upon piers of freestone cemented to
large plates of freestone fixed to the wooden laboratory floors. In
this manner the adjustment of the interferometer cannot be disturbed by
vibrations proceeding from the tubes. At the right of the horizontal
projection the four large valves may be seen, by turning which the
current was made to flow in either direction through the tube systems.

The mountings containing the glass plates by which the tubes
are closed are not given in the Plate. One of these mountings con-
taining the plane parallel plates of glass is drawn to scale in Fig. 3
at one half of the natural size. The four plates of glass are by
Hiteer, they are circular of 24 m.m. diameter and 10 m.m. thick ;
in a second series of observations plates 7 m.m. thick have been
used. The accuracy of parallelism of the plates is excellent; they
are indeed cut from echelon plates.. The general plan adopted for
the construction of the plate mountings is this: one can only be
sure that no change will occur in the position of the plates during
the course of an experiment, if this position is entirely dejinite. In
order to attain this the glass plate rests upon the inner, accurately
grinded, surface of the brass piece d. This piece d fits accurately
into the conical inner part of a piece 4, itself rigidly screwed to
the tube a. Parts d and 6 are connected by means of the counter
nut c. The glassplate is held against d by the nut e. There is no
objection to the presence at the zmszde between e and d of rings of
hard india-rubber and of brass. (To be continued).

Physics. — “A new relation between the critical quantities, and on
the unity of all substances in their thermic behaviour.” (Con-
clusion). By Dr. J. J. van Laar. (Communicated by Prof. H. A.
LorRENTZ).

(Communicated in the meeting of April 24, 1914).

By way of supplement we shall add the calculation of three more
isotherms he/ow the critical temperature, for which (loc. eit.) data
are known from the unsaturated vapour region. If the p-values above
T; were somewhat too high on the whole, now we shall find values
which are much too low, lower even than #,, and therefore impos-

sible. These deviating values can only be explained, when with low
temperatures and large volumes association in the vapour is assumed,

452

For then, when R7 in the equation of state is made smaller by a
factor <1, also v—/ will be smaller, hence 6 greater. In this way
the too small /-values could therefore be raised to the normal amount.
We shall see in the following paragraph that inside the region of
coexistence the same phenomenon takes place: the 4-values in the
vapour much too small (even large negative), the 4-values in the
liquid phase normal and in harmony with the theory.

Something particular takes therefore place for the large volumes:
there is either association in the vapour, or the values of the pressure
have been measured too small, or the values of the vapour densities
too large. We shall presently return to this.

Ff. Isotherm of —130°,38 = 142,71 absolute. Hence m=0,9473,
3,424 m = 3,244.

p dy & | n €+5:n2 n— | B
| |
12.773 27.394 0.2661 10.873 0.3084 10.518 | 0.355
| | | | |
28.878 77.821 0.6016 3.827 0.9430 3.440 } 0.387
|
Mean 0.371 |

Here we should have y = 0,727, 4, = 0,415, &, = #8, K 1,475 = 0,421.

Hence the value of ”, found is too low.

g. Isotherm of — 139°,62 = 133,47 abs. Here is m= 0,8860,
424 77 = 31034:

p dy € n e+5:72 n—

11.986 28.122 0.2497 10.591 0.2943 10.308 || 0.283
14.586 35.573 0.3039 Sono 0.3752 8.085 0.287

Mean 0.285

With 7 = 133,47 corresponds y=0,719, 2, — 0411, 2,— Gee
<< 1,457 = 0,416. The found value of &,, viz. 0,285, is far below
the theoretical value O,42.

h. Isotherm of — 149°,.60 = 123,49 abs. For m is found

m= 0;8197, so 3,424 m= 2.807.

——

0.2323 | 10.206 | 0.2803 | 10.014 0.192
| 0.3341 8.401 0.195
|

o
tr
a
a
>
ioe)
or
vo}
-I

Mean 0.194 _

Here y=0,711, 4 =0,406, &,=8, X1,439 = 0,411; 0,19
again remains considerably below this.

Combining the found values of &, in a table and comparing them
with the theoretical values, we get the following survey.

m | OS ele AS meets oie elt, OFemenl Ot | 0.95 0.89 0.82

0.49 0.46 0.435 0.43 0.43

0.42 0.42 0.41

|
B, cale. |
OF55) v0: SIN O45" 043i 0242 | 0.37? 0.28? 0.19?

B, found

As was already remarked above, the great deviation, especially
below 7i.(m<1), mmst not be ascribed to the theory, but to the
experiment, or to association in the vapour.

For the found values of &, become, as we shall see, even negative,
henee impossible, at still lower temperatures — while also yop, is
continually fornd smaller than @j,,, which of course points to
something particular in the vapour: either association, or inaccurate
vapour- or volume determinations, in consequence of a systematic
error. (Consult also g. of § 18 for a possible explanation.)

18. The region of coexistence. (Cf. Comm. 131 and These Proce.
of Nov. 1913 (Comm. 138)).

For the calculation of & from the given values of the coexisting
vapour and liquid densities it is to be regretted that the vapour
pressure observations (see also Comm. 115) have not been made at
exactly the same temperatures as the density observations. This has
rendered interpolations necessary, which of course impairs the
perfect accuracy of the ¢, which will make its influence felt chietly
on the #-values which are calculated from the vapour densities.

In this connection we should not omit mentioning that the value
of /, caleulated from the first observations of the vapour tensions
(Comm. 115), is much too low, viz. 5,712, whereas the much better

Proceedings Royal Acad, Amsterdam, Vol. XVII,

454

value 7 > 5,933 follows from the values given in Comm. 1204
(see p. 10)’).
We had even sufficient reasons (see § 17) to fix the value of
7’ at 6 (f could be still somewhat larger then).
Rankine-Bosr’s interpolation formula (see These Proe. of Noy. 1913,
or Comm. 188), namely
c d

b
log pa + i Ser

gives by differentiation :

hence

T 2,3 A ied ve Oo 61538,18 32293927 ~
Pas aca ity eae Wael eV Yop cesta 2
tp die OT To) a /

T?
But this formula, which is caleulated from all the observations
of p (so also from those below — 140°,80), and corresponds pretty

well with it, gives the value /;,= 5,628, which is much too low,

at 7), (150,65), hence still lower than the value fj, = 5,712, given
at the conelusion of Comm. 115, and ealeulated with / = — 524,3169,
c= + 11343,28, d= 0.

In virtue of this I think I have to recommend caution in the

use of the values of p, at least in the neighbourhood of the eritical
temperature.

We shall now give the following survey of the values found for
the densities 9, and 9, (Comm. 131), and also the corresponding
values of p (Comm. 115, and These Proe. of Noy. 1913 or Comm. 138).

— 125°.17
— 131°.54
—. 1359.51
—— 140°. 20
— 150°.76
— 161°.23
— 1759.39
— 183°.15

have

calculated

. 771289
.91499
.97385
.03456
.13851
22414
.32482
.37396 |

from

0.29534
0.19432
0.15994
0.12552
0.06785
0.03723
0.01457
0.00801

and o

p=42.457 (for — 125°. 49)

35.846 ( >» — 129°.83)
29.264 (» —134°.72)
22.185 (» — 140°.80)
13.707 (» —150°.57)
7.4332 ( » — 161°.23)

1.3369 ( » — 183°.01)

given in the following tables by means of 0; = 0,53078.

the values of d, and d,

1) Slightly below 7%, at —125°,49, f = 2,577 K2,3026 = 5,933 was namely found,

455

@. t= —125°,17, hence T= 147,92, m= 0,9819, 3,424 m = 3,363.
By means of linear interpolation p = 42,944 has been calculated,
so «= 0,8947.

0.292 0.394 (Lig.)
1.376 0.421 (vapour)

0.687 1 11.50
P07 —l|° 2.443

d, = 1.4563
dy = 0.5564

As theoretically @ ranges from 0,42 to 0,29 (see above), both the
values found can be correct.

by = — 131° 54, P= 141,55. Hence m =0)9396, 3,424m=
= 3,217. Linear interpolation, giving p= 38,545, «= 0,6989, would
be too uncertain here, as —129°,8 differs too much from —131°,5.
Van per Waats’ formula — log’ =f gives with /= 2,444")

_ the value «= 0,6964.

| | | |
d | n | e+5 ad? | n—£ B
| l |
d, = 1.7238 0.580 | 15.55 0.207 | 0.373 (lig)
d, = 0.3661 Ques 1.367 | 2.354 | 0.377 (vapour)

As £2 ranges from 0,42 to 0,29, the @-value in the vapour is too
small.

c. == —135°,51 = 137,58 abs. Hence m = 0,9132, 3,424 m=3,127.
A linear interpolation gives p= 28,344, ¢=0,5905; van per Waats’
formula with f= 2,420 gives «= 0,5890.

| j
|

=e = 7 TI
d n e+5d2 | n—B } B
| | |
dy =1.8348 | 0.545 | 17.42 | 0.179 | 0.356 (4ig.)
d, = 0.3013 3.319 1.043 | 2.998 | 0.321 (vapour)

1) The values of f have in each case been calculated by me from the vapour-
pressure observations.

30*

456

The .2-value in the vapour begins to be smaller here than that
in the liquid!

d. t= —140°,20 = 132,89 abs. Hence m=: 0,8821, 3,424 m=3,020.
For p we find through linear interpolation p= 22,795, ¢=0,4749;
from — log’ «= ete. with f=2,415 on the other hand «= 0,4757.

d n |) et5d2 | n— &

d; = 1.9491 0.513 || 19:47 ety te
| | |

0.358 (Lig.)

| 0.230 (v.)
|

48, should be about 0,42. Besides 0,23 is again < 0,36.
@) $= —150°176 = 122533 abs.; Hence yn 0138120, 33404 7—
= 2.780. Linear interpolation gives p = 13,595, « = 0,2832.

d>—=0.2365 | 4.229 || 0.7553 | 3.999

1 e+5a2 | n—Z B
| )
|| ||
d, = 2.1450 0.466 || 23.29 | 0.119 | 0.347 (Lig)
dy=0.1278 | 7.823 | 0.3649 | 7.619 | 0.204 (v.)

The value of @, is 0,41; 0,20 remains far below this. We moreover
point out that also / of § 17 at t= — 149°,6 yielded a perfectly
harmonious value for the vapour, viz. 0,19. The two series of
observations, therefore, cover each other entirely.

f. t= 161°,23 = 111,86 abs. From this m = 0,7425, 3,424 m =
= 2,542. Linear interpolation gives p= 17,4332, «= 0,1549.

d n We 52) n= G | B
| || \|
d; =2.3063 | 0.434 || 26.75 0.095 |, 0.339 (lig.)
d>— 0.07014 | 14.257 | 0.1795 | 14.167 | 0.090(v.)
| | |

£2, begins to be more and more impossible. We point out that
when f— 1 is iaken not =5, but e.g. =4,95, the value
Bi,, does not appreciably change: 0,339 then becomes 0,338. But
2, would then become still smaller, viz. 0,07 instead of 0,092).

If p=7,58 instead of = 7,43, so ¢ = 0,158 instead of = 0,155, we should
also have found 0,34 for the value of g in the vapour, the same value at
least as that for the liquid. (Also the ,assumption °, = 0,C366 instead of 0,0372
might lead to the desired purpose).

vA¥

457

g. 1=—175°,39 = 97,70 abs. Hence m = 0,6485, 3,424 m = 2;221.

The value of « interpolated from —/og™ «= ete. with f= 2,322,

gives ¢ = 0,05518.

—— ——— ——- ———
d n € +5 @?2 n—P ie)
d, = 2.4960 0.401 31.21 0.071 || 0.329(diq.)
dy = 0.02745 | 36.43 0.05894 | 37.67 —1.24!(v.)

Can the clue to the singular behaviour of the vapour perhaps be
found in this that Crommenin has not determined the vapour densi-
ties directly, but that he has calculated them from the law of BoyLE?
With a too small value of » one naturally gets then a too slight
value of @ from @ =n — (38,424 im: ¢). Then no association need of
course be assumed in the vapour, and the impossible values of 2,

below 7%. are at once accounted for. The found values of 2, would
then be quite worthless. The question is therefore: where has
CromMeLIn begun not to determine the given values of the vapour
| density directly, but to ca/cuéate them from the (not yet valid) law
of Borin ? *)
he t= — 183° 15=6994 abs. Here m= 035970, 3.494 m = 2.044.
From /og'*e= etc. we find the value «= 0,02742 (p = 1,3162)
with f= 2,314.

dy | a i etsa| ne | |B

OS SF SS SSS SS ;
d; = 2.589 | 0.386 || 33.53 | 0.061|| 0.325 (dig.)

dp = 0.01509 66.26 |) 0.02856 | 71.87 | --5.31! (2)
| |

We point out that the liquid value duly decreases gradually, and
is still higher than 8, = 0,29 at 7’ = 90 (absolute). So there is nothing

impossible here °*).
1) Otherwise p= 2,78 would have to be taken here instead of 2,64, hence
, e — 0,058 instead of 0,055; or else o; should be assumed somewhat smaller, in
order to find at least the value 0,33 (that of the liquid) for 8

vapour’
2) A rise of p to 1,44 instead of 1,32 (s to 0,030 instead of 0,0274) — or else a
diminution of 03 from 0,0O8O ts 0,0075 — might reduce 6, to 0,33 here. The
first supposition is impossible, for then the value of p at —183°,15 would be

greater than at 183°,01, where 1,34 was found. But a diminution of g. by 6%/,
in consequence of an erroneous calculation of e, (probably from the law of Boyte)
is very well possible.

458
Summarizing, we get the following survey for the region of coexistence.

m | 0.98 0.94 0.91 0.88 0.81 0.74 0.65 0.60

Blig.| 039 0.37 0.37 0.36 0.35 0.34 0.33 0.325
Bo. | 0.42 0.38 0.32? 0.23? 0.202 0.09? —1.24? —5.3?

At the lowest temperature, viz. t= 89,94 abs., y would be about
0,688, and 8, accordingly 0,393, 8, = 8, « 1,889 = 0,397, so that
8 ranges from about 0,40 to about 0,29. The liquid value 0,825 at
n= 0,4 can be in harmony with this.

In order to examine whether the values of Biiy. also agree quan-
titatively with our theory, we will in the first place indicate for the
different values of 7(m) the corresponding values of m and y (caleu-
lated from 2y — 1 = 0,038 V 7). Besides the value of v: vy, =v: bd, =
=n: 8, is given. (8, = 0,286).

m | 0.98 0.94 0.91 0.88 0.81 0.74 0.65 0.60 0
n | 0.687 0.580 0.545 0.513 0.466 0.434 0.401 0.386 | 0.286
% 0.731 0.726 0.723 0.719 0.710 0.702 0.693 0.688 | 0.5
D:0) | 2.40 © 2.03 1:91" 1-79" 1.63 4.52) “1 -40mieiegs 1
hence p:jy| 1.33 1.245 1.215 1.18 ° 1.14 1.11 - 1.08 1.07 1
acalc.| 0.381 0.356 0.348 0.338 0.326 0.318 0.309 0.306 | 0.286
afound| 0.394 0.373 0.366 0.358 0.347 0. 39 0.329 0.325 | (0.305)

The values 8:8, =6:6, have been calculated from the tables of
§ 16, viz. from those for y=0,75 and y=0,70. We have inter-
polated for the values of y given in the above table. On an average
the found values of 8 are 6°/, higher than the values ealeulated
from our formula (30). If 8, = 0,30° were taken instead of 0,28°,
the agreement would have been perfect. In connection with this it
is remarkable that the dzjference between Bround ANd Beale, AaMounts
almost constantly to 0,018 or 0,019. The course of the §-values is
therefore perfectly identical with the course calculated from our
formula; identity in the numerical values may be obtained by simple
change of B, from 0,28° to 0,30°.

459

In fact, something is~ to be said in favour of this. In § 17 we
namely calculated the value of @, from 2y = 6;:b,= &;: ?,, so
that &, = &,: 27 = 0,429:1,5 became = 0,286. But in this it is
assumed that the direction of the straight diameter remains the same
down to the absolute zero point — which (as we already observed
at the conclusion of § 14 (III p. 1051) cannot be the ease. On the
contrary the coefficient of direction will approach to about 0,5 for
all substances at low temperatures. It follows from this that the
value of the liquid density at 7 =O, viz. @,, which is extrapolated
from the direction of the so-called straight diameter (at the critical
poit), will always be too great, hence v, too small, and also 6, =v,
too small. Accordingly also the value of ?, = 6,: vz will be found
too smali, when the inadmissible extrapolation is performed.

The real value of &,, occurring in our formula (30) for b= /(v),
will therefore be always greater than that which occurs in our
relations found in I (which are valid aé the critical temperature).
For the calculations of the real ,, in order to test our formula
(30) by the observations, the calculation from &, = &,: 2; (which
is based on this extrapolation) has therefore to be rejected.

The above table need, therefore, give no occasion to conclude to
any deviation with respect to the calculated and the found values
of &; the more so as the course is perfectly the same, in consequence
of the fact that in the relation (80) not 6, but b—b, occurs, so that
through simple increase of 2 to 0,305 the found values of b—d,,
resp. B—, will agree perfectly with the values of 8— 3, calculated

from our formula.

Remark. We saw that the found values of 3, from the unsaturated
gas state (§ 17) were all found too great for values of m>1; for
values of m< 1 all too small i.e. larger or smaller than the values
of p, or By caleulated from our formulae. Also in the region of
coexistence (7 << 1) we found values for 3, which are all too small,
nay even negative, hence impossible. Now the too small values may
be easily accounted for either by association in the vapour at low
temperatures, or through a faulty method of calculation of 8, from
the law of Boynr (see above). But the too large values of By at
m > 1 cannot be aecounted for in this way.

It is, however, remarkable, that those too large values of 3, at
m<c1, combined with the Uquid values at m< 1, seem to obey
the relation

B=0,4Vm

pretty well, as appears from the table on the next page.

460

m= 1.95 1.43 1.13 1.04 1.01 | 0.98 0.94 0.91 0.88 0.81 0.74 8.65 0.60
Vm= 1.40 1.20 1.06 1.02 1.005 | 0.99 0.97 0.954 0.94 0.90 0.86 0.806 0.775

0.4 V\m= 0.56 0.48 0.42 0.41 0.40 0.40 0.39 0.38 0.38 0.36 0.34 0.32 0.31
|

8 found 0.55 0.51 0.45 0.43 0.42 | 0.39 0.37 0.37 0.36 0.35 0.34 0.33 0.325

The values on the lefthand side of the dividing line might have
a somewhat higher factor, viz. 0,42; those on the righthand side of
the line (the liquid values) a somewhat smaller factor, e. g. 0,39,

Yet this relation can hardly satisfy for several reasons. First because
the formula ~=0,4’m would yield too large values of p, for
larger values of m; it is at least inconceivable that the increase of
6, with the temperature will continue indefinitely. But secondly the
variability with v would disappear through this consideration, and
only dependence on 7’ would be assumed. It would then be quite
indifferent, whether 6 was considered at large or at very small
volumes. That this, however, is entirely impossible, is at onee seen
when we bear in mind that only by the assumption 6= /(v) we
duly get r<3, s>*/,, and /’ >4! Only for “ideal” substances,
i.e. at the absolute zero point, can ) be independent of the volume.

Other relations could’ also be derived, among others between the
found values of 8, 2—p, and m'‘), but they may also be due to
chance. We shall, therefore, no longer dwell upon them.

19. The characteristic function.

It is known that for “ordinary” substances the value of the
ee Pettey aa :

characteristic” function @, 1. e.

j—1 «¢
iS =
4 fi-—l1 did.
; é . m d&cocx.
in which #=— —— is not constantly = 1 — as would have to

e dm

be the case, when a or } should either not depend on 7’ or only
linearly — but with diminishing m inereases from 1 to about 1,4
at m=0,6, with about 1,5 as probable limiting value when m
approaches to 0. See vAN pEk Waars, and also my Paper in These
Proc. of 25 April 1912, p. 1099—1101, in which it appeared that
g~ =1-+ 6,8 (1—m) can be put in the neighbourhood of the eritical
point. (loc. eit. p. 1101).

1) When e.g. in the region of coexistence for the different values of m we write
the corresponding values of n and n— f,

viz. +0,23.

i
a appears to be about constant,

461

bavin¢ a
For this it is however required that either —{ — ] = 6,8, or
Om? \ an) i

O20 :
== {= | 6,9. (Cf. These Proc. of 3 Sept. 1913; p.56 and 57).
Om? \ by. / 7.

It is now certainly interesting fo consider how this will be for a
substance as Argon, where yz is not 0,9, but 0,75.

For the calculation of the values of / I bad to make use of
RanktnE—Posr’s interpolation formula drawn up by Crommenin and
treated already above (§ 18). This gives, indeed, the much too low
value 5,628 instead of 6 for /;,, but 'as also the following values of
J will possibly be too small in the same degree, there is a chance
that the value of the ratio (f—1):(/,;—1) will not differ too
much from reality. We then find the following table.

|
147.92 | 0.9819 | 0.8047 | 0.8103 | 1.104 | 5.696 | 1.015
141.55 | 0.9396 | 0.6964 | 0.6311 |
137.58 | 0.9132 | 0.5890 | 0.5529 | 1.965 | 5.987 | 1.078 | 1.15
132.89 | 0.8821 | 0.4757 | 0.4609 | 1.032 | 6.137 | 1.110 | 1.15
122.33 | 0.8120 | 0.2832 | 0.4742 | 1.033 | 6.534 | 1.196 | 1.24
111.86 | 0.7425 | 0.1549 | 0.1618 | 0.957 | 7.047 | 1.307 | 1.25
97.70 | 0.6485 | 0.0552 | 0.0685 | 0.805 | 8.080 | 1.530 | 1.23
89.94 | 0.5970 | 0.0274 | 0.0391 | 0.702 | 8.945 | 1.717 | 1.21

It is certainly remarkable that it would follow from the found

04 :
values of g that here too 4 would be about — 7, just as for
me) I.

Og
ordinary substances as Fluorbenzene e.g. (see above). For (5 =
k

2)
= — ee = — 6,63 (whereas it is — 6,8 for C,H,F). But on this
head little can be said with certainty, as we have too few observations
in the immediate neighbourhood of 77, at our disposal.
The limiting value for m—0,6 is now, however, much lower,
namely about 1,23 against 1,41 for ordinary substances. Now for

462

C,H,F the value of yz, is = 0,95; hence 0,:b, = 2Y~ = 1,90, and
(6, : 6. )e = 1,90 <1,06 = 2:01,> whereas) 72,01 — 1,42. Further for
Argon k= 0,75, hence 0: 6,=1,50 and (6,:5,),=1,49 X 1,018
(See II, p. 986) = 1,516, whereas 1,516 =1,231.

It follows from this that with great accuracy

9, =V bo: be = V By 2 sw ee. DD)

may be written for the limiting value at low temperature of the
characteristic function ¢.

It is therefore again only for “ideal” substances (6 = const.) that
(> = 1, and hence ¢ continully =1 from 7% (then = 0) to the
absolute zero. but for all the other substances the value of gy will
increase from 1 to a limiting value, which will depend on the
degree of variability of 6.

As according to (36) (b,—d,),: 6, = 2y’ — 1 = 0,041 V 7; (see IIL
§ 15), we have also :

G, = VIS 004A ss

We shall not enter any further into this subject, leaving it for a
possible later discussion.

In conclusion we shall just repeat what we have already remarked
in I, p. 820, that the temperature dependence at extremely low
temperatures, where the departures from the equipartition law make
themselves felt, undergo a modification. But we shall not enter into
this any further either, and we only mention that for Argon the
departures from the said law fall entirely within the errors of ob-
servation even at 90° absolute (the lowest temperature at which
observations have been made). Besides, at those extremely low tem-
peratures all substances will probably have passed into the solid
state, and this state is controlled by other laws than the liquid and
the gaseous state, for which our considerations exclusively hold.

20. Conclusion. Though there are still many questions to be
answered, and many difficulties left, we may already conclude in
virtue of the foregoing to this:

1. The quantity a of van per Waats’ equation of state seems
within a large range not to depend on the density, so that the

: a é
molecular attraction can be represented by —, both in the gaseous
y?

and in the liquid state. *).

1) Cf. also the conclusions in a paper by Tyrer in the just published number
of the Zeitschr. f. Ph. Ch. (87, Heft 2) p. 198.

463

2. Whether the quantity @ is also independent of the tempe-
rature, cannot be stated with perfect certainty yet. For as I think
I have fully set forth in my Communieations of These Proce. of 25
April 1912 (p. 1091 —1106) and particularly of 3 Sept. 1913 (44—59 ,

ae ; (One ; 0°
the assumption of a darge value either of { — ] or of —
k k

or OL
(see p. 56—57 loc. cit.) is necessary for the explanation of the
course of the characteristic function g (see §19). And as, aceord-

ing to the above, 6, is, indeed, variable with the temperature, but
2

probably not so much that —(r) gets the required value, besides
t~/) i

6 possibly also @ might depend on the temperature. Only a separate
investigation ean furnish certainty about this.

3. The quantity 4 depends both on v and on 7. The way in
which 4 depends on v — which is expressed by a formula of the
form (see I] p. 981 et seq., Ill p. 1048, formula (29)]|

= j) xv y
peel oie ;
b,—b, Zi,

in which «= (b—4,):(v—yv,), and n depends on the quantity y,
which is in connection with 4,:4, — leads us to suspect that the
variability of 6 is possibly chiefly a real change after all, caused
by the action of the pressure p+ “/.2 and of the temperature, in an
analogous way to that which van Der Waats had in mind when

drawing up his “equation of state of the molecule’, with which the

above expression shows a close resemblance. [ef. also I p. 980—-931

(23 April 1914)|. Particularly also with regard to the temperatare

dependence, viz. [see HI p. 1051—1058, formulae (85) to (36)|
b,—b

7 _* — 9y'_] — 0,047,

this agreement is remarkable. But whereas vAN per WaAAtLs’ two

exponents are different, our two exponents are the same and
dependent on 7, i.e. on 7 so that m can vary from 3'/, (for y = 1)

to © (for y='/,, ite. T=0), as has been set forth in II, p. 935.

4. It seems to be unnecessary to ascribe the change of / to “quasi
association’. It might namely be assumed that the complex mole-
cules possess another volume than the simple ones, and from this a
relation b= /(v) might be calculated — according to the known
thermodynamic relations which indicate the degree of complexity as
function of v and 7. R7'is then however multiplied by another factor
which depends on the degree of association.

What van ver Waats has treated in that sense on p. 1076 of

464

his Paper in These Proc. of 25 Jan. 1913 (published March 13%),
had then already been treated very fully in a series of four papers,
written by me at Clarens 1911—1912 (On the variability of / ete. ;
see These Proc. of 26 Oct., 22 Nov. 1911; 24 Jan., 22 Febr. 1912).
That a good deal may be attained in this way can sufficiently appear
from these Papers. That difficulties present themselves of the same
nature as have been advanced by van perk Waats on p. 1076 at the
bottom (loc. cit.), has also appeared at the end of the 4 Paper
(p. 716 et seq.).

In any case it is a kind of relief that according to all that proceeds
the assumption of quasi association does not seem absolutely necessary.
The change namely of 4 with v and 7’ can very well be explained
by other influences.

5. That 6, gradually decreases with the temperature, so that b,
would coincide with 6, at Z’—0, and accordingly the variability of

4 would have quite disappeared — in consequence of which we
approach more and more to the ¢dea/ equation of state with constant
4, on approaching the absolute zero — this points to the invalidity

of the kinetic assumption, that for very large volume (for b, only
refers to /arge volumes) i.e. in ideal gas state, b, would be = 46,.
For according to the well known kinetic derivation, 6, would then
still be = 46, at the lowest temperatures, whereas it has clearly
appeared that 4, approaches more and more to }, at low tempera-
tures. Compare particularly Ill p. 1051, formula (85) and the sub-
sequent eloquent table.

6. Thus after all it would prove true what I wrote in I p. 809
(These Proc. of 26 March 1914), that namely in v—é the quantity
6 always refers to the real volume of the molecules m and is not
= 4m, as the kinetic theory would lead us to assume. And in this
way the difficulty, which I emphatically pointed out in II, p. 925
(at the bottom)—926, would have naturally vanished.

So it is getting more and more probable that the so-called quasi
diminution of 4 does not exist, and that there remains only real
diminution, which is represented by a formula of the form (29), as
far as the dependence on v is concerned, and by a formula of the
form (36), as far as the dependence on 7’ is concerned.

Why the earlier kinetic assumption 6, = 4m is really a fiction,
and what circumstance has been overlooked then — this I shall
demonstrate in a separate Communication.

It will then have become clear that only v—m, and not v—4in
determines the thermic pressure -- which becomes already probable
when the kinetic energy of the moving molecules is thought to be

465

uniformly absorbed by the surrounding medium (see p. 809 of I,
already cited above).

7. Hence at bottom the whole thermic behaviour of a substance
does not depend on/y on the two quantities @ and 6, which deter-
mine the critical quantities, which in their turn govern the law of
the corresponding states — in such a way that all the substances
behave correspondingly when they are only considered in equal
multiples or sub-divisions of their critical temperature and critical
pressure, but also (and the deviations from the said law are governed
by this) on the absolute height of the temperature, at which the
substance is considered. According to (86) every substance passes
namely through the different types — characterised by the variable
ratio b,:,, from the type of the “ordinary” substances, where
i b, is about 1,8 (y= 0,9) to the type of the ‘ideal’ substances,
where },is—=06, (y='/,) — when we descend from the ordinary
temperatures to the absolute zero point (see the tables in I, p. 819
and III p. 1052).

The individuality of the different substances, which they continue
to preserve within the region of the Law of the Corresponding States,
is therefore entirely determined by the rea/ height of the (absolute)
temperature.

Hydrogen at 328° absolute (77’=107%) will e.g. on the whole
(Law of Corresponding States) exhibit the same behaviour as Helium
at 52° absolute (7’ also = 107%) — but H, will show a value of
about 1,7 for the ratio 6,:4, at that higher temperature, while He
at the same “corresponding” temperature shows a value of about
1,2 for that ratio.

For ve: hr we shall find about 2,7 for Hydrogen and Helium at
their critical temperatnre, while vz: 6, = 2,1 is found for an ordinary
substance at its critical temperature. Ete. Ete.

And this may suffice for the present. I hope to come back to
some separate problems later on, which are still awaiting solution.
I may mention: the temperature dependence of / (see I, p. 811),
the change of direction of the “straight” diameter from 77, to very
low temperatures (III p. 1051), the form of the vapour-pressure
equation p= 7(7'), the dependence of the densities of liquid and
vapour on the temperature (in connection with the problem of the
direction of the straight diameter); and finally the course of the
characteristic function in its dependence on 7.

But the very first point that will be elucidated in a following
Paper is the circumstance mentioned under 6 of the conclusions,
that 4, cannot possibly be = 4m.

Fontanivent sur Clarens, April 1914.

(September 26, 1914.)

ons

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.

PROCEEDINGS OF THE MEETING
of Saturday September 26, 1914.
Vout. XVII.

DGC = .

President: Prof. H. A. Lorentz.
Secretary: Prof. P. Zeeman.

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Zaterdag 26 September 1914, Di. XXIII).

(SSyany Bwaa AN, PRISE

H. vu Bots: “Modern electromagnets, especially for surgical and metallurgic practice”, p. 468.

A. Wicumann: “On the Tin of the island of Flores”, p. 474.

M. J. van Uven: “The theory of the combination of observations and the determination of
the precision, illustrated by means of vectors.’ (Communicated by Prof. W. Karrryy),
p- 490.

H. Kameriincu Onnes and G. Horsr: “On the measurement of very low temperatures. XXIV.
The hydrogen and helium thermometers of constant volume, down to the freezing—point
of hydrogen compared with each other, and with the platinum-resistance thermometer,”
p. 501. E

H. Kameriincu Onnes and G. Horsr: “On the electrical resistance of pure metals ete. 1X.
The resistance of mercury, tin, cadmium, constantin and mapganin dowa to temperatures,
obtainable with liquid hydrogen and with liquid helinm at its boiling point,” p. 508.

H. Kamertiscn Onnes: “Further experiments with liquid heliam. L. The persistence of
currents without electro-motive force in supra conducting cireuits’, p. 514.

Hl. Kameriincu Onnes and K, Hor: “Further experiments with liquid helium N. Harr-effeet
and the change of resistance in a magnetic field. X. Measurements on cudmiam, graphite,
gold, silver, bismuth, lead, tin and nickel, at hydrogen- and helium-temperatures.” p. 520,

H. Kameruingu Onnes and H, A. Kuyrers: “Measurements on the capillarity of liquid
hydrogen,” p. 528.

F, A. H. Scurememakers and Miss W. C. bE Baat: “The system: Copper sulphate, copper
chlorid, potassium sulphate, potassium chlorid and water at 30°, p. 533.

J. Borsexen: “The Catalyse.” (Communicated by Prof. A. F. Hlotteman), p. 546.

F. M. Jagger: “Researches on the Temperature-coefficients of the free Surface-energy
of Liquids between —80° to 1650° C. Vil. The specilic surface-energy of the molten
Halogenides of the Alcali-metals”. p. 555. “Ibid VIL. The Specific Surface-energy of
some Salts of the Alcali-metals’’, (Communicated by Prof. H. HaGa). p. 571.

G. pe Brur: “A crystallized compound of isoprene with sulphur dioxide.” (Communicated
by Prof. P. van Rompurcn), p. 585.

J. P. van per Srox: “The treatment of frequencies of directed quantities. p. 586.

J. J. van Laar: “Some remarks on the values of the critical quantities in case of asso-
ciation.” (Communicated by Prof. H. A. Lorentz), p. 598.

J. J. van Laar: “On apparent thermodynamic discontinuities, in connection with the value
of the quantity J for infinitely large volume.” (Communicated by Prof. H. A. Lorenrz),
p- 606.

H. R. Kroyr: “Current Potentials of Electrolyte solutions.” (Communicated by Prof. Ernxsr
Couen), p. 615.

Hi. R. Kruyr: “Electric charge and*limit value of Colloids,” (Communicated by Prof Ernsy
COHEN), p. 623.

ol
Proceedings Royal Acad. Amsterdam. Vol. XVIL.

468

Physics. — “Modern electromagnets, especially for surgical and
metallurgic practice.’ By H. pu Bois. (Communication from
the Bosscua-Laboratory).

(Communicated in the meeting of May 30, 1914).

Carrying-Magnets. The lifting-power of the famous steel magnets
of Logrman and van WertrrEN, has for a long time belonged to the
somewhat antiquated subjects. However, traction-electromagnets are
now being much more used in different forms, especially for loading
and transportation purposes.

In general we may say, that for sueh magnets with armatures at
a very small distance Maxwetw’s well-known law holds; accordingly
B*/8Sa measures the carrying-power per unit cross-section of an
almost closed magnetic circuit. Prof. TayLtor Jonus has entirely
confirmed this by experiment in the Bosscua-Laboratory. The mag-
netic balance as a measuring instrument is equally based upon this
fundamental law. Electro-magnetic brakes on this principle are also
being more and more used.

Field-Magnets are of more interest for a variety of scientific and
practical purposes. In these Proceedings a description was given of
semicircular magnets’), one of which, weighing 350 kg., with an
interferrum of 3 0,5 mm. gave a uniform field of 59 Kilogauss,
while using only a few Kilowatts. With a cryomagnetic “immersion-
armature’ in a liquid gas at low temperature this reduces to 45
Kilogauss. With the heaviest type weighing four times more (1400 kg.)
we may cet. par. expect no larger increase than 10°/, , thus reaching
65 and 50 Kilogauss respectively. Until now these field values have
not been superseded, no more than the Haarlem magnets were.
For the investigation of several highly interesting problems they are
absolutely necessary.

With regard to so small a rise of the field however it requires
dne consideration whether a further increase of the size of the magnets
appears justifiable. For while the weight increases as the third power
of the limear dimension, thus becoming quite unwieldy, the field
rises logarithmically only, which means a great disadvantage. In fact
for a given field we practically obtain only a larger interferrum.
However convenient this may be, it is questionable whether it justifies
the very high expense which gradually begins to surpass an average
laboratory-budget.

1) H. pu Bors, These Proceedings 12 p. 189, 1909; 13 p. 386, 1910.

469

The results mentioned are partly due to concentration of the
Ampere-turns near the air-gap and also to careful calculation and
design of all details; the theory of polar armatures ') communicated
to the Academy, contributed its share to the result.

Intestinal magnets. Incidentically the formulae for attractory arma-
tures were also given in the paper referred to. They show, that the
attraction of saturated ferromagnetic particles is a maximum for cones
with a semi-angle of 39°14’, and for prisms of 30°; for non-
saturated ferromagnetic or for paramagnetic substances these angles
are 42°11’, and 32°8’ respectively. According to the principle of
Farapay and Kervin the attraction is determined by the gradient of
the first [second] power of the intensity 9 of the field for the first
[second] group of substances.

Some time ago Prof. Payr*) proposed a magnetic diagnosis,
prophylaxis and cure of peritoneal adhesions and similar deviations.
For this purpose a ferromagnetic intestinal filling is introduced either
per os or per rectum. Then magnetic force is applied from outside
without the necessity of more or less dangerous laparotomy. At the
request of this well-known surgeon I was glad to collaborate in the
attempt towards a practical solution of this peculiar a¢traction-problem ;
for a rational treatment of it the above-mentioned armature-theory is
absolutely necessary. The existence of an indifferent intermediate
zone and the necessity for exciting large attractive forces only beyond
this, characterizes this particular question.

The ordinary type has a core of high permeability (of 12 cm.
thickness and 40 em. length). It is somewhat concave at one end and
thus fits the average form of the human body. In the paper referred
to the formula is given for 9, 05/dr and 0?.9/dx? on the «x-axis
for the case of a segmental spherical armature and for that of a
coneave paraboloid of revolution. For the latter case it was shown
that a certain distance not before a maximum of the field was reached.
In this “neutral” point the gradient is zero and therefore the attraction
also vanishes; the latter then increases, reaches a maximum and de-
creases again gradually. This distribution of the field is favoured by
the higher magnetisation at the periphery of the core compared with
that of the centre, which makes this case similar to that of hollow
cores. In the outset I even used a core with a conical bore in
order to allow an eventual radiologic transmission through it; this
however proved later on to be practically unnecessary. A central

a) H. vu Bois, These Proceedings 15 p. 330, 1912.
*) E. Payr, Miinch. med. Wochenschr. 60 p. 2601, 1913.
31*

+70

filling of the core with a substance of higher permeability might be
made -to compensate the distribution of the field above described. -
In our case however this very topography of the field is desired ;
for it is within the peritoneum only and not in the surrounding
layer (the thickness of which individually varies from 2 em. to 10 em.
and even more) that an attraction may be usefully exerted. Towards
its other end the core gradually becomes thicker and the end is
formed by a flange in order to decrease the magnetic reluctance ;
the counter-action of this pole compared with the attraction of the
working pole is negligeable.

The coils are wound with enamelled copper wire or with oxydized
square aluminium wire the thickness of which increases by steps
from the working pole towards the other end. This principle is
well-known for galvanometers and has also found partial application
in my semicircular magnets. The increased efficiency of the “polar
windings” must necessarily cause a greater heating effect which may be
counter-acted by water circulation. ;

Until now this precaution proved unnecessary, the more so because
too cold iron may cause undesirable vasomotoric reflexes of the
patient. The front flange of the coils is conical, in order not to be
in the way of the operator’s eyes and hands; it may be provided
with a corrugated peripheric radiator. The use of alternating currents
is not advisable; but a pulsating current may be caused by periodic
short-circniting of the magnet, while a non-inductive resistance remains
switched in the circuit. The relaxation-time is a few seconds; by
exciting the polar coil only it may be diminished to a few tenths
of a second; when pulsations are often to be applied, it is advisable
to use a subdivided core.

In order to reduce the weight as much as possible the core onght
to be saturated only to */, or */,. A minimum total weight is
obtained for a dimensional ratio’) between 3 and 4; then the power
required is only little above its minimum value; it amounts at most
to 4 K.-watt, for most operations it is considerably less; and con-
sidering the short duration of an operation the energy consumed
(K.-watt-hours) is but very small. The magnet weighs about 100 ke.
and is suspended by a kind of crane above the operation table, in
such a way that its 6 degrees of freedom may be disposed of, i. e.
a displacement along the vertical and a rotation around it, and the
same for two horizontal axes parallel to the body of the patient
and normal to it. Below the patient the ROnrcEn-tube is placed, as

1) Calculated from the demagnetizing factors for short cores, as measured by
S. P. Taompson and E. W. Moss, Proc. Phys. Soc. Lond, 21, p. 622, 1909.

471

far as possible from the magnet, in order to diminish its deviating
action on the cathode rays'). In some cases the patient may be
treated while standing, which is much simpler.

Deep-seated intestines (7—20 em. under the skin) are treated
without pole-shoes. For those lying nearer the skin, the following
pole-shoes are used which may be made of a highly saturated,
polished and nickeled, substance, such as ferrocobalt.

1. A “drawing-pole” in the form of a truncated cone with a semi-
angle of 40°; the attraction is strongest in the apex of the cone.
The contents of the intestines may be first drawn towards a par-
ticular spot and then attracted towards the magnet.

2. A prismatic pole with a semi-angle of 32° for the treatment
of longer intestinal sections.

3. An unsymmetric hoof-shaped “dragging-pole” for applying force
parallel to the peritoneum. Starting from the above-mentioned principle
it may be shown that a maximum gradient of §* is reached when
the narrow pole front forms an angle « = 65°54’ = t7-1V5 with
the direction of dragging. For a very long prism on the other hand
it ought to be ¢ = 60° = tg—'!V3. In this way the best adapted shape
of the pole-shoe may be determined, also fitting the cylindric core.
For special purposes pole-shoes of various shapes may be designed.

The forces used bere have often been measured with small iron
test-spheres. The force component is

3 ‘ 0 r 04°
Iie = vi) ’

An Ou 2 Ox
v denoting the volume, 7 the radius, there being no question of
saturation. This expression is quite independent of the nature of the
substance if only this is not too weakly ferromagnetic. The force,

expressed as a multiple of the weight G of the ,test-sphere will be
greater, the smaller the density of the latter. The value f,/G—=1
corresponds to the case that at a certain distance under the magnet
the sphere is just being prevented from falling down. Considering
this, spheres were made of magnetite (/’,O, = ferroferrite = ferr.
oxyd. oxydulat. nigrum.) which quite fulfilled my expectations. Best
of all proved small spheres of 1 cm. diameter of /’,O,-powder
mixed with a little mucilage and some light neutral powder; generally

1) The Rénreen-tube is moved by the foot of the operator. The deviation of
the cathode-current is proportional to its own strength, the value of the field at
that place and the sine of the angle between these two directions; these three
quantities onght to have low values. An iron-clad Réyreey-tube might prove useful ;
but sparking constitutes rather a dilficully. In some cases a compensating coil
near the cathode rays may be arranged.

472

these were used as test-spheres. This substance which fulfils all
magnetic conditions is also to be recommended from a clinical point
of view; it is neither poisonous nor soluble; it does not rust nor
causes hydrogen to develop; it is not resorbed and hardly irritates
the mucuous membrane. It gives good R6NTGEN-contrasts, even without
addition of bismuth carbonate and it is more satisfactory than ferram
reductum pulverisatum; it is the principal ingredient of the emulsions,
which are given per os or per anum, the prescriptions of which
vary in practice. On this point and on the very satisfactory surgical
results I need hardly give full details. The following will suffice *).

The operative conditions were fulfilled and even surpassed. The
practice gained with a number of patients led towards a reliable
diagnosis of the normal or abnormal mobility of the intestines and
of adhesions and their exact place. It was often managed to stretch
and to raise them carefully either in the stage of fibrous adherence

hat of lasting mutual connexion. Of course reliable

day lave a great effect on the position of the intestines or of their

special sections; such a locomotion highly influences the peristaltic

function; this ought to be especially the case with pulsating magnetic

fields of smaller or greater frequency up to about 10 or 20 per
second and of different form of pulsation-curve.

The accelarated or retarded displacement of intestinal substance
containing ferromagnetic ingredients ; the dragging of this into organs,
which are too deeply seated to be reached in any other way, especially
the appendix, with a view to radiologic diagnosis, the turning and
loosening of intestinal slings remain subjects for further research.
The principal advantages of this method are its localisation on a
special part of the intestines, the precise regulation of the displace-
inent, the easy dosing of the effect by regulating pole distance and
current and the simultaneous radiologic examination. :

In order to determine the topography of the field for various distan-
ces and currents, it was fixed by iron filings, with or without pole-
‘oes und if necessary it was measured with a standardized test-coil.

yuicing along the axis, from the start at the concave pole front

uinimum of the field is first met, then a maximum. To these cor-
respond theoretically a transverse maximum and minimum respecti-
vely, and also an unstable and a stable zero-point of attraction. This is
easily shown with a test-sphere in an axial glass tube, which is seen
to remain suspended in that very point. With a plane pole front
such singularities do not appear.

) See also E. Payr, Ber. D. chirurg. Congress, Berlin April 1914.

473

The attraction of a number of test-spheres or pills was measured
under different circumstances with a spring-balance; its maximum
was found at a distance of 4—5 em. and amounts up to 25-fold
weight; the greatest “carrying distance” is 22 cm., for test cylinders
even more. For a round drawing-pole the maximum was found at
2 or 3 cm. and reaches 50-fold weight; at distances greater than
7 cm. the attraction becomes smaller than that observed without
the use of a pole-shoe. The coils were constructed in such a way
that their purely electrodynamie attraction, which is determined by
the square of the current, contributes considerably to the total force.
With a dragging-pole a transverse force is obtained up to 25-fold
weight at a distance of 2,5 cm.

Though for our purpose the type described proved amply sufficient,
it appears however interesting to study the properties of a similarly
enlarged or reduced instrument. If the linear dimensions be n-fold
the weight of the iron varies as n’*, that of the copper as n* (or as
n*, depending on the mode of winding), tle kilowatts consumed as
n (or respectively as n*), the attraction of non-saturated particles at
a given distance however nearly as 7‘. This 4° power (in fact
about the 3,7") is evidently very favourable, especially as compared
with the above-mentioned very uneconomical logarithmic progression
for field-magnets. We may safely predict that it will be possible to
produce any necessary force with magnets which do not yet become
unmanageable and the cost of which will hardly prove a serious
obstacle in this case, where life and health of the patients may be
at stake.

Extracting magnets. In this way it ought to be possible to move
about ferromagnetic probes brought into the body on purpose or to
extract undesirable objects, such as steel bullet shells, broken needles
or injection-syringes and various iron or nickel objects, which are
daily met with in the surgery of accidents.

Also an effect on other organs, less soft than the intestines may
be thought of. It has long been known that all tissues are diamagnetic;
Faraday already showed that this is also the case with blood; the
iron atoms in haemoglobine are bound in such a way that no para-
magnetism occurs, no more than e.g. for potassium ferrocyanide.
Picker’) showed that a magnet repels the red blood globules
relatively to the serum. It is moreover also known that the flow of
diamagnetic liquids through tubes and their dropping may be con-

1) A. PLiicker, Pogg. Ann. 73 p. 576, 1848.

A474

siderably influenced under special circumstances by very strong
fields *).

By putting 2 <4 the effect of reducing the dimensions is at once
evident; this is interesting with a view to the design of the usual
ophtalmic magnets which may also be improved by the above caleu-
lations and experiences; the maximum distance in this case is not
more than 2,5 em. A type is now being made of 8,5 em. diameter
of core, serving the double purpose of an intestinal magnet of less
strength than the above and at the same time of a very powerful
ophtalmiec electromagnet.

Ore separators have long been applied in metallurgy to separate
unmagnetic from ferromagnetic or only paramagnetic powdered ove
by the dry or the wet method. These apparatus are variously con-
structed; the principal magnetic organ is however essential and
common to them all and is a more or less finely ribbed polar arma-
inve. The best cross-section for a definite mean size of the grains
may be determined by means of the theory above-mentioned for a
prism semi-angle between 30° and 32°8’.

Mineralogy. — “On the Tin of the Island of Flores.” By Prof.
Dr. A. WicHMAnNn.

(Communicated in the meeting of June 27, 1914).

During the last decenniams very contradictory answers were given
to the question regarding the occurrence of tin-ore in the Isl and
of Flores. The fact that the solution of this question does not only
regard the interests of a mining-scientifical nature, but is likewise
very interesting from a mineralogical and geological point of view
may justify the attempt of elucidating this subject.

In ihe first place we have to bring into remembrance the fact,
that in the Sunda Islands the older geological formations gradually
disappear if we move in that range of islands in an_ easterly
direction, till — beginning from Bali — only neogenie and _pleisto-
cenic sediments are found, and at the same time tertiary and _post-
fertiary eruptive rocks with their tufas begin to play a predominant
part. The question rises then: Does Flores make an exception to
‘iis rule and do we find in this island remains of ancient granite
siocks, accompanied by deposits of tin, or are all the reports regarding
the occurrence of this ore only of a legendary nature ?

1) QO. Lresknecut and A. P. Witts, Ann. d. Phys. 1 p. 183, 1900. W. J. pp Haas
and P. Drapier, Ann, d Phys. 42 p. 677, 1915.

475

The first report originates from J. P. Freyss, who wrote on account
of his information received in 1856 in Manggarai (West Flores).
“In the mountains of Rokka at Sui Tui’) gold is found, whilst
“Mount Aspana produces tin)”.

In 1866 a resolution was taken by the Governor General L. A.
J. W. Baron Storer van ps Berrie “to send a trustworthy funetionary
“to the isle of Flores in order to investigate if on the south-coast
“of this island in the neighbourhood of the village of Rokka tin
“is found”. It is unknown whether the resolution (of January the
15 N°. 3) was ever put into execution *).

Five years afterwards J. A. vAN per Cus fixed the attention to
the fact, ‘‘that every year a rather considerable quantity of arm-
“and leg-rings made of tin and of a rude construction was exported
“from the district of Rokka, situated on the south-coast of the isle
“of Flores’ *). The Indian Government having been requested to
order the controller S$. Roos, established in the isle of Sumba, to
make an investigation whether in reality tin occurred in Flores, a
resolution was taken to this effect November the 13! 1871 N°. 3,
and the Board of Directors of the Soeiety of Industry and Agricul-
ture received a short time after from the above-mentioned functionary
“a few specimens of tin-ore from Masara’.

According to the investigation which was entrusted to C. br
GaveERE, the mineral in question was pyrites*). In the mean time
the Governor General Piwrer Mier had authorised, by resolution
of April the 18% 1872 N°. 59, the resident of Timor to send an
expert to Rokka “that he might convince bimself on the spot, in
“how far tin-ore is dug up and melted there, and at the same time
“to collect some specimens of ore and rocks” °). This investigation
had neither any result, for, as was reported, the native chief’) —
this was the expert — “had until now, on account of ill health and

1) The place is called Sui (manggaraish) or Tui (endehneish) and is situated on
the west-side of the Aiméré bay. There can be no question of the occurrence of
gold there, for behind that place rises the extinct vuleano Komba.

2) Reizen naar Mangarai en Lombok in 1854—56. Vydschr. voor Ind. Taal-,
Land- en Volkenkunde. 9. Batavia 1860, p. 507.

*) Koloniaal Verslag van 181, p. 29.

4) Tijdschr. voor Nijverheid en Landbouw in Ned. Ind. 16. Batavia 1871, p.
158-159.

5) Tydschrift voor Nijverheid en Landbouw in Ned. Ind. 17. Batavia 1572, p. 184.
21. 1877, p. 40—41.

6) As quoted 17. 1872, p. 385.

7) He proved afterwards to be an Arab who had settled in Sumba. (Koloniaal
Verslag van 1591, p. 22).

476

“the unfavourable disposition of the population of the island, not
“vet fulfilled the order given to him. ’)

A short time after 5. Roos communicated the following inform-
ation concerning tin. “The people of Rokka often sell on the shore
“bracelets made of tin, but they do not allow anybody to visit
“their village... The Endehnese admit as rather certain that much
“tin-ore oceurs in the ground of Rokka, but for fear of being mur-
“dered they dare not venture into this village; this was likewise
“the reason why nobody, even for ample payment, would accom-
“pany me thither, so that I had to desist from the journey: It is
“however known to me that proas of Endeh and likewise Chinese
“of Kupang and persons of other places from time to time come
“there to trade with the natives i.e. they anchor at Wai Wau or
“at Aimeré and carry on their trade on the shore with the people
“of Mangarai and with the inhabitants of the mountains, the latter
“offering for sale a trifle e.g. a parang or a pair of bracelets made
“of tin to the merchants. The bracelets are heavy, of rude work-
“manship, more than a hand broad and are worn above the elbow.” ?)
According to J. G. F. Riepen the tin is collected in Liu and Langgi
(read Langga) by the natives ‘fin a mysterious manner.” *)

Hitherto there had only been question of the supposed occurrence
of tin in the district of Rokka, but in 1877 F. C. Hnynen wrote :
“according to reliable reperts a considerable quantity of tin is found
“in the territory of the Rajah of Larantuka, somewhere in Flores...
“the tin objects resembling silver gave lately to a traveller whom
“we met in Flores, the conviction, that the tin there is of an excel-
“lent quality.” *)

A request made by L. P. pen Dekknr d.d. Kupang July 1s* 1882,
but not granted, to obtain the permission of prospecting in Flores,
tbe Solor and the Alor Islands fixed again the attention of Govern-
went to the tin. The mandate of trying to obtain, if possible, some

1) Verslag omtrent het Miynwezen in Ned. Indié voor het jaar 1872. Jaarboek
van het Minw. in Ned. Indié. Amsterdam 1873. I, p. 327. — Koloniaal Verslag
over 1873, p. 260. — Two years afterwards it was reported however that, on
account of the distrust of the population, it could not be ascertained whether the
territory of Rokka was really rich in tin. (Koloniaal Verslag van 1875, p. 26).

*) lets over Endeh. Tijdschr. voor Ind. T. L. en Vk. 24. Batavia 1877, p. 515.

8) The island cf Flores or Pulau Bunga [sic.!]. Revue coloniale internationale 1.
Amsterdam 1886, p. 66.

4) Het ryk van Larantoeka op het eiland Flores. Studién op Godsdienstig,
Wetenschappelik en Letterkundig Gebied. 8, No. 6. ’s Hertogenbosch 1876, p.34—35.
A. JAcoBSEN described tin bracelets of East Flores (Reise in die Inselwelt des
Banda-Meeres. Berlin 1896, p. 606—61).

477

of the tin objects originating from Rokka, given to the resident of
Timor and to the magistrate of Larantuka was complied with. *)

From the investigation made by H. Crermr it appeared that a
tin bracelet contained lead, whilst a specimen of tin-ore was very
ferruginous. *)

The examination of some bullets led further to the result that they
were not composed of tin, but chiefly of lead and zine with traces
of tin, copper and iron. Should the “strongly ferruginous” ore be
identical with the specimen “stroomtinerts van Oost-Flores”, mentioned
in the catalogue of the Mineralogical Collection of the Office of the
Department of Mines at Batavia under N°. 3302 and really contain
tin, then it is certainly not originating from this territory, where in
several places titaniferous iron-ore but no tin is found.

In consequence of the resolution of the Governor General O. van Rens
of August the 5 1887 N°. + the resident of Timor was authorised
to order the magistrate E. F. Kurran to go to the district of
Rokka, situated on the south-coast of this island, in order to obtain
reliable evidence about the occurrence of grounds containing tin-ore
in the interior of the isle of Flores.*) Kieran had supposed that he
would reach his aim by choosing as place of issue the village of
Nanga Lian in the district of Toa *) situated on the north-coast, where
he landed the 12 of September. The 17 he marched to Nbai *)
(about 8°34’ S., 121°10’ E.), he was however decidedly refused to
go further to Soa and Poma, the supposed finding-places of the
tin-ore. An inhabitant of the mountain of the village of Dora told,
that at a few days’ walk distance in a place called Watam Kadjan,
situated between Poma and Soa, specimens of native tin were collected
in the ravines, when the rainy season was over, to make bracelets
and other ornaments. After having returned to the coast on the
19% he continued his journey as far as Rium on the 20. The
Rajah here, however, did not know anything about tin, nor was he
inclined to procure an interpreter or a guide for the journey to the
interior. Without having attained his end Kian returned home again
to Kupang.

1) Verslag van het Mijnwezen in Ned.-Indié over het jaar 1882—83. Jaarboek
van het Minwezen in Ned.-Ind. 12. 1884. Techn. en administr, ged, p. 376, 304.

2) Bydragen uit het scheikundig laboratorium van het hoofdbureau van het Mijn-
wezen. Jaarboek van het Mijnw. 13. 1884. Wetensch. ged., p. 312.

3) Koloniaal Verslag van 1891, p. 23.

4) He had already paid a visit to this district in 1875. (en voetreis over het
oostelijk deel van Flores. Tijdschr. v. Ind. T. L. en Vk. 34. 1891, p. 530—582.

5) Embai according to J. W. SroursEspuK..

478

When in 1888 two applications for concession were made, one
by A. Laneen, who had received from a Chinese a specimen of granite
and likewise a specimen of tin-ore, said to be originating from “the
river Aspana’, and a second by R. van pen Brorx') with 4 others,
who requested to be allowed to explore 100000 bouws (!), the
Governor General C. Prnakker Horpisk resolved to have an investigation
made by an expert into the supposed abundance of tin-ore in Flores.
By resolution of the 20 Sept. 1889 n°. 18 the mining-engineer of the
Department of Mines C. J. van ScHEt.u was appointed leader of
the expedition. Tie expedition left Batavia on the 15 Nov., and
arrived the 30% next at Kupang. After the resident of Timor had
ordered the magistrate E. F. Kieran to accompany the expedition, they
left on the 3°¢ Dee. for Larantuka and afterwards to Endeh, where
the assistant magistrate F. A. Broeman joined them. On the 10" they
disembarked at Soa, situated on the westside of the Aiméré Bay, and
a reconnoitring-expedition was undertaken in a north-eastern direction
as far as the village of Foan, where however none of the inhabitants
could be prevailed upon to accompany the expedition to Langga,
“which village is said to be situated in the neighbourhood of the
“tin-region”’.

After their return. on the 11 December they went into bivouae
which they left again on the 15%. After a 1O hours’ march in a
north-eastern direction the mountain-ridge of Watu Loko was reached
in the neighbourhood of Ekofeto. The next morning, a short time
before their departure, they had to sustain an assault in which
Van Scnette and Kieran were wounded by sword-thrusts. In a
forced march the expedition drew back to the Aiméré Bay, which
they left in the afternoon of the 17 to sail back to Kupang °).

Krom the information he had obtained Van ScueLLE came to the
couelusion “Ist that none of the Endehnese, who had visited the
“eoast-region of Rokka and the neighbouring Mangarai knew anything
“of an importation of tin under any form whatsever. 2°¢ that the
“mountaineers of these regions with whom they came into contact
“possess tin ornaments, and use likewise tin to make their fishing-

1) This gentleman undertook in 1889 a scientifie journey by order of the Kon.
Nederl. Aardrijkskundig Genootschap Tie results obtained have however never
been published.

2) Koloniaal Verslag van 1890, page 21. — Verslag van het Mijnwezen over het
4e kwartaal 1889, p. 11. — J. CG. van Scusie. Verslag van het onderzoek
paar het voorkomen van tinertshoudende gronden op Flores. Extra-Byvoegsel der
Javasche Courant. Batavia 1890, No. 10. — Tijdschr. voor Nederlandsch-Indié
1890. 2, p. 77 —79. — Tu. Posewrrz. Die niederliindisch-indische Zinnerzexpedition
auf Flores. Das Ausland 64. Stuttgart 1891, p. 145—149.

479

“nets heavier; 3° that tin has little value for them and iron and
“copper is valued higher by them; 4% that constantly as finding-
“place of tin a special spot is indicated, situated northward from
“Mount Roukka, and the natives possess there considerable quantities
“of tin’ '). Further lhe asserted “that the idea formerly occasionally
“suggested, that the tin that the people of Rokka possess, should
“be imported or proceed from solder of petroleum- or other tins
‘must be rejected as utterly unfounded”.

The summary of his considerations was: ‘ As far as the information
“I obtained reaches, | must admit that the soil to the north of the
“Mountain of Rokka is very rich in tin-ore...... Along a fissure
“running probably from East to West along the South-coast of
“Flores, the volcanic products have found a way and partly covered
“the other formations. The region containing tin-ore is situated at
“the frontier of the two formations, and we must admit, that the
“older formation there is strongly impregnated with tin-ore, and that
“by the desaggregation this comes free at the surface’.

The favourable expectations raised by VAN ScHELLE’s report
induced the Indian Government to send out a second expedition this
time however supported by a strong military power. (Resolution
of the 31st March 1890) ’).

On the 11 May 1890 a detachment departed from Surabaya and
arrived on the 14 in the Aimeére Bay, where on the left bank of
the Wai Moké (Aiméré River) a bivouae was pitched. On the 8" July
the well-known Watu Loko was occupied. On the 24% and 25 under
protection of a strong patrol C. J. van Scretie made from this
place in an eastern and north-eastern direction reconnoitring excursions
to the supposed tin-region. Instead of grounds containing ore he
found however crater-mountains, of which Kopo Lebo and Lebi Sega
were ascended. On the 29! the patrol reached the top of Wolo
Meré, 1650 feet high, and discovered that, as far as could be seen,
it was of a voleanic nature.

Atter this complete failure a last effort was ventured to reach
the ‘“tin-region” from the district of Toa situated on the north-coast,
where E. F. Krein had taken information in 1887. By resolution
of 10% Sept. 1890, N°. 1 it was stipulated that vAN ScHELLE and

1) In reality more than a dozen places were mentioned.

2) Koloniaal Verslag van 1870, page 22., 1891, p. 2329. — Verslag van het
Mijnwezen over het 2de kwartaal 1890, p. 16; dde kw. 1899, p. 12. — P. G.
ScumipHAmEer. De expeditie naar Zuid-Flores. Indisch Militair Tijdschrift. 24.
Batavia—'s Gravenhage 1893, p. 101—115 %7—218, 289-307, 315—404,
493—504, 25. 1894, p. 1—11.

(tT to
Wolorsfok /
(o>

PE INGASS

his companions were to leave the south-coast, to repair to the
district mentioned above. In the mean time a division had arrived
there on the 26" September, that transported their head-quarters to
Nbai on the 27" October. When van Scue.Le had been obliged to
leave the spot on account of ill-health, he was replaced by the
overseer A. F. H. Heusch and along the river Koli they marched
into the interior towards Mundé, but on this expedition likewise
only voleanic formations were found.*) Inereasing cases of illness
rendered a longer residence impossible, so that on the 23'¢ of November
Nbai and on the 2°* of December Remang had to be evacuated. *)

In the mean time information about the oceurrence of tin was
gathered from other sides. J. W. Merersure on his march across
Manggarai in 1890 did not see anywhere an object made of tin;
only at Nanga Mborong he obtained a tin bracelet, which was said
to originate from Anduwa to the W. of Wai Moké, where, as was
said, the tin-ore was to be found. *) In the beginning of 1891 the
controller J. F. Horpr was sent to the North-coast of Flores, in

1) According to P. G. ScHMIDHAMER Poré was the real finding-place of the tin
(p. 404) and not Poma, Mundé and Soa (p. 500).

*) Koloniaal Verslag van 1891, p. 26—29. — J. W. SroursEspiuK. Een mede-
deeling over het eiland Flores. Tijdschr. K. Nederl. Aardr. Gen. (2) 8. 1891, p.
748—749, map N°. IV.

5) Dagboek van den controleur van Bima, J. W. MEERBURG, gehouden gedurende
zijne reis door het binnenland van Manggarai. Tijdschr. y. Ind. T. L. en Vk. 36.
Batavia 1893, p. 143, 148.

48]

consequence of a report of ALBerT CoLrs') according to which the
inhabitants of Potta bring tin to market. That information was not
confirmed by him, on the contrary he was told that in the district
of Dua to the South of Potta, tin, gold and even diamonds occurred.’)

The last investigation took place in the end during the years 1910
and 1911 by J. J. Pannexork van Ruepen. In the second of his
papers *) mentioned at the foot he says with regard to the occurrence
of tin: ‘According to the reports of WichMann and VAN SCHELLE
“there was sufficient foundation for the supposition that the tin that
“was used by the population of Central Ngada was originating
“from ore found in the district itself. *) As the presumable finding-
“place the region to the North of voleano Inié Rié is indicated. On
“the occasion of the expedition in North Ngada in 1890 a slight
“quantity of fine cassiterite was collected near Torang. The investi-
“gation L was charged with about the occurrence of tin-ore in these
“regions could not yet be brought to an end on account of the un-
“favourable political situation.” *)

After the above historical explanation we shall now try to answer
the question whether there is sufficient ground to admit that tin
occurs in Flores. C.J. van Scuenie had answered the question affirm-
atively and supported his answer by the 3 following hypotheses.
1st. nothing is known about the importation of tin objects, 2°¢ the

}) CoLFs made a journey through Manggarai in 1880. In the description of his
journey not a single word is said about the above communication (Het Journaal
van ALBERT Cours. Batavia 1888, p. 71—72).

®) Verslag van de reis van den Controleur Horpt naar de noordkust van West-
Flores. Tydschr. voor Ind. T. L. en Vk. 36. 1893, p. 281, 292.

8) Eenige geologische gegevens omtrent het eiland Flores. Jaarbock van het
Mijnwezen in Ned. Ind. 39. 1910. Batavia 1912. Verhandel. p. 132—138, pl. X.
— Overzicht van de geographisclie en geologische gegevens verkregen bij de
Minbouwkundig-geologische verkenning van het eiland Flores in 1910 en 1911.
Jaarboek van het Mynwezen 40. 1911. Batavia 1913. Verhdlg., p. 208—226.

4) This remark is, in so far as regards myself, entirely invented. The only
thing ever wrilten by me about this subject runs as follows: “Ebenso schleier-
“haft (namely, as the origin of the Muti Tanah) ist die Herkunft des Zinns, dem
“eine gleiche Entstehung zugeschrieben wird. Es bedarf keiner eingehenden Ausein-
“andersetzung, um darzuthun, dass Zinnerz durch brennendes Gras nicht reducirt
“werden kann. Man hat auch noch niemals die geringste Spur von Zinnerz auf
“Blores gefunden. Die uns zu Gesicht gekommenen Gegenstiinde aus Zinn hat
“WEBER beschrieben. Sie sind siimmtlich bleihaltig.”” (Tydschr. K. Nederl. Aarde.
Genootsch. (2) 8. 1891, p. 2830—231). It is exactly the same with P. G. Scumip-
HAMER’s remark concerning the information of the... professors WICHMANN
and Max Weper’, (J. c. p. 106).

5) ]. ¢., p. 226.

482

mountaineers possess tin ornaments, and 3°¢ tin has little value for
them and iron and copper is valued much higher by them. Though
in general the correctness of these hypotheses will be readily acknow-
ledged, we cannot help remarking that they do not prove anything,
for in the possession of the Rokkanese objects of another nature
are found, the origin-of whieh is as littlke known, whilst they can
by no possibility be constructed by them. Among these are e.g. the
lens-shaped pieces of brass, ealled by the Endehnese “mas di Rokka”
(gold of Rokka), and the dirty-red beads known in the Timor Ar-
chipelago by the name of Muti Tanah or Muti Salah. These are
made of artfully manufactured glass and certainly not originating from
the Malay Archipelago’), but of these the same story is told as of
the tin, ie. that they appear on the surface when the grass is burnt.’) -

With regard to the “mas di Rokka” A. feunzer indicated already
that it is an alioy of tin and copper.*) When I was in 1888 at
Mbawa the mountaineers asked me a gold-piece “with the leaping
horse’ (£ 1) for it. This “gold of Rokka’ can no more be originating
from Flores, for a nation that stands so low, is not able to manu-
facture such an alloy.’) With respeet to the so-called tin objects the
same can be asserted. As early as 1884 it was known, that they
consist in reality of an alloy of tin and lead, a fact which has not
been taken into account, in the first place C. J. vAN ScHELLE did
not do so, not even afierwards, when a piece of “tin” obtained
during the campaign of 1890 appeared to consist of 59,8°/, tin and
40,2°/, lead. *®} Max Weper brought likewise into relief, that the
bracelets bought by him in 1858 were composed of these two
metals.") The fact communicated by him that the natives of East

1) This subject was treated very elaborately by G. P. Rourramr (“Waar
kwamen de raadselachtige moetisalah’s (aggrikralen) in de Timor-groep oorspron-
kelijk vandaan ?”’ Bijdr. v. de T. L. en Vk. (6) 6. ’s Gravenhage 1899, p. 409—
675).

2) J. E. Teysmann. Verslag eener botanische reis van Timor... Natuurk. Tyd-
schrift van Ned. Ind. 34. Batavia 1874, p. 350. — S. Roos. lets over Endeh.
Tijdschr. voor Ind. T. L, en Vk. 24. 1877, p. 501.

») Mineralogisches aus dem Ost Indischen Archipel. Tschermaks Mineralog. Mittheilg ,
Wien 1877, p. 3U6.

') With regard to copper, it is quile certain that at least since the middle of
the 18th century it was imported into Flores, (J. C. M. RapemaAcHER. “Korte be-
schrijving van het eiland Celebes en de cilanden Flores, Sumbawa, Lombok en
Bali.” Verhandel. Batav. Genootsch. vy. K. en W. 4. Batavia 1786, p. 252.)

5) Koloniaal Verslag van 1891, p. 26.

6) “Mededeelinger over zijne reizen in Indié.”’ Tijdsch. K. Nederl. Aardr. Gen.
(2) 7%. 1890, p. 457. — Ethnographische Notizen tiber Flores und (elebes. Intern.
Archiy. f. Ethnographie, Suppl. 3. Leiden 1890, p. 15, 16.

483

Flores opened tins in order to work the solder into bracelets ete,
made VAN ScsELLE remark that such an idea, with regard to the
Rokkas, “must be rejected as utterly untenable’. Weber on the con-
trary had positively asserted that this origin of the tin objects of
the province of Rokka was unacceptable. The fact that among the
constituents of the bracelets in question lead occurs, the import of
which was in former times as little known as that of tin, would
lead to the conclusion that this metal must likewise be originating
from Flores itself.

Leaving out of consideration the fact that lead-ore occurs only
sporadically *), nobody will certainly suspect the natives of under-
standing the art of reducing the metal from it.

A boy of fourteen years who was taken prisoner in 1890 with
the object of being able to interrogate him, rightly remarked “he
“could not possibly give any information concerning the tin; the tin
“that is in their possession, they have as pusaka from their ancestors’. *)
If one should object that objects regarded as pusaka are as a rule
higher valued, we may point out that for several years, the gold
that is brought by Australian horse-dealers in the shape of sovereigns
to Sumba, from where it has found its way to Flores is more to the
taste of the natives. During the bad harvests which are by no means
rare, they are moreover compelled to part with objects that are
dear to them, in order to obtain food.

Consequently we come to the conclusion that the metallic objeets
in the Rokka territory are not originating from the island itself, but
that they were imported in former times. Their origin is as unknown
as that of the different metallic objects found with the natives of
other islands.

The last question that must be answered is, whether the geolo-
gical condition of the island is of such a nature, that there is any
prospect of being able to detect tin-ore — in whatever form it
may be. The following summary may serve for this purpose. In
Western Flores, the eastern frontier of which is situated between

1) Galena was found by J. J. PANNEKOEK VAN RHEDEN in small quantities in
the neighbourhood of Lowo Sipi (Endeh) and in the penimsula of Batu Asa
(Manggarai). J. P. FReyss supposed that the same mineral occurs near Rium and
near Geliting on the north-coast, which is very unlikely. R. EverwisN mentioned
lead from Mount “Himendiri in Western-Timor” (Jaarboek van het Mijnw. 1872.
I, p. 261). The mountain is really called “Ilimandiri” and situated in Eastern
Flores. The piece mentioned is an augite-andesite containing hematite, lead however
is not present at all.

2) Java-Bode, Tuesday 8 July 1890, N°. 154.

wo
Ww

Proceedings Royal Acad. Amsterdam. Vol. XVII.

484

120°53' E. on the north- and 120°47' E. on the south-coast, an
orographical difference presents itself already between the northern
and the southern part. Here very accidented grounds, steep moun-
tains 2646 m. high, and deep valleys and ravines, yonder a more
hilly region in which only few mountains reach a height of 1000 m.
and more. This northern part is chiefly covered by a formation, to
which J. J. Pannekork vAN Rugpen has given the name of Reo
formation, and which consists of limestones — especially coral lime-
stone — resting occasionally on eruptive rocks and sometimes
enclosing volcanic products. Here and there they are covered with
tuffas'). PANNEKOEK writes regarding the organic remains that are
found: “A cursory investigation stated the presence of: Orbitoids,
“Corals, fragments of Spatangus, Natiea, Corithium, Conus, Lima (Pla-
“ojiostoma), Ctenostreon, Gervillia, Isocardia, Teredina’. A curious
mixture indeed. It is to be hoped that this “cursory” examination
may soon be followed by a more correct one. From the remark
that the strata of the isle of Rindja, “seem to be younger, most
“likely tertiary” we must deduce that he supposes the sediments
of the Reo formation to be of a mesozoic age, which however cannot
be the case. H. Zor.ineer has already drawn the attention to the
similarity of these strata with regard to their petrographic character
with those of the south-coast of Java (Besuki, Kediri)*). They have
entirely the character of neogenic rocks, as appears already from
the occurrence of Globigerina limestones *). PAaNNekorK however
rightly makes distinction between these and the younger pleistocenic
coral limestones, as they are found in the isle of Longos in the
neighbourhood of Reo. On the bay of Reo they rest on andesite
conglomerate. *) A continuation of the Reo formation is most likely
still found as far as the Kolitang Bay (Soho Kolitang) 120°77' E.
J. F. Horpr found eastward from the exteusive plain a low range

1) Overzicht van de geographische en geologische gegevens verkregen bij de
Mynbouwkundig-geologische verkenning van het eiland Flores. Jaarboek van het
Minwezen in Ned. Indié. 40. 1911. Batavia 1913. Verhandel. p. 217—218.

®) Verslag van eene reis naar Bima en Sumbawa .. . . Verhandel. Batay. Gen.
y. K. en W. 27. Batavia 1850, p. 14. Remarkable is his annotation accord-
ing to which at Badjo (meant is perhaps Padja) a day’s journey behind Bari
a hot spring is found, forming a pond, on which a brownish mass floats, which
hardens in the air and can be used for tarring proas.

8) J. W. Reraers describes likewise from Dangkawai 15 kilom. S. W. from
Reo, a limestone containing foraminifera. (Jaarboek van het Mijnw. 24. 1895,
Wet. ged., p. 135)

4) A. WicumaNN. Bericht tiber eine .. . . Reise nach dem Indischen Archipel.
Tijdschr. K. Nederl. Aardr. Gen. (2) 8. 1891. p. 194.

485

of hills consisting of limestone, and in the plain itself a few isolated
hills of limestone °*).

Up to the present moment only younger tertiary and post-tertiary
eruptive rocks were found in the entire southern half of Western
Flores. In the utmost south-western part i.e. in the Madura Bay the
Siboga Expedition collected in 1899 rocks that on more exact examin-
ation proved to be augite-andesite. According to D. F. van Braam
Morris Mount Sosa 1212 m. bigh farther westward 8°46’ S, 129°58’ E.
must be a still active voleano’). By the voleano called by him
Toda (5000 ft.) will most likely be meant Potjo Wai L740 m. high,
the highest mountain of the province of Todo. Potjo Leo 2696 m.
high was already called a voleano by J. P. Freyss *) and is still
active according to Braam Morris. J. W. MergrsurG, who marched
along its slopes in 1890, does not remark anything in this regard *)
Potjo Lika (2212 m.) situated in the immediate neighbourhood to
W.N.W. is, according to PANNekork’s map, voleanic, and the same
can most likely be said of Potjo Rea (2006 m.) and Mata Wae (2077 m.)
rising at a short distance. J. W. Reremrs has microscopically examined
the rocks collected in this region by J. W. Mewreure.*) He mentions
pyroxene-andesite from the Wai Renu near Dége, quartz-augite-andesite
of the same place, quartz-hyperstene-andesite and hornblende-hy per-
sthene-andesite from the Wai Leédé near Rute at the N.E. foot of
Potjo Lika, hornblende-hypersthene-andesite from the Wai Soki,
between Lidi and Todo, pyroxene-andesite from the Wai Madjo near
Todo, hornblende-pyroxene and hornblende-hypersthene-andesite from
the Wai Mau, a tributary of the Mése, 9,4 kilom. N. from Nanga
Ramo. Toren Island 780 m. high (8°54’ §., 120°15,4’ E.) °) situated
to the south of this place is most likely also of volcanic origin.

According to PaNNEkork’s map the whole region situated between
Nango Ramo and the Aimeéré Bay, the frontier of Western Flores
is of a voleanie nature. It is wellknown, that Mount Komba (926 m.)

1) Verslag van de reis van den controleur Honpr naar de Noordkust van West«
Flores, Tijdschr. v. Ind. T., L. en Vk. 36. Batavia. 1893, p. 292.

2) Nota van toelichting behoorende bij het contract gesloten met het landschap
Bima. Tijdschr. v. Ind. T. L. en Vk. 36. 1893, p. 186.

8) Reizen in Manggarai en Lombok. Tijdschr. v. Ind. T. L. en Vk. 9. Batavia
1860, pp. 506 —507.

4) Dagboek van den controleur J. W. Merrsurea, gehouden gedurende zijne reis
door het binnenland van Manggarai. Tijdschr. v. Ind. T. L. en Vk. 36. 1893, p. 290.

5) Mikroskopisch onderzoek van gesteenten uit Nederl. Oost-Indié. Jaarboek van
het Mijnwezen 24. Amsterdam 1895, Wet. ged., p. 135.

6) Also called Pulu Ramo, Nusa Sigo, Gili Enta or Embuanga.

486

and Mount Lumu (663 m.) rising on the west-side of the mentioned
bay over Sosi are extinct voleanoes.

The expedition of 1890 had communicated regarding Central
Flores that in the province of Toa, in the river-basin of the Nanga
Koli, they had marched exclusively through a volcanic territory. In
the upper-river-basin of this river, in the neighbourhood of Soa

(about 8°40’ S., 121°2’ E.) — one of the repeatedly mentioned
finding-places of tin-ore — Pannekork found at a height of = 400 m.

a territory of horizontally stratified marls with interjacent light-yellow
tufas containing impressions of leaves, molluscs, insects and fishes.
He supposed these strata to be sediments, deposited in a fresh-water-
basin and called it Soa formation '). More eastward, between Mautenda
and Dondo on the North-coast another territory is situated whieh,
according to PANNEKOEK’s map, is covered by sediments of the Reo
formation.

The southern half of Central Flores, on the contrary, contains most
of the still active voleanoes of this island. To the East of the Aiméré
Bay rises in the first place Inije Rije (Imé Rié) 2494 m. high, more
known by the name of Gunung Rokka, which is in a solfatarie
activity. Winiiam Brien saw it smoking for the first time on the
229d of August?) and Pannekork perceived on his visit in 1910
that the solfataras are situated on the east-side of the crater bottom *).
The long ridge of the Langga Mountains seems to be, according to
PANNEKORK, a Somma-edge of Mount Rokka. To the East of this
mountain rises Watu Sipi 1466 m. and another mountain 1533 m.
the name of which is unknown. Both are extinct volcanoes. In
the North-east of the Rokka a group of voleanoes is found that are
no longer active among others Kopo Lebo, Wolo Mere, about 2000 m.
high, Pipodok, Wolo Lega, Lebi Saga, which were discovered during
the military expedition of 1890 °).

Inije Lika (Inié Like) 1600 m. high, hitherto entirely unknown, was
discovered in 1910 in North Ngada and described by G. P. Rourranr °).

1) Eenige geologische gegevens omtrent het eiland Flores. Jaarboek van het

Mijnwezen 39. 1910. Batavia 1912. Verhdl., p. 135. — Overzicht van de geogra-
phische en geologische gegevens.... van het eiland Flores. Ibid. 40. 1911. Batavia

1913, p. 220—221.

2) A Voyage to the South Sea undertaken by Gommand of His Majesty. London
1792, p. 246. Dr. R. D. M. Verpeex kindly informs me that this is a mistake.
Instead of Mount Rokka has to be put Mount Keo.

3) Eenige geologische gegevens. as quoted p. 135—136.

4) P. G. SCHMIDHAMER as quoted p. 389, 390, 393 and map.

5) De Inije Lika op de hoogvlakte van Ngada. Tijdschr. K. Ned. Aardr. Gen. (2)
27. 1910, p. 1233—1239, vide likewise J. J. PANNEKOEK VAN RHEDEN, Overzicht van
de geographische en geologische gegevens. l.¢., p. 219, 223.

487

The heavy eruption, lasting only five hours, took place in 1905.
About- Ambu Rombo 2147 m, high, also called Suri Laki, better
known by the name of Gunung Keo, we do not know much more
than that it has been for more than half a century in a situation
of solfataric activity. According to PAnNnrKork') the solfataras are
especially situated in the neighbourhood of the northern edge of the
top’). As far as it is known only augite-andesite is found as
rock on the coast. Ngaru Tangi (1537 m.) rising over the S. W.
corner of the Endeh Bay is a voleanic ruin.

In the territory of the Endeh Bay the western part of its north-
coast, especially the environs of Nanga Pandan, was examined in
1910 by Jon. Exserr*). He wrote in his first communication that
Central Flores had been “durchquert” *) by him and that he had
found: gray wackes, diabase-tufas, melaphyre-breccias, quarzites, marls,
which were perhaps{ of palaeozoic age. In his work published
two years afterwards he does not mention these at all, neither are
the above-named rocks found back in it, but quite different ones
are indicated. Referring to the determinations of M. BrLowsky and
G. Rack he says, that he has found on the Wawu Manu Balu as
fundamental rock hypersthene-diorite-porphyrite, over it hornfels,
which was succeeded by tufa-rock. On the steep declivities of
Woro Weka in the valley of Oto Weka he perceived at the bottom
augite-diorite over it hornfels and further quartz-sandstone. He
surmised the existence of a contact of the plutonic rocks‘). In
GrorG Rack’s deseription of the collection gathered by Enprrr (39
specimens in all) however the name of not a single one of the
above-mentioned rocks occurs. On the contrary he describes from
the river Manu Bala dacite and andesite, from Oto Weka and
Langa Weka exclusively andesite!"). According to Ensert a gray
limestone containing numerous Globigerina’s and a few Rotalia’s
occurs near cape Ngaru Kua on the North-coast of the Endeh Bay ’).

1) J. J. PANNEKOEK VAN RuepEN. Kenige geologische gegevens. |. c., p.
136—137. — Overzicht van de geographische en geolog. gegevens... |. ¢., p. 220.

®) A. Wicumann. Bericht tiber eine... Reise nach dem Indischen Archipel.
Tijdschr. K. Nederl. Aardr. Genootsch. (2) 8. 1891, p. 231.

8) B. Hagen. Bericht tber die von Dr. ELperr gefiihrte Sundaexpedition des
Frankfurter Vereins fiir Geogr. und Stat. Petermanns Miltlg. 56. 1. 1910, p. 308.

4) A somewhat eupbemistic expression, if we consider that the direct distance
between Nanga Pandan and Geni is only about 10 km.

USGI ZO.

6) Petrographische Untersuchungen an Ergussgesteinen von Sumbawa und
Flores. N. Jahrb. f. Min. Beil. Bd. 34. 1912, p. 73—82.

ON MG (ce fon PADI

488

Also at Liana in the northern part of the province of Endeh PANNEKOEK
found a lime stone rich in Foraminifera, in which moreover fragments
of quartz, plagioclase and biotite were detected). From this it appears
that the limestone is younger than the dacite. In the valley of
Ndona, eastward from Ambugaga, I found a boulder of Globigerina-
limestone. For the rest effusive rocks with their tufas and loose
eruptive materials are prevalent in this region. The southern part
of the peninsula of Endeh is formed by Mount Ta, usually called
Gunung Api (6385 m.). The material from which it was formed is
angite-andesite. For a long time it has been in a solfatarie activity.

To the north of this mountain rises Pui or Gunung Medja only
394 m. high, which has retained a regular craterform’). In a
northern direction Mount Kengo (514 m.) and Mount Wongo (723 m.)
which Ensert regards as the two cupolas of one encircling mountain,
are connected with the peninsula of Endeh*). Most likely the
eruption of a mountain, situated behind Brai, in 1671, which P. J.
Vurn mentions*) relates to Kengo, and not as I supposed formerly
to Pui.

To the West of the Ndona valley rise Geli Bara (1731 m.) and
Geli Mutu (1494 m.), the latter of which is in a situation of solfatarie
activity °). The pyroxene- and labrador-andesites originating from this
territory were described by G. Rack’). I found in 1888 in the
valley of Ndona numerous boulders of dacite, labrador-andesite,
augite-andesite and on the deelivity of the mountain andesite. To
the east of volcano Ndona Expert still mentions Nduri, which has
a solfatara’). The island of Nusa Endeh situated in the Endeh Bay
is likewise of a volcanic origin.

In the eastern part of the island of Flores the limestone formations
have become very scarce. The little information we have about it
is limited to the hillrange in the W.N.W. of Sikka situated in the
province of Liu on which, according to H. Ten Karr, the villages
of Kiara (+ 275 m.),and Riipuang (+ 350 m.) are situated.*’) The
rock collected by him is a Globigerina limestone. In the farthest

1) Overzicht van de geogr. en geolog. gegevens |. c¢., p. 219.

2) A. WIcHMANN l.c., p. 222.

8) l.c., p. 202.

*) Het eiland Flores. Tijdschr. voor Nederl.-Indié. 1855. Il. p. 157.

®») J. J. PANNEKOEK vaN Ruepen. Eenige geolog. gegevens l.c., p. 157. —
J. Expert. Die Sunda-Expedition. II. 1912, p. 202.

6) l.c., p. 78—82.

D) lacsmpsecO2:

*) Verslag eener reis in de Timorgroep en Polynesié. Tijdschr. K. Nederl. Aardr.,
Gen. (2) 11. 1894, p. 221,

489

Northeast occurs then limestone in the vicinity of Tanjung Bunga
or Kopondai, the well-known Cape Flores, to which the island owes
its name. At a distance of 300 m. eastward from the cape men-
tioned, G. A. J. VAN DER SANDE discovered a grotto with stalactites.
And at last, according to A.J. lL. Couvrnur, coral limestone is found
to the North of Larantuka from Panté Lela to Panté Beli Beting,
especially between the village of Labao and Ili Labao.

The entire remaining part is covered with volcanic material the
monotonousness of which is only interrupted by the numerous partly
still active voleanoes. In the North westward from Maumeri rises
the voleanic ruin of Kiman Buleng (1446 m.). Gunung Dobo or
Iliang (900 m.) situated behind Geliting but nearer to the South-
coast is on the contrary still active.

Most known, though likewise not sufficiently examined, are the
voleanoes situated on the East-coast of Flores. For times immemorial
Ilimandiri (1570 m.) has not given any sign of activity. The rock
of which it is composed is chiefly augite-andesite.*) Kabalelo (1075 m.)
situated eastward is an old voleanic ruin. *) Westward from it Leworoh
is situated where on the 16% of March 1881 an explosion-crater
formed itself.*) The largest, highest and most active voleano however
in this territory is Lobetobi, consisting of two cones Lakilaki 2170 m.
high and Parampuan 2263 m. high.

G. EF. Typrman perceived about 37 km. westward from Lobetobi
a high voleanie cone; most likely Dara Woér is meant by it. *)

As appears from the above, there is in Flores no room for
praetertiary sediments and eruptive rocks. Repeatedly however the
existence of such like rocks in the form of boulders was hinted at.
Near the bay of Bari I found in 1888 quartz-porphyry, clay slate
and quartzite.°) I may now add to this the communication that in
the river Reo amphibole-granite and diabase occurs, the hornblende
of which has changed into chlorite. More eastward in the territory

1) Ken dicnstreis benoorden Larantoeka (Oost-Flores). Tydschr. K. Ned. Aardr.
Genootsch. (2) 25. 1908, p. 554.

2) A. |WicHMANN I. c., p. 159. — G. Rack. Beitriige zur Petrographie von
Flores. Ceutralbl. f. Mineral, 1913, p.p. 134—139. — H. Méutu described from
Okka, situated on the south-western extremity of Ilimandiri sanidine-trachite and
Hauyn-andesite (N. Jahrb. f. Min. 1874, p.p. 694—697). The determination however
was not correct.

3) J. P. vAN DER Stok. Uitbarstingen van vulkanen... gedurende het jaar 1881,
Nat. Tidsch. Ned.-Ind. 42. 1882, p. 241.

4) Hydrographic Results of the Siboga Expedition, Siboga Expedition 3. Leiden
1903, p. 56.

lca oo.

490

of the mouth of the Nanga Koli A. F. H. Heuscn collected in 1890
according to PANNEKOERK ') quartzite and greywakke(?). On the south-
coast at Nanga Mbawa I found granite (read quartz-diorite) and
gabbro*) and finally in the valley of the river Ndona quartz-diorite.
None of these rocks were ever found as rock, they are con-
sequently at least “auf tertidrer Lagerstatte’. They are the last
remains of rockmasses that got into the conglomerates by washing
from which they got afterwards free again.

The oldest formations of Flores belong to the effusive rocks of
the character of dacites, labrador-andesites and hornblende-andesites
with their tufas, on which those of the limestones of the Reo-form-
ation and those of the tuffas of the Soa formation follow. They
were uncovered by subsequent elevation. Afterwards the island was
over its entire length the scene of violent voleanic eruptions, from
which the only partly known crater mountains proceeded. The

material produced by them consists — as far as our knowledge
reaches — exclusively of pyroxene-andesites belonging to the Pacific

type of rocks. The younger coral limestones occurring only spora-
dically have only been formed after the formation of the volcanoes.

Von Scuenie’s postulation that the bottom “to the north of Mount
Rokka is very rich in tin-ore” appears to have been not only vain
but also very expensive.

Mathematics. — “The theory of the combination of observations
and the determination of the precision, illustrated by means of
vectors.’ By Dr. M. J. van Uven. (Communicated by Prof. W.

”
’

IC APTEYN)
(@ommunicated in the meeting of June 27, 1914).

By L. von Scurutka*) and C. Ropricuez*) a method has been given
of illustrating geometrically the theory of the combination of obser-
vations by the method of least squares, namely by means of vector
operations. RoprieurZ however chooses in the case of rigorous equations

idition another way, whilst VON ScHRUTKA, who consistently

1) Overzicht der geographische en geologische gegevens I. c. p. 229.

*) I. ce p. 229.

3) L. von ScHruTKA, Eine vektoranalytische Interpretation der Formeln der
Ausgleichungsrechnung nach der Methode der klemsten Quadrate. Archiv der
Mathematik und Physik. 3, Reihe, Bd. 21, (1913), p. 293.

4) C. Ropriauez, La compensacion de los Errores desde al punto de visto geo-
metrico. Mexico, Soc. Cient. “Antonio Alzate’’, vol. 33 (1913—1914), p. 57.

491

operates with vectors, restricts himself to two variables and one
rigorous equation of condition.

It is our purpose not only to extend their method to the case of
an arbitrary number (JV) of variables and an equally arbitrary
number (») of conditions, but also to derive the wezght of the unknown
quantities in the same way.

I. There are given N quantities wv, 7, 2,... which are to be deter-
mined from (approximate) equations of condition (equations of
observation) :

qe+tbhy +qze+...+m=0 Te epee On

These equations have the weights g; resp., and so are equivalent
to the equations

aVg-t + bY g-y + aVg.2 +... +mVg=0 C= oss
each of which has the weight unity.

We now introduce

ah aV 9 pee bY gi fe V9 me mi V Gi f
Tea es ey ie
A— miles], B= V [bz C= 2V [gras [gimi*]
AAG: —=0,|-gi0a . By BUA gue, Ci C0 Yi; (/G;. 2 0:

el Mi oi.
[| | denoting summation over 7 from 1 to n.
So the equations of observation run in the form
A;+ B+ ¢C;+...M=0 il Ieee)

We now consider A;, B;, C;,... 4; as the components of the
vectors WU, 3, €,..©, resolved parallel to the rectangular coordinate
axes of an n-dimensional space. Thus the tensors are 4, B,C... J/,
@;, (Fi, Y¥i,++- ui representing the direction cosines.

The set of m equations of observation may now be condensed in
the single vector-equation

YL SLC +...4m—0,

which expresses, that the vectors 2, %,€,...9¢ must form a closed
polygon. The coefticients a;, ;,¢;,... and the weights g; being given,
the unit vectors a,6,c,... of the vectors U,%,&,... are determi-
nate. So the vector-equation requires that 2% may be resolved in the
N directions a,6,¢,..., in other words: that lies in the V-dimen-
sional space Ry, determined by the vectors a,6,¢,... and called
the space of the variables (or unknown quantities).

In consequence of the errors of observation this condition is not ful-
filled. The most probable corrected value of M is the projection of
® on the space Ry of the variables.

492

Denoting the projecting vector by 8 (tensor A, direction cosines
x;, components A;) we have really
U+B+E C+... FM=HK.
As & is perpendicular to U, 3, 6,..., we have
Q,k)=0, (8, K=O, C6 R=, ete
or
GLa => (o: 2 10; ly7iAG] =, ete:
or because
R=A4+ B+ C4...4+ M4=qG4A4+ 8:8 +7C04+...4+ mM,
[a7] A+ [afi] B+ faiyi]C+...4+ [a Mi] =0,
[Pia] A+ [@?7] B-+ [Fix] C+...+ [FM] =,
ya] At [yi fi] B+ [yi?] C+...+ [yd] =0,

By multiplying these equations by V[giai?], V[gibi?|, V[ gic’),
. resp., We obtain the ‘normal equations” :
[gia] @ + [ocai bi] y + [gcaicz] s+... + [giaim:] = 0,
[gbiaila + [oib?*)])y + [gibi] 2 +... + [oibimi] = 0,
[giccai]a + [gcbily -+ [gie?]e +...+ [gicim:] =9,

II. After these developments which also are given by VON ScHRUTKA
and Ropricurz we proceed to determine the weights of the variables.

For this we notice that all the quantities J/; have the weight 1,
and therefore have an equal mean error ¢. From this ensues, that
the projection of 2X in any direction has the same mean error é.

We have to investigate the influence on % due to the variation
of M, if the other variables B,€,... do not undergo that influence.

A variation of % which does not displace the foot on Ay of the
projecting vector &, does not act upon any vector 4, 3, ©... So we
have only to do with a variation of the projection ®’ of Mon Ry.
In order to leave the vectors 3, &,... intact, the foot is to be moved
in a direction $§ perpendicular to 3, &,..., and, because it lies in
Ry, also perpendicular to 8.

Denoting by 6; the direction cosines of 8, we may put the equation

(4, 8) + (Mm, 8) = 0,
obtained by multiplying the equation of observation scalarly with
8, in the form
A [ajo; |] = — MU,

M, designating the projection of MN on 8.

As M, has the mean error ¢, the mean error ¢4 of A equals

493

é4 = =
[ao;|?

whence
GA = la70; \7-

The vector 8, lying in Ry, may be resolved in the directions
a,%,¢,... Denoting its components in these directions by X,Y, Z,...
we find

B= Xo Picea cee
or
6;= Xa;+- VP; 7; -+ -.-.
Now, 8 being perpendicular to &, €,..., whence | /?; 6; |=0,| y; 6; |=0,..,
we have ‘
— [o;? == xX [ai 6; |
or
1

X = ——_..
[a; 6;
From the equations

[az03|(—= (256; — 05) (7:6; |= 078:

xX 5]
which may also be written

[a*] X + [afi] Y + [aiyi] 7+ -..=

[(Piei] X + [82] Y + [ivi] 7+ --=
[ye:i]X + fifi] Y + 7) 2+--=

or
-[ai?] X? + [a; i] XY + [eiyi] XZ + .. —1=—0,
[Pia;] X? + [7] XY + [Aixi] XZ +
[vi aj] X? + [vi (7: | XY+ [yi] A Z+.t0=0,

the first unknown quantity X? takes the value
oes ae,
[a o;]? = GA
The reciprocal value of the weight of A is therefore found to be
the first unknown of the “modified normal equations”.
Putting further
X=EY[gia7], Y=Hyv[gib7], 2Z=—SV [gic], ---
the modified normal equations pass into
[giai?] §* + [giaibi] Sy + [giaics]§5+..—1=—0,
[gi b; a; | 5? + [gi bf] Sy + [gi bic) 65+..+0=0,
[gicra: |] §? + [giccdi] y+ [gie?] 66+ ..+90=—90,

494

Now, from A=xV|g;a;7] ensues
€4= &/ [gia],
hence
een eee eat ig es Ca |
les is [qia;? | Si [gi ai” | ee
which is the well-known theorem on the weights of the variables.
Example: 3 equations of observation with 2 variables.

M The unit-vectors a and 6 determine a
plan &,. The extremity J/ of —M=OM
mM is projected on this plane in the point
A M’. OM’ is resolved parallel to a and 6
: .y into the components OA=% and OB=%,
In the plane A, (4,3) the vector 8 is
M aS "erected perpendicular to 3. On this vector
A A OM—=-—M® and OA=Y have the same
Fig. i. projection OA,—= M,. This segment J/,
has the mean error €; the variable A, i.e. the segment OA there-
; €
fore has the mean error &4 = PETE

III. We now suppose that besides the n approaimate equations
of condition (equations of observation) » rigorous equations of con-
dition are given, viz.:

An pie + bn+ jy Sip Gaeta oo ge Og =D (RM con D)

For the sake of regularity in the notation, we will also provide
these equations with factors g,4; (which afterwards disappear from
the calculation). Thus we really operate with

Ant jV Int j-% + ont GV In45-Y Font gV Int y-2 feet Wnt 5 V Jn+j—0(J=1)-0)-
Agreeing, that eal now means a summation over 7 from 1 to
n+», we may, retaining the notation used above, consider 2, 3,
@,..., M as vectors in a space of m+ v dimensions.
The vector-equation
YB ie 22 Wt 0
is again not fulfilled on account of the errors of observation. The
last r component-equations (2 + 1)...(-+ ») however hold exactly
this time.
Putting again
Y4+HLC+. .+mRM=—K
the » projections An4i,.. Any, of # must be zero, whence
tn4+; = 0 (j= 1,..>).

495

So the vector ® is perpendicular to the space R, ‘of condition”
determined by the coordinate-axes 7,4; and therefore cannot generally
be any longer assumed to be perpendicular to the space Ry (2, 3,6...)
of the variables. # lies in the n-dimensional space Pn ap4j= M4;
(j=1,.v), which is parallel to the space R, “of observation” determined
by the axes a, (h=1, .. 7).

The parallel-space f', cuts the space Ry of the variables in a
linear space of NV + 2—(n-+-r) = N—»y dimensions, which we shall
denote by e'y_,. This latter is parallel to the space @y_, of inter-
section of the space /, of observation with the space Ry.

We now project the extremity of M lying in R', in this space
on the space e'y_, of intersection. The projecting vector will now
be the ‘correction-vector” §.

Translating & to the origin into the vector OP, OP wiil be per-
pendicular to the space gy—, common to Ry and R,.

Next we construct the normal space of @y—, which passes through
the origin O. This space has n—-- vy —(N—v)=n-+ 2r»—WN dimens-
ions. It contains the space &, of condition (as normal space of &,),
further the line OP, and also the normal space of n+ »— N
dimensions which can be drawn from P perpendicular to Ry.
This latter space therefore lies together with #&, in a space of
n-+2r— N dimensions and thus cuts #, in a space of (n-+r—N) +
+ » — (n+2r—N) =O dimensions, consequently in a point. As for
this point Q, it thus lies both in A, and in the normal space drawn
from P perpendicular to Ay, from which among other things
follows, that PQ makes right angles with each line of Ry, more
particularly with the vectors W,%,@,... So, projecting OP and OQ
on 4, these projections are equal. The same holds for the projections
un 2), Crook

Representing OQ by the vector St'(K', x;', K;'), we have, as St
lies in R,

Ky! = 0 and x;' = 0. (A=1,...n)
From
Get) (I) (St) i ( Da (ts i — (RO),
follows
EG [oe nee Nl = RG [estrella see (sil KG [ote Sigil 2 [see |i Ee [ee Vg] 5 «2
AS: tpi Oh tory sa. the sum [x;e;| is only to be ex-

tended from 1 to n; hence [x;@; |] = S x,¢, = [*naq}'; and since
1

z, =0 for h=1,..n, the sum [x,'@;]| is to be extended from n--1

496
v
to n+», so that [x;'a; | Sh On — [%n4j'en4j |" Here and in
1

what follows [;|' will denote a sum over h from 1 to n, and [n4; |"
a sum over 7 from 1 to ».
We may therefore write
[e@,Ky)' = [an+; K45]",
or, because
Ki — Ae Be Oe ae ee yiC +... + Mi,
[en?)'A + [enPi]'B +- Leaya]'C + .. + [andG]' = [en4jKn4j]"s
[Pren}'A + [Fr B + ([Pryi]'C + + (PM! = [2n4j Kn,
[ynceal'A + [vaFil'B+ [yO + + [vaMi]! = [vn jKn4j7':
Putting
Cn jpg Pn j=PP's Prt j= Ty's + Kny'=— Qi Mn4j—=MG, mn j= mj),
we have
fan?) A = enh Be lanyniGeonen [en Ma] fe [a;'Q;]" == (I)
[PrenJA + [2VVB + [Prvi]'C + -. + [PaMal + [7;'Q;]"=0,
Lyneny'A + [ynPalB+ [yO +... + LyaMal' + [77 Q)"=09,
Introducing
aj V [gi a?) PV [9 627]
S77 a ae = er a
V Inj , V oni
i'V [oie]
V Int)
we obtain, after multiplying successively by Vigia;*], V(gib.7),
Vigier), =
Lonan?)'@ +- Lonanba]'y + [onanen]'e + -- + Cgnanmal! + [ay'g;]" = 0,
Lonbranl'e + Landa? ly + Lonbrenl’e +--+ [gabama]' + [b;'q;]" = 0,
Lonenan)'e + Loneabay'y + L[gncn*}'2 ++. + [gncnmal' + [e;'q/]" = 0,

’

Qj = On 5 =

Ul
Cj = 4 yj =

19 9 = QV Ont;

N equations, which together with the » conditions

aja + by + c'z2+.. + mj =0
serve to determine the N variables «, y,2z,... and the » auxiliary
quantities g;.

IV. In order to determine the weights of z,y,z,..., i.e. of
A, B,C,..., we must examine the influence undergone by % from
a variation of MN, the vectors 3, &,.. remaining unaltered.

A variation of ® only acts upon %, 3, €,.. when the foot of & on
the space 9'y_, of intersection moves. If the foot is fixed, #* may freely

move in the space S, common to the normal space of @!y_, (of n+ 2»
—N dimensions) and the space 7’; parallel to 2. The space S obviously
has (n--2r—N ) + n —(n-+v) =n + v— N dimensions. A component
of M in this space has no effect on the vectors U%, 3, ,... A com-
ponent of M® will only have any effect on 2, B,&,..., when it lies
in the normal space S’w of SS, which has n + »— (n4+-r—N)= N
dimensions. By translating this normal space S'y to O, it contains
both R, and oy_, (intersection of Ry and R,).

The variation of ® will exclusively influence %, when the com-
ponent of M undergoing this variation is perpendicular to B,€,...

These considerations lead to the result that we want that direction
8, which lies in S’y and is perpendicular to %,@,... The vectors
¥, ©... determine together a space of N—-1 dimensions. The vector
8 must lie in the normal space (of mn -- »— N+ 1 dimensions) of
the space (8, &,...). This normal space cuts S’y in a space of
(n+ v— N+ 1)+ N—(n+ vr) =—1 dimension, hence ina straight
line. So there is always one and only one line 8 fulfilling the

imposed conditions.
Since 8 lies in S’y, i.e. in the space joining R, with oy_., the
projection t of 8 on 2, will fall into ev_,.
Now we have for the direction cosines 1; of the projection f of
gon R,:
On

h= Sere aae

V [on]

As t, being a line of ey_,, also lies in the space Ay and therefore
may be resolved in the directions %, %, &,..., we have

(SS he OME (paar)

ty, = Po, + Q2, + Ryn +. (= 1,---n)
ie QP Ryn 0. (7 = 1,..0)
Putting

PVG OY fora) 0 *s, = Ay for-|- = hi. .<.
we obtain :
wP' + fQ+yR +... =i (ie, an)
nt jP! + Pn4jQ + yn Rh +... = 0, Gi lb)
and, 8 being perpendicular to %, &....,
27Ga| == 0%, Ree]| == enc (ops) Stk
In this way we have collected n +» + N equations to determine
the n+» unknown quantities o, and the NV unknown quantities
Eko OE i pers Ve
S’y being perpendicular to &, $ is also perpendicular to ®. By
multiplying the equation

498

Y1 $416 +4..4M=—=K
sealarly by 8, it reduces to
(a, 8) + (M, 8) =0
or
A [ajo;] = —

In order to determine the mean error of J/,, we remark that of
all the lines through O in Ry t is that which makes the smallest
angle with 8. The error of J/, therefore depends for the most part
on the error in the components JZ, of M in the direction t. We
may consequently write

m. e. of M, =m. e. of Mi X cos (8, t) = € cos (8, f)

we arrive at
aX | PY 3 yiZ es. = Ph (AS i1,...0)
@tn = ;X + Pn+j¥ + yntjZ+--=0 (ji 15 =-P)
lapl=1 , (Cal=0 .\ irpl— 0.
From these 2 -—+ » + V equations we ean solve the 2+» unknown
quantities p; @—=1...2-+ yr) and the NV auxiliary quantities X, Y,Z....

Il
The quantity —-—J|p,°}' in question is also found as follows
GA

499

1 ‘ . ;
= =p?) =[pilenX+(21V +724...) =X [preeny+¥ [pr Pn\+Z[piyil'+--

= X— NX [pnp jang yl" — VY (pot yiFr45)" — Z [patra]!
= X— [png lang jg X + Bn V + ny Z +o)!

=X
Returning to the original variables x,y,2,..., we derive from
A
Ss ——
Vigia*]
tirstly
&A4
& = ———
V [aai"|
and
ee Vall
qa eee loner |e
Further, putting
V laa; | Vi[gai*]
Li ky Saas oe Pr+j = Ken-tj Se
Von V Inj

X= § iovas* |; Ye) [loons ZAG Chall stelle =

the n +--+ NV equations pass into

L F ky
age ibpap S cyS 2... = =, (6 == Ne oe nia) =
ah
Ont76 + Open tentgs +... = 01, Gly een)
fark] = 1, [br k; | = 0, [feathered == O ener,

whence

Example: 2 equations of observation with 2 variables and 1
condition. The unit-vectors a and 6 determine a plane /?,(NV=2),
the plane of the variables. This plane euts the plane of observation
R,(m=2) in the line ev, N--»=1), which thus coincides with
the line t. The line OP is drawn in the plane &, perpendicular to
on, (0. Through the extremity J/ of the vector M a line is drawn
parallel to OP; this line euts the plane Ry of the variables in 17’.
The veetor JIM’ —//— PO is the correction-vector 8. OJ’ is resolved
in the directions a and 6 into the components OA = %and OL=,
The lengths of these lines represent the most probable values of the
variables A and ZL.

The line PQ is perpendicular to the plane ty and meets the
normal /, (line of condition), erected in O on /2,, in the point Q,
The vector OQ is ealled St’.

99
vv

Proceedings Royal Acad. Amsterdam. Vol. XVII.

Fig. 2.
erected in O perpendicular to ¥, interseets S'y in the line 8, which
therefore is perpendicular to 3 and S&. So A and J/ are projected
on § in the same point Ag.

The normal plane A As VW of g cuts t in a point 7. the distance
of which to QO amounts to J/, (with mean error ¢). The mean error
e, of A, thus has the value &; = «cos (8,t), and that of A the value

Es cos (8, t)
a cas (8,0) i: cos (8,a)

V. The errors (residuals) of M,, M,,.. Mf, are K,, K,,.. Ky resp.
The sum of their squares is [Aj?| = A®.

For the ease that no equations of condition are given, ® must be
perpendicular to /y. So S& may dispose of a space of »—NV dimen-
sions (the normal space of /?y). Hence ® has 2—N components,
all with the same mean value ¢. Consequently

K? = (n—N) X &
hence
[Ai]
S== -——.,
n—N
In case p conditions are imposed, & may dispose of the space S
of n+xr— N dimensions. Consequently ® now has n+ »— NV

components, all with a mean value ¢. In this case we have therefore

cee L LGA
ae n+ v—N-

501

Physics. — “On the measurement of very low temperatures. XXIV.
The hydrogen and helium thermometers of constant volume,
down to the freezing-point of hydrogen compared with each
other, and with the platinum-resistance thermometer. By Prof.
H. KAmMertinGH Onnes and G. Horst. Communication N°. 1444
from the Physical Laboratory at Leiden.

(Communicated in the meeting of May 30, 1914).

§ 1. Introduction. The measurements which this paper deals
with bring the investigations undertaken in Leiden for the purpose
of establishing the seale of the absolute temperatures as far down
as the freezing point of hydrogen, to a conclusion, in so far that a
direct comparison has now been made between the helium and
hydrogen scales, by measurements with a differential thermometer,
which had the object to test the corrections to the absolute seale of
temperatures below 0° C., obtained separately for the helium seale
(in XIX of this series) and the hydrogen seale (partially given in
XVIII of this series ')). For the place which the mutual control of
these corrections occupies in the more general investigation of the
measurement of low temperatures which is being carried out in
Leiden, we refer to § 6 Suppl. N°. 34a. The test could be extended
as far as the freezing point of hydrogen, after the compressibility
of hydrogen vapour had been determined by KAmERLINGH ONNEs and
pe Haas, Comm. N°. 127¢c. June 1912) *). Our comparison of the
helium seale with the hydrogen seale*) by means of the differential
thermometer to which was added a new calibration of the Leiden
standard platinum thermometer /7¢;' (formerly Pt,) shows that a
very satisfactory agreement has been attained in the temperature
determinations.

1) Compare also H. KaAMeRLINGH OnNes, CG. Braak and J, Guay, Comm.
N°, 101@. (Nov. 1907) § 1 under 40. {

*) In this Comm. a difference was discussed which existed between the tempe-
rature delermination with a hydrogen thermometer according to the resistance
thermometer Ply',-which was calibrated by means of it and the temperature deter-
mination by extrapolation of the isotherms. According to caleulations by Dr.
Kersom, suggested by SACKuR’s interesting‘ investigation, this deviation might be
connected with the theory of quanta (Gomp. Suppl. N°. 30 and N® 34a § 11).

3) The comparison of the hydrogen and helium thermometers by Travers,
Senver and Jaquerop, Phil. Trans. A 200 (1903), p. 105, has been discussed
in Gomm. N° 102, In general their results are in good agreement with our
measurements,

3o*

S02

§ 2. Apparatus. Two identical thermometers of Jena glass GUL,
such as had been formerly used by H. Kammrirmcn Onnes and C.
3RAAK, Were connected to one manometer. The arrangement was
otherwise exactly the same as that used before. The standardmeter
was divided into '/, m.m. and allowed a direct estimation of '/;, m.m.
This gave a considerable saving of time, as it made the use of the
measuring eye-piece of the cathetometer unnecessary. The amount
of gas in the capillary was measured by an auxiliary capillary of
much larger section, as described by Crapputs.

Besides the two thermometer bulbs, the cryostat contained the
platinum resistance thermometer /’;) and a large pump, which
provided for a good circulation of the liquid.

The hydrogen and the helium were purified by distillation, and
were both free from other gases.

§ 3. Calculations. The temperature for each of the thermometers
forming the differential thermometer was calculated from the formula
given in Comm. N°. 95e, but with a few alterations. The expansion
of the glass f(t) of the bulb was not calculated from the quadratic
formula given there, but taken from a graphic representation in
whieh the curve was drawn through the points experimentally deter-
mined and extrapolated by means of the expansion for a different
kind of glass as determined by Cu. Linpemann. The influence of the
different temperature function for the expansion of the glass is
about ?/,,,° at hydrogen temperatures, at all other temperatures it
is negligible. Moreover the volume was divided into three parts.
a. The bulb at the temperature ¢ of the bath. >. The capillary in
which the mean density of the gas was determined, by means of
the auxiliary capillary: the mean density is proportional to ss he

L
being the pressure in the auxiliary capillary at 0°, 4 the measured
pressure. c. The steel capillary and the volume about the point, the
temperature of which is the same as that of the room.

If we divide all the members of the above mentioned equation
by the volume of the bulb it becomes

IT i 3 Wear h, ue dvo 273
—_ |: tO hg tga Oo ayer ae a=
h + ath

l+at
273
1+ at). :

The provisional temperature, which is needed for the calculation

of the various corrections, was calculated from the resistance of Pt’.

508

i, ;
Even move this temperature with sufficient accuracy. The zero-
0

pressure for the hydrogen thermometer was H/4, = 1191 m.m.'), for
the helium thermometer //, = 1124 m.m. Circumstances unnecessary
to be mentioned here, had prevented these pressures from being made
more equal. A new set of determinations in which this will be
attended to is planned. The pressure coefficient of hydrogen at the
above mentioned pressure was taken at 0.0036625 ; for helium at
0.00386614, the value derived by KaAmertincH Onnes *) from the
isothermals at O° C. and 100° C. If we ecaleulate with the pressure
coefficient 0.0036617 deduced from the isothermals of 20° C. and 100°C,
we find, after the introduction of the necessary corrections, almost
the same temperature on the absolute scale.

§ 4. Arrangement for the resistance measurement. In order to
measure and to compare resistance thermometers two identical differ-
ential galvanometer circuits were fitted up according to KoHLRauscn’s
method. Both galvanometers can be read from one place, so that
nearly simultaneous measurements can be made. This removes all
irregularity in the temperature of the bath in the comparison of
resistance thermometers. Two moving coil differential galvanometers
from Hartmann and Bracn were used. With an additional resistance
of + 1000 2 in each of the coils these are practically aperiodic in
the measurement of resistances less than 180 2, as with all our

other thermometers. The sensitivity is sufficient to measure ——-— 2
100000

with a current of + 5 milliamperes, while the condition of propor-
tionality between deflection and current-strength is very well fulfilled.

Test-measurements have shown, that with this arrangement resist-
ances of about 100 2, such as our thermometers have at ordinary

1
temperature, can be compared to TGuGE without any difficulty. Our

1) At these pressures even at the melting point of hydrogen no attent.on need
be paid to the thermo-molecular pressure according to KNUDsreN (Comp. Suppl.
NY, 34 § 7 and a Comm. by H. KamertinGH OnneEs and 8. WEBER which is
shortly to be expected, on the determination of the temperatures which can be
obtained with liquid helium).

2) H. Kamertincu Onnes. Comm. No. 1020. The value is here increased by O0.0000001,
in consideration of the value 273.09 since assumed for Too ¢, Gomp. H. Kamertinex
Oyves und W. HL. Keesom. Die Zustandsgleichung. Math.Enz. V 10, Suppl. No, 23)
Einheilen c, and § 820.

504

experience with moving coil differential galvanometers, for this purpose
at any rate is very favourable ').

In the manner described we attained a much greater rapidity of
measurement than was possible by the method described in the
previous papers of this series, and this in its turn increases the accuracy.

We must also refer to our experience with thermometers in which
the wire was sealed to the glass (Comm. N°. 95) § 1). For tempe-
ratures above that of liquid air they are not unsuitable, although
even here they are less constant than those with a free thread.
After immersion in liquid hydrogen their resistance was found to
have increased by about one tenth of an Ohm. Each further immers-
ion in hydrogen carried with it a permanent change of resistance,
so that we replaced these thermometers by other ones with free
threads wound on porcelain tubes with a double screw thread baked
in. After a thermal treatment, consisting in several immersions in
liquid hydrogen followed by moderate heating, these became satis-
factorily constant.

§ 5. Results. In the following table the results of our researches
are found. The two first columns contain the hydrogen and helium
temperatures calculated from the formula given above. Column 3
and + contain the corrected temperatures on the absolute scale
deduced from the hydrogen and from the helium thermometer,
column 5 contains the resistance of the platinum thermometer P¢/.

The agreement is on the whole very satisfactory.

We have already mentioned that with thermometers of the kind
described an accuracy of about */,,° might be expected. Our meas-
urements show this to be the case; only in a few points larger
deviations occur. These can readily be explained by a small defect
which will be avoided when we repeat the experiments, namely that
the eryostat which had to be used was not quite symmetrically
built. When both auxiliary capillaries worked properly this was
not of much consequence. But (except fortunately in the determina-
tions most important for us viz. at the hydrogen-temperatures) the
helium capillary got out of order, so that the distribution of the
temperature of the stem of the helium thermometer had to be deduced
from the observations with the hydrogen capillary. This cireumstance
has the greatest influence at temperatures at which the methyl
chloride and the oxygen evaporated under reduced pressure, and it
is exactly there that the greatest deviations occur.

1) Compare JarGer, Zeitschr. f. Instrumentenkunde 1904.

or
S
or

TABLE I.

fee | fete sO ee 9 tHe W pyr

0 | | 135.450
fal eesrea: |); = 23.96) |) = 23706 = 23, 94 | 122.613 |
2 43.09 | 43.07 3.00 | 4g.07 | 112.278
3 qps0. | 61.40 | 61.50 61.49 | 102.280
4 79.57 79.51 79.57 79.51 | 92.422 |
5 102.72 102.69 102.70 102.69 | 79.674 |
6 113.58 | 113.55 113.56 113.55 | 73.629 |
7 | 130.46 | 130.41 130.43 130.41 64.189
8 | 182.88 | 182.81 182.82 182.79 34.180 |
9 | 186.79 186.70 136.73 186.68 | 31.904
10 | 195.24 | 195.15 195.18 195.13 26.988
11 | 204.79 | 204.69 204.71 | 204.67 | 21.491
12 212.61 212.52 212.52 | 212.50 | 17.097
13 | 216.25 | 216.15 216.16 | 216.13 15.119
14 | 252.80 | 252.68 252.66 | 252.64 | 1.924
15 | 256.23 | 256.10 256.08 256.06 | 1.601
16 | 258.56 | 258.41 258.39 258.37 1.453
17 252.80 | 252.66 1.925
1S 253.78 253.64 | 1.819
19 255.20 | 255.05 1.685
20 257.22 257.05 1.531

The readings of P/ allow a comparison with the measurements
of 1906—1907.

WW
In fig. 1 the deviations from the linear formula ¢/—= — 248 + 245 ae

0
are represented for all three calibrations, at temperatures above
—-217°C. The circles refer to the calibration of 19138, the triangles
to 1907 and the squares to 1906. For the calculation of temperatures
in this field the above formula with the deviation curve belonging
to it has been recently used in the Leiden researches,

506

Riess

The differences between the calibrations of 1913 and 1907 are
less than */,,‘¢ of a degree throughout. The fact that the differences
with the first calibration (4906) are more considerable must un-
doubtedly be attributed to the mechanical treatment of the wire:
after the first calibration the wire broke, and had to be re-wound.
It must be ascribed to chance, that the deviations are so small just
at the points of the second calibration.

§ 6. The jield of utility of the platinum resistance thermometer
at low temperatures. Resistance thermometers for other fields of tem-
peratures. The curve in fig. 1 shows at onee the peculiar behaviour
of platinum below — 200°. At this temperature a change of direction
in the line which gives the resistance

as a function of the temperature is
sharply marked. In fig. 2 the deviations

from the formula given above in the
oxygen field are once more represented
(circles) and also those for the thermo-
meters (Pt; (squares) and /, (triangles),
which were also directly compared with
the hydrogen-ihermometer by Dr. C.
DorsMan and us. It is clear from the
curves that we have to deal with a
specific peculiarity of platinum, which

Fig. 2. makes it very unsuitable to be used
as a thermometer in this field, as accurate interpolations ave im-
possible. For this reason in the field of temperatures below —200°C.,

507

a gold thermometer is preferable to a platinum one, as has already
been pointed out by Kamertincn Onnes and Chay ').

At hydrogen temperatures both platinum and gold are no longer
approximately linear. Here and at helium temperatures manganine
and constantin proved to be nearly linear and fit for resistance
thermometers. Concerning these we refer to a future comm. dealing
with resistance measurements in particular for the determination of
the specific heat of mercury at helium temperatures.

§ 7. Comparison of our thermometer Pty with other platinum
resistance thermometers. Comparing our measurements with those of
F. Hrnnina *) formulae of the form:

aN aN ;
AR = M(R—1) - N(R—1)? and e' =— M=—— (11000) — 1.
i :
were used. This was done because there were objections to a direct
determination of the temperature coefficient by measuring the resistance
of Pfr at O° C. and 100° C. which since the first calibration bad
never been brought to a temperature above the ordinary. We found

W W
—— = —
We W,
t (K.O. and H.) (Hennine) 10° A R Tel
= WR INS 0.90523 0.90449 74 0.09551

43.09 0.82895 0.82775 118 0.17225
61.50 0.75511 0.75340 alfa 0.24660
79.57 0.68233 0.67989 237 0.32011
102.72 0.58822 0.58492 330 0.41508
113.58 0.54559 0.54007 do2 0.45995
150.46 0.47389 0.46986 403 0.55014
182.88 0.25254 0.24686 548 0.75314
186.79 0.23554 0.22998 556 0.77002

These numbers give: J/ = — 0.0078758
N = — 0.0007605.
And further ¢ = — 0.30.10-°
100e’ = 0.38821

From the results it appears that our platinum thermometer, as
regards its constants, lies between the platinum thermometers N°. 1
and N°. 7 used by Henning in his investigation. This was to be
expected, as these thermometers, like ours, were obtained from
Heranus, N°. 1 and Pr being of earlier date. The difference with
the values calculated by Henninc is caused by the fact that his
caleulation was based on our calibration of 1906, which differs from
our present one and that of 1907 (Comp. § 5).

1) Comm. N°. 95, Used also by Grommenin, Comm. N°. 140u.
*) Ann, der Phys. 4te Folge Bd. 40, 1913.

508

Physics. -— “On the electrical resistance of pure metals ete. 1X.
The resistance of mercury, tin, cadmium, constantin, and
manganin down to temperatures, obtainable with liquid hydrogen
and with liquid heliwn at its boiling point.’ By Prof. H.
KAMERLINGH OnnEs and G. Horst. Comm, N°. 142a from the
physical Laboratory at Leiden. (Communicated by Prof. H.
KAMERLINGH ONNES).

(Communicated in the meeting of June 27, 1914).
§ 1. The resistance of wires of solid mercury.
Several mercury resistances were compared with the platinum

resistance thermometer /7/ of the laboratory, first in liquid oxygen,

| r Wobs. W cate, AW |

< 4.19 | supra- |
conductor |

4.19 0.0560 | 0479 | 0,421
427 | 00600 |. 0489 ° | 0.429
4.33 0.0636 | 0.496 0.43
4.37 0.0656 | 0500 | 0.434

| 14.57 0.9390 1.667" |) 70,788

| 15.78 1.069. | 4,806. |" 0787

hn Eizo 1.298 2.047 ||P o no
20.39 1563. «S| Ss 2333Ss|CSs.770 |
80.92 8.086 9.261 1.175
90.13 9.088 10.316 1,228

| 116.52 ~ | -2/000,) | * 18.337 9 4).7 seaaan

| 12281 | 12604 | 14056 | 1.962
132.72. © | 13800 ~ "|- “15490 1.390

| 141.83 | 14.855 | 16.233 | 1.278
154.22 16.354 | 17.651 1,297
165.80 | 17,806 | 18976 | 1.170
e402) | “anata en ieies 0.853
21869 | 24716 | — 25.029 | -O3I8
233,53 | 26.694 | 26:731. |. 0.037
234.16 26,800 26.800 =| 0.000

509

then at a number of other temperatures, with the differential-galvano-
meter according to Konnravscu’s method.

The result of these determinations was as shown in the table (7 =
temperature on the Ketvin scale, with Zov¢, = 273°.09)

In the third column are given the values, which would have been
obtained. if the resistance diminished linearly from the melting point
down to the absolute zero.

: seen We tk sae
Weatc. = — Wy, = —— 26.800 = 0.11445 7.
ie 234.16
ts Column + gives the deviations
w :
S ool of the real values of the resistance
us | 4 | | from those, calculated by means
os 5 , 3 1 °
| of the linear formula. These devia-
ra 4 - tions are also plotted in the figure.
| | . :
The relation between electrical
msg +— : resistance and temperature seems
to be of a very complicated
ctl | character.
aa | 3 § 2. Direct determination of the
change im resistance at the melting-
F yebeorse ih \ | point.

’ 2 1 9 Ee) 9 : é A
AE aarp Of two resistances, which were
Fig. 1. frozen without auxiliary bath, the

change in resistance in melting was determined directly. The first
consisted of a narrow capillary filled with mercury, section + 0,0015
mm’. At — 49°.88 the resistance was 25.095 2, immediately above
the melting point 115.0 2,
a eh Wa
the ratio —“ = 4.66.

Wsol

The second capillary had a section of 0.48 mm’. With this resis-
tance the ratio 4.50 was found.
As a preliminary value of the melting point — 38°.93 C. was found.*)

§ 3. Indirect determination of the change in resistance at the
melting point.

During the numerous determinations of mercury resistances in
liquid helium (Comm. N°. 133), we always measured the resistance at
ordinary temperature too. By means of the resistances of solid mercury of

1) Our measurements date of 1912. In the meantime was published the paper
of F. Henning Ann, d. Ph. (4) 43 p. 282, 1914 who finds —38°.89 C,

5LO

§ 1 and of the well-known behaviour of liquid mercury, we calculated
lig
Wsol

As in these experiments the mercury resistance was suspended in

in each case the ratio

a vacuum-vessel cooled from the outside, the freezing took place
very slowly.
We found:
23 May 1914 4.40

a0) as - 4.63
WA (OX 3s 4.41
4.54

12 Jan. 1912 4.30 wso

9.06 wys0

7? Bebrs 4.69
4.19
eed; % 4.30
14 June ,, 4.37
4.90

As probably the highest figure thus obtained comes nearest to
the true value of the ratio, we will be not far from the truth, if
we assume the number 5 for the mean ratio.

This result has also been found by Bavrruszaitis'), who obtained
4.90 as highest value in his melting-experiments.

It is remarkable, that the ratio of the change with temperature
of solid and liquid mercury is also about 5; the increase of resistance
per degree remains thus fairly constant in melting.

§ 4. Some determinations of the change in resistance with the
temperature of metals and alloys.

a. Object of the experiments. We made a series of determinations,
mainly for orientation, about the change of resistance of different metal
wires down to helium-temperatures. The purpose of those determinations
was to find a metal or an alloy, which could be used asa resistance
thermometer down to the lowest helium temperatures. The results
of these measurements are plotted in figure 2. Of special interest is
the behaviour of manganin and constantin. While with copper, tin,
iron and cadmium no further change of resistance could be established
in the region of the lowest temperatures, it appeared, that the resistance
of manganin diminished considerably and in a linear way with the
temperature, from the lowest oxygen temperatures down to the region
of the helium temperatures. So that wires of manganin might be

1) A. Barrruszastis, Cracovie Bull. Acad. Nov. 1912.

used equally well as wires of constantin (the suitability of which
was shown on a former occasion), as resistance thermometer in
this region of temperatures.

bh. Pure cadmium and pure tin. Pure cadmium (KAHLBAUM) was
east in a glass tube like mercury. From the tin (KaHLBAUM) a thin
wire was cut on the lathe.

t Resistance t : Resistance |

of tin | of SAE

| 16.5 | 271.1030 16.6 | 76.7 10-30

--183.2 | 66.2 | —183.2 209 |
—201.4 | 46.9 —201.2 | 15.7
2529 | 2.99 | —252.9 | 1.45
—258.3 | 1.18 | —258.3 | 0.58
—268.9 | 0.132 — 268.9 | 0,032

ec. Copper and iron. The eopper wire was made of commercial
electrolytic copper’). The iron was from Sweden (Kolswa II). It

1) W. MEISSNER (Verh. D. Phys. Ges. (16), 262, 1914) used much purer copper.
In his determinations the resistance at the boiling point of liquid hydrogen was
only 0.26 °/9 of the resistance at O° C.

had already been used by Dr. B. Buckman for measurements con-
cerning the influence of the magnetic field on the resistance.

| : W copper Wiron
— 183.7 34.5 3.90
— 201.7 24.7 3.05
— 253.5 10.5 2.04
— 269.5 10.0 2.00
— 272.0 10.0 2.00

The resistance approaches here to a definite limiting value, in the
same way as this has already been found for other not quite pure
metals (Comm. N°. 119).

d. Constantin and manganin. The temperature coefticient of con-
stantin which is extremely small even down to oxygen temperatures,
increases considerably in the region of the hydrogen temperatures,
so that constantin wires are suitable thermometers in this region
and especially in the region of helium temperatures.

. =
| | |

| r Weonstantin Teale. r- Teale. |
aie Aer

| 90.75 145.680

| 65.18 144.320

| 20.36 | 138,259 20.36 0.00

| 18.985 | 137.988 | 19.00 | —001

| 17.33 | 137.662 17.37 | —0.04

| 15.83 | 137.3555 15.83 0,00

| 14.32 137.050 14.30 0,02

cale ave the values calculated by means of a linear formula of
the form
t=a-+ bu

through the points at 20°36 and 15°.88. The deviation does not
amount to more than 0°.04 and shows thus the suitability of eon-
stantin wires as thermometers in the hydrogen region, where the
platinnm-thermometer would require complicated calibrations (comp.
Comm. N°. 142c).

| 4 | W manganin
| 465C| 124.20
—183.0 119.35
—201.7 117.90
—253.3 | 113.42
—258.0 | 112.91
=I G00e met O2
Sie es Ghul

e. Gold. With a view to measurements -of specific heats, which
will be published before long and to investigate the suitability of the
‘gold-thermometer in the region of oxygen- and hydrogen-temperatures,
we determined the resistance of a gold wire at a great number of
temperatures in those regions.') The result shows, that in the region
of the reduced-oxygen temperatures (mainly below — 200° C.) the
gold thermometer does not give rise to the difficulties, which make
the platinum thermometer nearly worthless in that region (Comm.
N°. 141@ § 6 and tig. 2).

| T Resistance |

of gold
1418K 0.2910
15.83 0.3037
17.30 0.3190
19,00 0.3412 |
20,35 0.3621 |
65.18 | 2.2901 |
| 72.58 | 26763 |
83.31 3.2312
87,99 3.4710
90.75 3.6110

1) Calibrations of other gold wires will be given in the paper by W. H. Kersom
and H. KAMpRLINGH ONNes on specific heats Comm, N°. 143,

514

Physics. “Further experiments with liquid helium. L. The persistence
of currents without electro-motive force in supra-conducting
circuits.’ (Continuation of J). By Prof. H. Kamerinen OnnEs.
Communication N°. 1416 from the Physical Laboratory at
Leiden.

(Communicated in the meeting of June 27, 1914).

§ 9. The preservation af an electro-hinetic momentum. All the
phenomena that were dealt with in the preceding sections (J) *)
showing the persistence of the magnetic moment of the coil,
without the acticn of an electro-motive force, agree with what was
deduced on the supposition that a enrrent flows through the coil of
the value calculated, and which diminishes according to the time-
of relaxation calculated. At the same time, it was desirable to have
a conelusive proof that the magnetic moment of the coil is really
caused by a current. We should then be able to prove conversely
by the continuation of the moment, that the time of relaxation of
the current is very long, and a value, or otherwise an upper limit
could) be given for the micro-residual-resistance of the conduetor in
which this current flows.

I got this proof in the following manner.

On either side of the place, where the ends of the windings of
the coil are sealed together and close to it, two wires b, b (see
fio. 2 and 1) were fixed which lead to a ballistic galvanometer.
Between these points of attachment the current can be cut through
under helium, by pulling up by a thread a bronze loop provided on
the inside with a knife edge at m (see figs 3 and 1. Figs 1 and 2 give

1) Disregarding the existence of threshold-values of current and field and consi-
dering that, below these, supra-conductors add up algebraically without appreciable
loss the inductional impulses which act on them in the course of time, two points
of view may be very simply contrasted in connection with the experiments so far
described on the production of currents persisting for a long lime.

The first is analogous to that taken up in Weser’s explanation of diamagnetism.
In this case we deal with supra-conducting circuits which are currentless outside
the magnetic field. By bringing these into a field currents may be oblained which
persist as long as the field remains unchanged. But when the field disappears the
circuits become again free of current. In this manner a good imitation is obtained
of diagmagnetic polarisation. The other point of view may be called the antilo-
gon of that of Weser. We provide in a magnetic field’ supra-condueting cireuils
which are free of current. When these circuits are brought outside the field, they
show a current persisting for a long time. Outside the field they imitate permanent
magnets. It, must, however, not be lost sight of, that. this imitation is in so far
incomplete, as when the circuits are brought back into the field, they return to
the currentless condition.

S18

a combined view of the experiments of sees
tions 9 and 11). The thread runs through a

2 Sk eee mee
4 tube, the lower part of which is of glass and
can be moved by means of a rubber-tubing
calles attachment at the top of the apparatus (fig. 1).

The coil was cooled to 2°.4 K. in a field
of 200 gauss by helium evaporating under
reduced pressure. The current was again

produced through induction by removing the
field. When the compass needle with the com-
pensation-coils was arranged, as before, beside
the cryostat, a moment corresponding to a
current of 0.36 amp. was registered. The
observation was continued for an hour, in
which the diminution of the current in 45
minutes was within the limits of probable
error of the measurement (2°/,); after this
the circuit of the coil was cut through. The
(| needle of the compass fell back to a deviation
| that corresponded to a current of 0.05 amp.
in the coil. The ballistic galvanometer (with a
negligible self-induction and with 2000 2 in

Fig. Fig the circuit) showed an electro-kiretic momentum
2. 3. Lj of 300000, from which follows with L—10',
that a current of about 0.8 amp. flowed in the coil. The remaining
moment is again the same fraction of the principal effect as was

observed previously, it was extinguished as soon as the coil was
pulled up above the liquid helium. The experiment proves conclusively,
that a current does really flow through the coil.

§ 10. Further consideration of the momentum produced in the
coil, when the circuit is not closed. Persisting Foucauiy-currents. In
the previous experiments the question arose in how far magnetic
properties of the frame of the coil, which developed at the lowest
temperatures had an influence, and whether a part of the moment
that remained, when the coil, without the ends being connected, was
cooled and exposed to the field, was due to windings which were
short-circuited. For this purpose first of all a tube of brass, exactly
like that used as the frame of the coil, was cooled in the field.
It showed no residual magnetism.

To get further light on possible short-cireuits in the coil Phx,
after it had been shown that cooling in liquid air did not alter

Proceedings Rayal Acad. Amsterdam. Vol. XVII.

iis moment, a new coil of 650 turns was wound, in which the
possibility of short-cireuiting was excluded by insulation of the
windings by picein ani paper. It is true that the magnetic
properties of these materials are not known, but from the extinction
immediately above the boiling-point of helium of persisting current
which was found in the course of the experiments it is almost certain,
that the phenomena are entirely due to the lead. It was ascertained
that this coil was superconductive, which was a welcome result also
for the reason that the wire had been manufactured by compression,
and this process gives a much better guarantee of getting the same
product again by using the same method, and therefore of obtaining
beforehand the certainty of the wires prepared in this way being
supra-conducting. In making the experiment with 200 gauss at 2°.4 K.
a residual effect of the same order as with Pbx7;; was found, but
smaller. The principal current was 0.5 and the residual current
0.020 Amp. It becomes probable, when these figures are compared
with those found with Pbx,7,, that in the latter there really is some
short-cireuiting, but there is also apart from the effect due to the
short-circuited windings a moment caused by the lead.

It seems as if in the mean time this may be attributed to circular
currents in the lead of the wire, which are possible owing to the
wire having a certain thickness. We must distinguish in the wire
between an inside which is turned towards the axis of the coil,
and an outside. In the wire, even when the circuit is opened, a
current arises, in which the electricity passes along the whele
length of the windings on the outside of the wire (that is not closed
in itself), in order to turn round at the one end of the wire and
go back along the internal side. With induction in the closed cireuit
this current is superposed upon the mean electric movement in
the cireulating current, so that in the wire there is say a stronger
current on the outside, and a weaker on the inside. If by means
of a galvanic cell a current is sent through the wire, the same
phenomenon arises through the action of the field of the current
itself. We are here evidently dealing with persisting Foucaun-

currents ').

§ 11. A supraconducting key. In the experiments so far de-
seribed the supra-conducting closing of the conductor tested for supra-
conductivity was obtained by melting the two ends together. Now
1) Several of the well known experiments by Exinu Tuomson with alternating
eurrents could also be made with parallel currents and supra-conducling experi-
mental objects.

517

that these experiments had proved that a current generated in a
circuit which is supra-conducting over its whole length, continues
without electro-motive force, we could investigate in how far an
electric contact interposed in an otherwise supra-conducting circuit,
measured by the amount of conductivity of supra-conductors, might
be considered as having no resistance. The immediate cause of this
investigation was a suggestion made by my colleague Kunnnn, whether
the current the relaxation period of which was to be studied,
might not be obtained in the coil by short-cireuiting.

I thought then, that the transitional resistance in a contact to
be manipulated under liquid helinm could hardly be made small
enough for this purpose. The transitional resistance of a stop-
contact treated with all due care at ordinary temperature is not
likely to be less than 0,0001 2, which is still 100,000 C.G.S. while
the micro-resistance of the coil itself is only 37. It has now been
found, however, that transitional resistances such as we are con-
sidering can become very small at low temperatures. A quite moderate
pressure, between two pieces of lead appeared to be sufficient for
the purpose. The arrangement is shown in Fig. 2. The small lead
plate p, provided with three small cones direeted upwards and
connected with the coil through a spirally-wound part of the lead
wire which acted as a spring, is attached to a thin rod (partly formed
of wood) and was pressed against the block soldered to the glass tube
by serewing up the rod, the force being accurately regulated by means
of a spring (see top of fig. 1). The tube is provided with a number
of side-openings to prevent the very much intensified heat convec-
{ion (caused by resonance phenomena) which occurs in tubes closed
at the top when the bottom is at a very low temperature, and
which would lead to excessive evaporation of the helium.

Ry means of this simple key we were enabled to arrange the
following experiment. To each extremity of the windings of the coil
two wires were attached (fig. 1 and 2). By means of the one pair ac a
current can be sent through the coil. The other pair 6 can be con-
nected toa ballistic galvanometer. Moreover the two ends are connected
to the two parts of the supra-conducting key. With the key and the
galvanometer open, a current is sent through the cooled coil, in
the neighbourhood of which the compass-needle has been mounted.
The coil is then closed in itself, which gives no change in the
deviation of the needle. One ean then convince oneself as long as
one likes, that the side-current, which in ordinary cases is imme-
diately extinguished, remains unaltered in the supra-conductor; the
galvanometer connection is then closed, which also brings no change

34%

S18

in the current, and if thereupon the current connection is opened
this is accompanied by a throw of the ballistie galvanometer in the
circuit of which the current is instantly extinguished and by a return
of the needle of the compass into the position which it would also
take up, if the current in the closed coil had been generated by a
magnetic field equal to that of the current itself. The continuation
of the movements in Maxwenr’s mechanism, when it has a supra-
conductor as carrier, is demonstrated by this experiment with equal
clearness and simplicity.

§ 12. Combination of parallel currents into one of greater strength.
In trying to make the same experiments with mereury that we have
made with lead, it will be necessary in so far to change the experiment,
that one winding will be sufficient. This might be got by. freezing
mereury in a capillary tube returming in itself with an expansion
head (like our other U-shaped mereury resistances). The chief
questions then are 1) if with a conductor of as large a section (keeping
for the present to the circular form) as would be necessary, with a
view to the threshold value of current density, in order to get an
action comparable to that with the lead coil, the threshold value of
current density — of which as in N°. 183 if is assumed that it is
determined principally by the current density —— does not undergo
a considerable diminution in consequence of the larger section, as
some considerations in N°. 183 would make us fear, and 2) if we
ean reckon with the microresidual resistance as an ordinary resist-
ance even for such a completely different section as that for whieh
it has been determined. An inducement to try the experiment imme-
diately with a lead ring*) was a remark by my colleague Enreneest,

1) f am glad to mention here that Mr. J. J. Taupin Caasor of Degerloch
(Wiirttemberg) shortly after my paper on the disappearance of resistance in mer-
cury and, as I found afterwards, only acquainted with my result, that the resist-
ance of gold and platinum in an absolutely pure condition would probably disappear
allogether at extremely low temperatures, communicated to me a number of suggest-
ions regarding the condition into which meta!s pass below this temperature and
which he would like to be considered as a distinct “fifth” state of aggregation.

Amongst these suggestions was the following: “if a ring (of gold) is brought
to the condition of absolutely no resistance (in helium), an impulse (viz. by im-
duction) will be sufficient to produce a permanent current, which will make the
ring into a magnetic shell, as long as the temperature of the metal remains below
a certain critical value”. By critical value was meant — nol the vanishing point
as discovered afterwards — but the temperature characteristic of each metal at
which, according to my earlier views, the resistance of the pure metal would
become zero independently of the current-strength. The idea, however, underlying
this speculation — which was further developed by supposing the cooled ring to

519

that the experiment could be made equally well with the windings
“parallel” as it had been made with the windings in “series”. A
calculation (by estimation and further proceeding in the same way
as with the coil) about the experiment with a lead ring of an internal
radius of 1.2 em. of a thickness of 0.38 em. and of a width of
0.35 em. and assuming that the threshold value found for the thin lead
wire would also hold for the thick ring, showed me, that it might
sueceed very well.’

This proved to be the case. The current of 320 amp. that was
registered in the ring remained constant for half-an-hour to 1°/,, hence
the current density of 50 was in this experiment not much smaller
than it had been in one of the experiments with the coil of lead
wire, viz. 49. This may for the present be regarded as a confirm-
ation of the supposition that the thresbold value of current strength
of a conductor is mainly a threshold value of current density for
the material of the conductor.

be subjected to a magnetic field which was to be removed afterwards — was also
applied in my experiments for the purpose of obtaining persisting currents in supra-
conductors, and in the above last experiment actually with a ring as the conduet-
ing circuit.

At the time I was so much occupied with the investigation of the peculiar laws
of electric conduction in mercury below the vanishing-point and of the degree to
which currents miglit be realised in resistanceless circuits without electromotive
force, that I had not yet attacked or was able to fully go into the problems relating
to currents to be generated in closed supra-conductors by induction (amongst which
proklems that of the imitation of diamagnetic polarisation was an obvious one).
Still Mr. Taupin Cuazor’s letter was the cause of my coming even then to the
conclusion, that in order to be able to obtain persisting currents outside the magnetic
field by induction, an artifice based on the peculiarity of supra conductors was
required. As such I then found, that the cooling which is to make the conductor
supra-conducting is not applied, until the conductor is in the field which
is to be used for the induction. Afterwards it was found, that by utilizing the
knowledge of the threshold values of current and field circumstances may be realized,
in which a permanent current may be obtained outside the field by induction on

a circuit which has been made supraconducling by cooling before the field is applied.

520

Physics. — ‘“/urther experiments with liquid helium N. Waut-effect
and the change of resistance in a maynetic field. X. Measure-
ments on cadmium, graphite, gold, silver, bismuth, lead, tin
and nickel, at hydrogen- and helium-temperatures. By Prot.
H. Kamerrtincn Onnes and K. Hor. (Communication N°. 1424
from the Physical Laboratory at Leiden.)

(Communicated in the meeting of June 27, 1914).

§ 1. Method. The method was the same as that used in the
measurements of this series by H. Kamernincn Onnes and BuckMANN
‘ef. Comm. N°. 129a and others). The notation is also the same as in
the previous papers. As regards the HA.t-effect, we used both the
method in which a galvanometer-deflection caused by the effect’ is
read and the compensation-method, in view of the fact, that the
latter, althongh in general to be preferred, as it allows the elimination
of various disturbances, is very troublesome, when small effects
have to be measured. The differential-galvanometer used was of the
Kervin-pattern with a volt-sensibility of 5 >¥ 10-8 ; it was iron: shielded
and was mounted according to Jurius. As to the resistance measure-
ments these were partly performed in immediate connection with
the determination of the Haxt-effect, in which case the resistance
of the plate used for this purpose was at the same time measured,
partly (by means of the compensation-apparatus) with wires which
were wound on thin sheets of mica and could be placed either at
right angles to the field or parallel to it, the latter specially with
a view to investigating the considerable difference between the trans-
verse and the longitudinal effect, which difference develops specially
at helinm-temperatures.

§ 2. Sismuth. In accordance with frequent practice (e.g. by
KAMERLINGH ONNES and BrckKMANN) we used this substance in the
form of pressed plates. The peculiarities in the resistance observed
by Srrewntz with conductors of compressed powder — although
occurring also in our plates at higher temperatures were not
observable, when the plates were cooled below 0° C.

The plates which served for our investigation were pressed in a
steel mould and heated to about 200°C. in an electric furnace.
When made in this way the granular structure was still clearly
observable with a magnifying glass. The plate ip; was made
without special precautions; with plate iyz, the metallic powder

521

was specially dried before moulding it. Diy; gave an abnormally
high temperature-coefficient at higher temperatures and even after
36 hours’ heating had not yet attained a constant resistance.

The metastable condition which according to Professor E. Conrn
is peculiar of most metals as mixtures of different modifications
manifested itself also in our experiments. The plates after being
heated in the electric furnace to 60° or 100° C. showed some dif-
ference as regards resistance and Hatt-effect after cooling, with the
further peculiarity, that this change fook place, although no change
in the specific gravity affecting the second decimal place could be
established.

The results are contained in tables I and II.

TABLE I.
; |
Biy,- |
H —R Resistance —R | Resistance |
} | |
| T=2899° K | T=20°5 K | |
2400 Gauss | 7.71 | 2.5°10-3 Serato
2420, 42.13
4800, 6.68 Is 22385958
i200); 4 6.02 35.44 | |
9650, | 5.37 | 3862
| | | if
11800, | 29.76 | 1.1°10-3 |
|
12000, 4.65 | 3.1°10-3 QO) |
TABLE Il.
Biyyy
H —R Resistance —R Resistance |
T=289° K T=20 K
2420 Gauss 10.57 2.4.10-3 80.03 3.10—-4
4800, 9.48 | 78.31
1200'= 5 8.11 | 75.15
9650, 7.26 72.51 |
12000, 6.28 3.2.10-3 | 70.82 | 1.6.10-3

522

§ 3. Hant-effect in graphite. The great change in the properties
of graphite through even small admixtures appears clearly from the
fact, that with different kinds of graphite the temperature-coefficient
of the resistance may even differ in sign.

The material we started from in our experiments was fine graphite-
powder, such as is used in electro-plating; the powder was first
treated with acids and alkali and carefully dried; the forming of the
plate was again carried out in a steel mould. The electrodes which
gave some difficulty at first were finally contrived in the following
manner: the powder was provisionaily moulded to a plate under
comparatively low pressure, the stamp was then lifted off and six
small pellets of solder were laid on the plate, after which a high
pressure was applied. By trial we succeeded finally in obtaining
suitable plates of */; mm. thickness with six point-electrodes of about
‘/, mm. diameter, penetrating through the whole thickness of the
plate.

The influence of insufficient drying of the powder was very
marked; such plates, as did not come up to standard as regards
drying, did not reach their final resistance until the current had
gone through for 6 seconds.

The following table contains the results. It may be specially noted
that the ftemperature-coefficient is positive and that the Hats-effect
falls strongly from 20° K. to 14° K.

TABLE III.
Graphite.
H 290° K 20°.5 K 14°.5 K
aes ee
+R: +R: +R:
| 4800 Gauss | 0.68 3.4 1.42
6000, 0.68
4200: te 3.39
8400, 0.68 1.52
96005 aa 2.81
11800, 0.74 2.22 1.52

§ 4. The Haut-ejject in cadmium. Two eireular rolled-out Cadmium-
plates of 1 em. diameter were experimented on, The results are
found in the following table.

TABLE IV.

| Cadmium.
| areas | eae | : |
| H | 2O0OT Ke se 20e owke | 149.5 K
| + R: \Neeeesce | +R:
| 3000 Gauss | 13.1104 |

2600 ye 4.6.10—4 |

4800 ot, tt e202 OSA eens Oe

6000, 6.3.10—4 |

7200 + 20.6.10—4 | 23.4.10—4 |
3400) 5.9.10-4
| 9600 : 19.6.10—4 | 22.3:10—4 |
| 11800 " LWie6.1054> | 191105255)
| 12000 4, | 5.5.10-4 | |

§ 5. The Haut-ejiect at helium-temperatures. The method was the
same as in the previous measurements. To check the results, measure-
ments were made both with the compensation-apparatus and with
the differential-galvanometer. Five different plates were experimented
upon in the helium-bath. These were chosen so, that they could be
regarded as representatives of metals for which the Hat-effect is of
a different type. Each set of six wires from the six electrodes of
one plate was completely separated from the other sets in the cryostat.

The following plates were investigated.

1. A tin and a lead plate: both metals are supra-condueting at
extremely low temperatures. Lead remains supra-conducting up toa
considerable threshold-value of current. It may be added that both
are diamagnetic: as pe Haas has shown, the diamagnetic properties
are of great importance for the Ha.u-effect.

At hydrogen-temperatures the Hatu-effect is still so small, that it
escapes observation. It was found that at 4°.25 K. both with tin
and lead the effect can be very well measured, when the field is
so high, that ordinary resistance is generated in the metals. As long
as the field is low enough for the metal to remain supra-condueting,
the Haut-effect, like the ordinary resistance, disappears.

2. A silver plate, as representative of the group of metals for
which at the ordinary temperature the Haz1-coefficient is of the

524

TABLE V.

Measurements in Helium.

H R
| 1. Sr (tin) |
Lane acs KK |
11300 Gauss + 2.6.10—5
Owe COn + 9.8.10—5
2. Pb (lead)
A. AZO
300 Gauss < 6.10-5
1000, < 2.10-5
5000, -+ 0.8.10—4
11300, + 1,8.10-4
BIO OR
300 Gauss < 6.10-5
11300 Si, + 1.3.10—-4
3. Ag (silver)
a. T={4925 K
11300 Gauss 16.10—4
b. T=2°S K
13000. 16.10—4
4. Ni (nickel)
a. T= 4925 K
1300 < 5.105
11300 <— Wet0=5
Ox i= 228K
11300 <<) OSs
5. Bi
TANK |
1000 Gauss | 86.3
5000, in = | 84.2
11300, 85.7

order of magnitude 10—4; silver is diamagnetic and does not become
supra-conducting at helium-temperatures.

As appears from the table, it was found that with silver also the
Hati-effect increases, when the temperature falls to 4.925 K. At
still lower temperature it does not show any further change, no
more than the resistance without a field.

3. A bismuth-plate B/y7,;, moulded from electrolytic bismuth-
powder. Bismuth has a very high Hant-effect at hydrogen-temperatures
and the change from 20° K. to 14° K. is still very small. It is the
strongest diamagnetic metal.

The table shows that below 14o K. there is not much further
change in the Haut-effect. From 71 at 20° K. & rises only to 85
at 4°.25 K.

4. A nickel plate as representative of the ferro-magnetic metals.
With nickel at higner temperatures the Hatt-effect shows a tendency
to saturation owing to the magnetisation of the metal (Comm. No. 129,
130, 132). At hydrogen-temperatures the effect is still easily measu-
rable; at helium-temperatures it disappears, although the resistance
of the plate is still considerable. Probably this is connected with the
fact, that notwithstanding the already fairly considerable field the
magnetisation of the nickel is still very small.

The results are collected im table V. (zie p. 577).

§ 6. Change of the resistance in the magnetic field. It was found,
that specially at helium-temperatures this change is very con-
siderable, but that at 20° K. also it is still quite well measurable.
In general there is a difference between the longitudinal and the trans-
verse effects, which begins to show itself especially clearly at helium-
temperatures.

We shall give our results in the form of curves (figs. 1 to 6) on
which the numerical values may also be read with sufficient accuracy

by using the scale-values indicated in the figures. So far thé meas-

28. co T i if [ieee (a 3 T Bea
29% + ———_-|—_ ee ee = =a | a eo = —

A |
fore os eee eae { = a 4 |} =e
ie a | |
191.1 ad lie 245 = = == =k
a 2000 yoo. dan C000 10000, moo

(yams.

526

urements both at hydrogen- and helium-temperatures have not gone
beyond 12000 Gauss. They will afterwards be further extended to
higher field-strengths especially at hydrogen-temperatures.

40S 127

Figs. 1 and 2 contain the results for the resistance of lead and
tin in a magnetic field. The difference between the longitudinal and

- > , .
aot7s syiolizitce Caio viv 1091.
1

Sa eral!

aoz23s. }—

oO £000 4000 do0a. e000 10000 12000
>
Gauss

Fig. 3.

transverse effects was not more than the errors of the measurements.
The abscissa gives the ratio of the resistance to that at 0° C.

2
Goss ] T |
> . pian
aos} 4 MNeoistance Mla tisrii ya

00381

aos4 }—

°
yamss

527

Fic. 3 and 4 represent the longitudinal and transverse effects
o | to)

for cadmium and for platinum. The abscissae give directly the
resistance in Ohms.

a Ja toa 190 100 t30 300 Dt

Fie. 5 and 6 show the results for graphite, Fig. 5 the dependence
of the resistance on ihe temperature, fig. 6 the dependence on the
magnetic field.

We have further made measurements on the resistance of a

Bicgane |
1 ak el

cy wat pbite. = ieee

e000 wove. 1x00

a)
Fig. 6. pice

plate of not-purified graphite. These are not concluded, however,
and will be published later together with measurements on polarisa-
tion-phenomena which may possibly show themselves with pressed
graphite.

598

Physics. — “Measurements on the capillarity of Viquid hydrogen”.
By H. Kamerninch Onnes and H. A. Kuypers. (Communication

N*. 142d from the physical laboratory at Leyden).

(Communicated in the meeting of June 27, 1914).

For the determination of the capillary constant of liquid hydrogen
in contact with ifs saturated vapour the method of capillary rise was
used. The apparatus are in the main arranged in the manner as used
for other liquid gases in Comm. N°. 18. On plate IA of Comm.

N°. 107a@ may be seen that part of the apparatus
which serves to condense the gas in the wide
experimental tube (fig. 1), inside which is the eapil-
lary ; for this purpose the tube of fig. 1 is sealed

— - Sty. in at g,.
The radii of the sections of the tubes were found
by calibration with mercury as follows :
radius of the capillary inside 7 = 0.3316 em
3 Sere, 3 outside 7, = 0.0801 em
¥ » >», surrounding tube inside = 0.554 em
Measurement of the capillary rise. The reading
of the ascension gave some trouble as it had to be
made threugh a number of glass vessels and baths.
The rise was measured with a eathetometer ; to test
the accuracy of the readings they were taken one
{ime on a millimetrescale which had been etched
Fig. 1. on the capillary and another time directly on the
scale of the cathetometer. When it was found, that there was no
difference between the heights obtained in the two ways, they were
afterwards only measured by means of the scale of the catheto-
ineter, because, when the eryostat was filled with the different liquid
gases, the divisions on the capillary were difficult to distinguish owing
to the rising gas-bubbles in the liquids.

Temperature. The temperature was deduced from the pressure of
the vapour in the hydrogen-bath using the vapour-pressure curve
(H. Kamerninco Oxnes and W. H. Kersom, Comm. N°. 137d. table
on page 41).

Observations. The heights measured and the corresponding tem-
peratures of the hydrogen are contained in the following table,

529

Repeated measurements show, that the accuracy of the reading of
the rise may be estimated at 0.002.

TABLE I.
| Temperature in | Rise
KELVIN-degrees | in cms,
[is A See See
20.40 | 1.616
18.70 1.794
17.99 1.869
16.16 | 2.064
14.78 | 2.209

The observed heights (4) have to be corrected for the curvature
of the surfaces by means of the following formulae : (1) the correction

. ib s . .
for the meniscus in the narrow tube is a ‘). (2) the correction for

the ring-shaped meniscus is (according to VerscHarreiT Comm, N*. 18).

: ipa 2
w=(1 -f ar (k =.

> (R—?,)

For this correction the height of the ring-shaped meniscus, as the
minor axis of the elliptical section with a meridian plane, is required
to be known. With the illumination used this height could not be
measured accurately. Afterwards for further correction we hope to
be able to determine its value by special measurements: in the
mean time the section was assumed to be circular with sufficient
approximation. The corrected values are given in column 6 of table II.

When the capillary rise is plotted as a function of the temperature
— fig, 2 —, a straight line is obtained. The constants determined
from this line give the formula

H= — 0.1124 7 + 40.44.

This formula gives H=0 for T'y7=0 extray. = 35.98 K.

Assuming the critical temperature to be 7), —= 31.11 1 (mean of
1) Laptace, Méc. Cél. Tome X, Supp. § 5, Paris 1805.
id. , Oeuvres Tome IV, p. 415, Paris 1845.
Attan Ferguson, Phil. Mag., p. 128, (6) 28, 1914.

530

oie
24 aS
35 | \
R
2.2 - x
NN
\
\
29 XS
: ®
19 <
Ht
1,8
7 1 he J I =
‘ 1S 6 ” 8 19 £0 %
- Fig. 2.

Drwar, Oszewski and BuLir)') it is seen, that the formula, as was
to be expected, does not hold up to the critical temperature and
that the curve which gives the dependence of // on the temperature
has its concave side towards the temperature-axis. The difference
T'H=0extvap.— 7, for hydrogen amounts to

T 77=0 extrap. — Lito eOits

If Vry—oextrap. — 77. is divided by the critical temperature the
I 4 |

3.87

positive value = 0.125 is obtained. For methyl-chloride*) and

ethylether*) similar values are obtained *).
Surface-tension. From the capillary rise the surface-tension yw, is
found by means of the following formula :

2, 1 1
i NET vr (- — az)
(tig. a! Ovap.) ANGE R =n

The densities for liquid hydrogen are taken from the observations
by H. Kamerninca Onnes and C. A. Crommetry (Comm. No. 137).

1) F, Burnie. Physik. Zeitschr. p. 860, XIV, 1913.

*) According to measurements by J. VeRSCHAFFELT; comp. A. v. ELDIK,
Comm. N°. 39, p. 14.

3) E. C. pE Vries, Comm. N°, 6.

4) The corresponding figures (deduced, however, from not-corresponding tem-
perature ranges) are 9.038 and 0.017 respectively.

531

For the calculation of the vapour-densities use is made of the second
virial coefficient, as deduced from the measurements by H. KamErLiIncH
Onnes and W. J. pe Haas (Comm. No. 127c).

|
|
{
{
|

| 7 = 3332 3 2
dD — eet SS eS) =
l SS. S25) Oi S2' Sk 1S
| & St WRehit hatte peices
West) panel eae taal ate
>
rec ae
@& |@&a 8 BER B®
6 & = = Ss OF ITD
COR Sn ecg i i
ie = QIN EN AW I a con cd
oe eal
o |
S || 10 16 0
“a
oa yen Cy SG Nil er eS)
| lmaeterenatrenentroy “al hse alse 1
. || eres
AS | ©
o
: Gere eel Gel oh ev Tse) Kat)
&. Seo) St ON TO Os IO
ze S
wT oO
= = im 10
4 CO = O) 00) Oecd Pe SE oH
o SS 1S) Qs ies)! Wo o
aa 4 LeSieg USaS ly ile Lah lah sal Soe
— oa oS |
faa) = ——
< | 19
[= — Cy oy OT
= Ste NO AOy a SHC cor =) (00)
ee Wi eS ES ey SS Gai Ge)
om NNON NN
i
ov o |
<= ro IN A tts et C=
= Sn | eens Us CCR CON SHE IOI COMO)
a QA | a Se Se Se ea BSB Se
23) 3 S
i>}
SQ | | —
Ore |
So |
met |S) ba ee ee
2 MS) Ss SS SSS SS
m
3 2
oO a oS
ie]
CO Tos oy sta a
= =- = = &® © & DB S
OO OR) 00 OS a ic
| J= ae we ae =z nna
|
4
| Qa, Ol any: 19
& io ee OC &) © ey ce)
3 {Vibe Seay ites Sines eee
= =) te fey ee) Te ke
N A AN Hee me Oe

With these data the values of yw, in table II are calculated. Under
O—C are given the differences between w, ops, and values of yp, caleu-
lated from vAN per Waats’ formula

w= A(1—p2
where

Proceedings Royal Acad. Amsterdam. Vol. XVII.

532

A = 5.792
B= 0.9885

From the value found for B it appears, that y, as a function of
T is nearly a straight line.

The constant in Eérvés’ formula for hydrogen deviates considerably
from the value 2.12, found by Ramsay and Surrips ') as the average
for a number of normal substances. In Table ITI the values of ps
for a few of these substances, together with those for some liquid
gases, are collected. As observed by KameriincH Onnes and Krgsom
(note 3881 Suppl. No. 23), normal substances form a series in this respect,
on the whole progressing with the critical temperature (although with
deviations which may be ascribed to particularities in the law of
molecular attraction, e.g. with oxygen).

TABLE Ill.
| Ethylether ) Pi ey
Benzene 2) 2.1043
| Argon 3) 2.020
| Nitrogen 3) 2.002

|
| |
| Carb.monoxide3) 1.996

| Oxygen 3) | 1.917
_ Hydrogen | 1.464

A calculation of the constant 4’ in Ersrer’s formula ‘*)

dw, 2
ip — LF jos Sk Api RL
i(« dT ) "Tig. I Oe AAG

for hydrogen gives
7.34 < 107
The fact, that hydrogen appears to have a considerably higher
value of 4’ than that calculated by Erystrein for benzene, might, in
view of the theory underlying the formula, indicate, that the radius
of molecular action is larger for hydrogen molecules than for sub-
stances like benzene.

\) J. chem. Soc. 63 (1893); ZS. f. physik. Chem. 12 (1893).

*) Ramsay and Surexps ZS. f. physik. Chem. 12 (1893), 15 (1894).
8) Baty and Donnan, Journ. chem. soe. 81 (1902).

4) A. Etnstern, Ann, d. Phys. 4. 34, 1911.

533

Chemistry. — “The system: copper sulphate, copper chlorid, potas-
sium sulphate, potassium chlorid and water at 30°”. By Prof.
F. A. H. Scurememakers and Miss W. C. bE Baar.

1. Introduction.

In previous communications ') we have discussed the quaternary
systems:
Cu SO, — Cu Cl, — (NH,), SO, — NH, Cl — water
and CuSO, — CuCl, — Na, SO, —NaCl — water
Now we shall discuss the system
Cu SO, — Cu Cl, — K, SO, — KCl — water,
which we have examined at 30°.
As solid substances occur at 30°:
the anhydrie salts: K,SO, and KCl,
the hydrates: CuSO,.5H,O and CuCl, . 2H,0,
the doublesalts: CuSO,.K,SO,.6H,O and CuCl, : 2KCI. 20,0.
Further a peculiar salt exists with the composition :
Cus@, kK Cl or K. sO, Ca Cl,
with or without one molecule H,O, while sometimes as metastable
solid phase a salt with the composition :
2CuSO, . 3K,Cl, . H,O
has occurred.
In fig. 1 the equilibria occurring at 30° are represented schematic-

G. SO,

222 (1911) and Zeitschr. fiir Phys.

Chemie 69, 557, (1909).

35*

5384

ally, the sides of the quadrangle have been omitted, only a part
of the diagonals with their point of intersection W is drawn. Fig. 1
is not the representation in space of the equilibria, but thew pro-
jection on the quadrangle. Before discussing the quaternary equili-
brium, we will first consider the four ternary equilibria.

2. The ternary equilibria.

a. The system K,SO,— KCl— H,O.

Only K,SO, and KCl occur as solid phases; in fig. 1 the satura-
tioneurve of K,SO, is represented by Ag and that of KCl by /g.
Consequently point ’ represents the solubility of K,SO,, point / the
solubility of KCl in water; point g is the solution, saturated with
the two salts.

b. The system CuSO, — K,SO,— H,0.

This system was examined already formerly *); as solid phases
occur K,SO,, CuSO,.5H,O0 and the doublesalt CuSO,.K,SO,.6H,0.
The isotherms of 80° and 40° are determined experimentally ; that
of 30° is represented schematically in the figure. The saturation-
curve of K,SO, has been represented by /z, that of CuSO, .5H,O
by ak and that of the doublesalt by 47. When we represent this
doublesalt in tig. 1 by the point D,.,., then the line WD,.,., intersects
the curve 7k in a point 7. The doublesalt is, therefore, soluble in
water without decomposition; its solution saturated at 30° is repre-
sented by 7.

The following is still of importance for the investigation of
the quaternary system. When we heat an aqueous solution of
K,SO, + CuSO, above 50°, a light green salt is separated from the
solution. Mrrrpure found for the composition of this salt:

4CuO . K,O .. 450, . 30,0,
while Brunner’), who examined first this basical salt has found
four molecules instead of 38 molecules H,O.

c. The system CuSO, — CuCl, — A, 0.

Also. this system was investigated formerly *), as solid sub-
stances occur: CuSO,.5H,O and CuCl, .2H,O. In fig. 1 ab represents
the saturationcurve of CuSO,.5H,O and cb that of CuCl, . 2H,0.

d. The system CuCl,— KCl — H,O.

In this system of which the invariant (P) equilibria were

1) P. A. MeerpurG. Gedenkboek J. M. vAN BEMMELEN, 356 (1910).

2) BRuNNER. Pogg. Ann. 15 476 (1829).

3) F. A. H. ScHREINEMAKERS. These Communications l.c. and Zeilschr. Phys. Chem.
69 557 (1909).

5385
examined’ formerly ') oceur as solid phases: KCl, CuCl, . 2H,0,
CuCl, . 2KCl.2H,0 and CuCl, . KCl. This last salt, however, occurs
only above 57°, so that, at 30°: KCl,CuCl,.2H,O and CuCl,.
2KCl.2H,O only occur as solid phases.

The isotherm of 30° is represented schematically in fig. 1; fe is
the saturationcurve of KCI, cd that of CuCl, .2H,O and ed that of
CuCl, .2KCl.2H,O. When we represent in fig. 1 this doublesalt by
D,.,.,, then the line WD,.,., does not intersect curve ed, but curve fe.
This doublesalt is, therefore, at 30° not soluble in water without
decomposition, but it is decomposed with separation of KCl.

This isotherm of 30° was determined already formerly *); we
have also still determined some points.

3. The quaternary system.

At first sight we may think that the examined system is built
up by five components; as, however, between four of these substances,
the reaction :

Cul, > Ke SOp a KCl CusOes = 2 D
oecurs, this is not the case.

In view of the above-mentioned double-decomposition (1) we shall
represent the equilibria with the aid of a quadrilateral pyramid, the
base of which is a quadrangle. The four anglepoints of this qua-
drangle indicate the four substances: CuSO,, CuCl,, K,SO, and K,Cl,
and in this way that the two substances, which are in reaction (1)
at the same side of the reaction-sign, are united by a diagonal of
the quadrangle. Perpendicular above the point of intersection W_ of
the diagonals, is situated the top of the pyramid, which represents
the water.

At the examination of this quaternary system we have always
remained below the temperature, at which the basical salt

4Cu0. K,O. 450,. 3H,0
is separated. If this had not been the case, the reaction :
4CuSO, + K, S50, + 4H,0 2 4Cu0. K,0. 480,. 3H,0 + H,SO,. (2)
would have occurred. We should then have had to examine a
quinary system, in which reactions (1) and (2) occur.

As the quaternary solutions saturated with a solid substance, are
represented by a surface in the space, viz. the saturationsurface, we
have seven saturationsurfaces. We find their projections in fig. 1 ;

1) W. Meyeruorrer. Zeilschrift fiir Phys- Chem. 0 336 (1889) 5 97 (1890).
2) H. Frutppo; not yet published.

536

from this it is apparent that six of these surfaces are side-surfaces
and that one is a middle-surface.

aklm6 is the saturationsurface of the CuSO,. 5H,0

ClO eee > 5 CU CIE ALG

adnoe. ae i 5 on POW). 2KCII2AE®
eopg ie AH ace 50 2 KCl

GG Cl es 4 Sy Ke SO,

iqlk » £ Re op OW SO KE ISO) .(Blal-(O,
pqlimno,, 5, 3 Rae es 58)

In order to get a better view, in the figure is indicated on each satura-
tionsurface the solid substance, with which the solutions are saturated.
For the sake of abbreviation we bave called Cu SO,. 5H,0 = Cu,,
Cu Cl,. 2H,0 = Cu,, Ca Ch. 2KCI. 2H;0 = D..,., and CuSO; Kes@2
GHEO Dg :

The middle-surface pq /mo is the saturationsurface of a salt, which
we have represented by J. In order to find the composition of this
salt we have applied the rest-method, viz. the analysis of the solution
and the corresponding rest. From numerous definitions it follows
that this salt has the composition :

CwsO Kk Ce Ke son CalCit— Ds
or CuSO,. K; Cl, 8,0 =K,S0,1Ca Cle HO ae

Some determinations pointed viz. to D,, others to Dx, again others
to a mixture of D, and Dx, so that in the region pqim no (tig. 1)
perhaps the two salts D, and Dx occur.

The probability that more than one solid salt occurs in this region,
is enhanced by the following observations. In some eases the solid
substance was precipitated after shaking (which lasted sometimes a
month or longer) within some hours as a greenish powder, in other
cases there was formed a greenish or blue-greenish paste, which
after days did not yet settle, but stuek to the sides of the shake-
bottle. In the first case we could easily remove a large part of the
mother-substance by suction, in the latter case this appeared practi-
cally impossible. From all this it is. apparent that in the saturation-
surface (fig. 1) indicated by D different salts may occur, two of which
have the composition D, and Dx.

[t follows, however, from the position of the solutions saturated
with D, or Dx in the region of fig. 1 indicated by D, that one of
these salis must be metastable with respect to the other, perhaps
they are both metastable with respect to a third, which we have
however not found in onr investigation.

537

In order to get the solutions of the saturationsurface D saturated
with solid salt, we put together the substances in such ratios
that the solid substance must be formed in one case from
Cu SO, .5H,O + KCl, in the other from Cu Cl,. 2H,0 + K, 50,. In
both instances now D, then Dx was formed.

In some cases also occurred as solid phase a double salt of the
composition :

2Cu SO,. 3K, Cl,. H,0 =D,
Later, however, we did not succeed again in getting this salt, but D, or
Dx, appeared instead. The salt D, will therefore, very probably exist
in a metastable condition only.

On account of the uncertainty with respect to the substance D,
we will further describe the equilibria as if in the region p q/in no
occurs only one solid substance D. When in this region more solid
phases may occur in stable condition, then the necessary changes in
this region will have to be inserted.

The intersectinglines of the saturationsurfaces represent the quater-
nary solutions, which are saturated with two solid substances, con-
sequently the quaternary saturationlines. The limit-lines of the
saturationsurfaces on the side-planes of the pyramid form the ternary
saturationcurves of the four ternary systems, which have already
been discussed previously.

The quaternary saturationcurves are the following :

gp the saturationline of K, SO, + KCI

COR ss a 9 it, SO, ce Dyas,
eles paous » Sa Dic.
bm ,5 3 » Cu, + Cu,
dn the saturationline of Cu, + D,.,.,
BIO) os i iy KOh = Ding
OU + +5 5 K,SO,4+ D

Gl ne ‘5 5 D4
ieee is 7 Cle
oe 3 » Cuy +D
WiOw 5 x oe Diet sD
OP os be + ACE tp

The first six saturationlines are side-curves; each of these has an
end on one of the side-planes of the pyramid. The last six satura-
tionlines are middle-curves; each of these has its two ends within
the pyramid.

538

The points of intersection of the saturationsurfaces represent the
quaternary solutions, which are saturated with three solid substances
consequently the quaternary saturationpoints. In each of these points
three quaternary saturationcurves come together. In the ternary
saturationpoints, which we already discussed previously, two ternary
and one quaternary saturationcurve come together.

The quaternary saturationpoints are the following:

p saturated with K,SO,-+ KCl + D

q - » K,SO,+D,.,..> D
l 7 » Cu, © = Dew dD
m 3 3. (Cu; ) =eiCiss ap
n 5 5 Olu. + D,.,., + D
Onan ICH SE Ds 25 1D

As it is easy to see from fig. 1, in presence of solution can exist: |
K, SO, by the side of: KCl or Dor D,.,.,
but not by the side of: Cu, or Cu, or D
KCl by the side of: K, SO, or D or D,.,.,.
but not by the side of: D,.,., or Cu, or Cu,
ig-, Dy the side of: KCl or D or Cu,
but not by the side of: K,SO, or D,.,., or Cu,.
Cu, by the side of: Cu, or D or D,..,
but not by the side of: KCl or K, SO, or D
Cu, by the side of: Cu; or Dior D;..,
but not by the side of: K, SO, or KCI or D
D,.,., by the side of: Cu, or D or K,SO,
but not by the side of: KCl or D,.,., or Cu,
D by the side of all other substances.

HOE Wy |

TSS

12353

Different conclusions can be made from the figure. Let us con-
sider the behaviour of the salt D with respect to water.

When D is the salt D,, it is indicated in the spacial represent-
ation by the point of intersection W of the diagonals (fig. 1). When,
however, D is the salt Dx, which contains water, it is situated in
the spacial representation on the line, which unites the top of the
pyramid with the point of intersection of the diagonals. Let us
assume that D—=D,z and let us call T the top of the pyramid, so
that point T represents the water. As the line D,T does not inter-
sect the saturation-surface of D,, Da is not soluble in water without
decomposition. The line D,T intersects, however, the saturation-
surface zklq of D,.,.,, so that the salt D, = Cu'SO,. K, Cl, = K, SO,.
Cu Cl, is decomposed by water, while D,.,., = Cu SO,. K, SO,.6H,O
is separated. From this we see that we can not wash out the salt

539

D, with water to free it from its mother-substance, as this will
lead to decomposition.

When we wish to examine accurately what will take place when
we bring together D, and water, we must consider which spaces
of the pyramid are intersected by the line D,T. From this amongst
others the following is apparent. When we add D, to water, then
firstly unsaturated solutions arise, which are represented in fig. 1
by the point W. (In this it is to be considered that fig. 1 is the
projection of the spacial representation and that point W is the
projection of the line D,T). ,

With further addition of D, the solution W arises, which can be
saturated with D,.,., (this D,.,.,. however, is not yet present as
solid phase) consequently the solution W of the saturationsurface zq//-.

With further addition of Dz now D,.,., is separated and the
solution traces in fig. 1 the straight line Ws, this straight line is the
projection of a curve situated on the saturationsurface 7q/k. When
we add so much D, that the solution attains the point s, then,
further addition of D, will no more change the solution and there
is formed:

D,.,., + Da + solution s.

When we wish to examine what will take place when we bring
together in variable quantities K,SO0,,CuCl, and water, then we must
intersect the spacial representation by the plane K,5O,—CuCl,—T.
When we bring together KCl— CuSO, and water in variable
quantities we must draw the plane K, Cl, — CuSO, — T.

As the manner, in which these sections with the saturationsurfaces,
saturationlines and the different spaces can be obtained, was already
discussed previously *), we will not apply this method now.

In tables If and III we find indicated the compositions of several
solutions; we have deduced with the aid of the restmethod graphically
the solid phases with which these solutions are saturated.

In table II the compositions are expressed in percentages by weight ;
of the four salts Cu SO,,Cu Cl,, K,SO, and K, Ci,; only three at the
same time are given. This is sufficient also because, if we wish to
express the composition also in the fourth salt, it may be done in
infinitely many ways with the aid of the reaction-equation

Cu SO, + K, Cl, 2 K, SO, + Cu Cl,

For this the quantities of the substances which take part in the

reaction must be expressed in quantities by weight.

1) k. A. H. Scoremnemakers. Zeitschr. f. Phys. Chem. 66 699 (1909).

540

ACE ese.
The ternary system K, SO, — KCl — H2O at 30°.

Composition of the solutions

in proc. by weight | in molproc.
|

Point Sie Solid phase.
K,SO, | KCl H20 | K,SO4 | KeCh | H,0

epee 0. Wests i a-33 0 | 98.67 K»SO,
2.55 | 17.45 | 80.0 | 0.32 | 2.56 | 97.12

”

ge |e 4209.) 26.20.) 72.7. |, OMS: |) 4516 *) $95.69 K,SO, + KCl
oe 0 222. 72.78 Oi 432 95.68 KCl.
ABLE Il
The quaternary system Cu SO, — Cu Cl, — Kz SO, — K,Clz — H20 at 302.

Composition of the solutions in procents by weight.

Point CuSO, | CuCl, | Kp SO, | KCl
K | 20.60 On ali 3%61 0 | 75.79 | Cie ee
14.60 5 23a seus 0 76.44 | .
Ex | 10.02 | 10.74 | 4.56 0 | 74.68 | i
7 1.70 | 24.48 | 6.92 0 | 66.90 | i
1 | 7.43 | 23.75 | “0 6.26 | 62.56 | Cue Dig gen
i 1.63 0. | 12.01 | 0 | 65.36.| | Kiso -=DRe
1.63 oll ave | 2.98 | 86.26 A
1.2] 0 6.76 | 6.01 | 85.51 7
Es | o | 213 | 5.74 | 9.84 | 82.29 :
% 0 5.05 | 3.82) |) Gl6s02) |) 75.11 .
2.96 | 6.07 | o | at.e6 | 69.11 .
q 2.97 | 6.68 0 | 21.97 | 68.38 | K,SO4+-Dj..6--D
g 0 o | 1.09 | 26.20 | 72.71 | kj S0,4+KC
ae | 1.75 4.80 | 0 | 25.32 | 68.13 5
“>. [acest “6-86 | 24.68 | 66.70 | Ky SO,-+ KCl-+ D

| |

541

TABLE Ir
The quaternary system: Cu SO,— Cu Clz — K, SO4 — KoCl, — H,,0 at 30°.

Composition of the solutions in procents by weight.

Point | CuSO, | Cu Cl. | Ky SO, | K Cl | H,0 | Solid phase.
p 2.06 | 6.56 | 0 24.68 | 66.70 | k_)SO,+KC1-+D
g_ | 234 | 61 | 0 23.32 | 67.60 | K,S0,-+D
Girl) /2-6f || "63 |. <0 22.17 | 68.59 | r
q | 2.97 | 6.68 | 0 21.97 | 68.38 KSOn= Dire eD
q 2.97 | 6.68 | 0 21.97 | 68.38 KeSOreEDaeeD
2.04 | 7.86 | 0 17.03 | 68.92 Be
[esate 111.00 On Slt. ste set -
Ee | 4:08 | 17.31 0 | 11.81 | 66.79 re
= || vaces | 20:80 0 9.44 | 65.41 7
| 7.53 | 23.31 0 6.63 | 62.53 | :
l 7.43 | 23.75 oO Weeo5 loose | Cue Die ED
p | 2.06 | 6.56 0 24.68 | 66.70 KeSO0, = KID
| i.54 | 9.22 0 23.64 | 65.60 KCI-+-D
| 1.34 10.86 0 93.11 | 64.69 i
g | 1.30 | 11.29 =O 22.80 64.11
S™ | 0.80 | 16.95 0 21.28 | 60.97 | i
0.75 | 17.51 | 0 | 21.35 | 60.39 | 2
0.72 | 18.56 0 21.37 | 59.35
0 0.56 | 21.43 | 0 | 20.47 | 57.54 KiCHED Dim
| |
Sar: 21.62 | 0 | 20.86 | 57.52 Keele oD pss
o 0.56 | 21.43 er | 20.47 | 57.54 | KCl+D+Dh.2
| |
oo O-scre| 21.48 0 20.47 | 57.54 | KCIED+Dio0
| 0.59 | 26.09 0 16.83 | 56.49 | Dee Diss
a 0.63 | 29.41 | 0 | 15.01 | 54.95 | '
S | 0.71 | 32.60 0 13.10 | 53.59 r
0.70 | 37.61 0 10.62 | 51.07 | ,
n 0.4 | 424 | o | 7.86 | 48.75 | €u+-D+Dio

| | | |

TABLE Il
The quaternary system: Cu SOy— Cu Cl) — Ky SOs — Ky Cl, — HO at 30°.

Composition of the solutions in procents by weight.

Point | Cu SO, | CuCl, | K,SO, | KCI H,O | Solid phase.
n 0.94 | 42.45 0 | 7.86 | 48.75 Cu, +D +Dj29
™ |
d 0 | 43.1 ou 84 48.5 | Ci, Dien
n 0.94 | 42.45 | 0 | 7.86 | 48.75 Cu, De apeee
zs | “1.59 | 42.30 | 0 4) 52884] 50Ke3 Cu, -+D
oe $.46.1\ 40.95 0s 0). lee anade | ates Cu; “Gus aR)
| |
m 3.46 | 40.95 | 0 | 4.34 | 51.25 | Cu, 42 Cu; D
b Deal LOR Ou) | SOU mlunstes4 Cu, + Cus
3.46 | 40.95 | 0 | 24.34 | {51225 Cus ens
, 4.15 | 36.69 | 0 4.79 | 54.37 Cuca
ae | 4.48 | 34.33 0 | 5.14 | 56.05 .
= 5.48 | 29.55 0 5.74 | 59.23
Phe) eas | 23.75 0 6.26 | 62.56 Cus 4 Dia
| 4.90 | 24.49 0 7.64 | 62.97
| 2.88 | 10.71 0 18.57 | 67.84
2.29 | 10.44 0 90.12 | 73.15
2.15 | 10.83 | 0 19.97 | 67.05 |
: outs | Giles 0 19.60 | 65.89
. teoeelp Cli be 21.24 | 66.00
E 1-31 4/16 267. lg ane 18.54 | 63.48
E 1.31 | 16.57 | 0 18.68 | 63.44
e 0.89 | 23.19 0 16.38 | 59.54
A 854 |e23.15° 4/10 16.25 | 59.17
0.669 |) =2160i-aO 15.92 | 61.62
|) 91:03 | ie2me0 0 13.70 | 58.17
| oc | 32.57 0 12.43 | 54.23 |
| 2.03 | 27.75 | a) 9.93 | 60.29 |
| 4.47 | 39.14 0 7.17 | 52.25
|
6.06 | 19.84 | 0 7.75 66.35 | Saturation surface Dj.;.g
\ i

543

TA BIE, Ul

The quaternary system: Cu SO4— Cu Cl, — Ky SO, — Ky Cl, — H; O at 30°.
Ions Cu, Ky, SO, and Cl, and Mol. H,O in a quantity of
solution which contains 100 Mol. in all.

Point Cu K, SOF) Cl; H,O | Solid phase.
|
K 2.96 | 0.48 | 3.44 | 6 96.56 . Gis -eDire
2.97 | 0.49 | 2.51 | 0.89 | 96.54 | i
a 3.34 | 0.61 2.10 1.85 | 96.05 $
: 4.88 1.01 1.28 | 4.61 | 94.11 .
l 5.98 112 1.25 | 5.85 | 92.90 Gust Dia oD
oe A So DS
i Oe | er ace 0 Ognash ly | a KaSOh Dit
0.21 1.49 1.29 | 0.41 | 98.30 ‘
0.22 1.64 1.03 | 0.83 | 98.14 é
Ex 0.34 Dai GE70) lee Te toe |cO7-55 >
> 0.86 | 2.98 | 0.51 3.33 | 96.16 <
1.58 | 3.62 | 0.46 | 4.74 | 94.80 ¢
q 1.70 | 3.68 | 0.46 | 4.92 | 94.62 Ke SO; oD
ig Oh Te) 4-31 Pros 15) |b 4516)" | 95.69 K SO,-+ K Cl
58 1.17 | 4.25 | 0.28 | 5.14 | 94.58 | p
. 1.56 | 4.21 0.33 | 5.44 | 94.23 K, SO,-+K Cl+D
p 1.56 | 4.21 0.33 | 5.44 | 94.23 K,SO,+KCl+D
wi 1.63 3.94 | 0.37 | 5.20 | 94.43 | K,SOn-D
Sie 1.64 | 3.70 | 0.41 | 4.93 | 94.66 | i
q 1.70 | 3.68 | 0.46 | 4.92 | 94.62 | K,S0y+-D+4 Dis
q (710i? 3.68 a fe O:46.4|-4 14.92 \)eod G2 Lh KG SO," DAL Dit,
1.92 3.51 | 0.46 4.97 94.57 DitesaD
2.52 2.89 0.49 | 4.92 | 94.59 A
aa 3.92 2501s.) 0.64 |- | (5.29 94.07 .
= 4.68 1.63 | 0.78 | 5.53 | 93.69 r
5.90°| 1.19 | 1.26 | 5.83.| 92.91 ‘
l 5.98 1.12 | 1.25 | 5.85 | 92.90 Gite Dates D

544

TABLE Ill.

The quaternary system: Cu SO,— Cu Clp — Kz SOy — K, Cl, — H, O at 30°.
Ions Cu, Kg SO, and Cl, and Mol. H;O in a quantity of

solution which contains 100 Mol. in all.

Point Cu kK, SO, Cl, HO Solid phase.
p 1.56 | 4.21 | 0.93 | 5.44 | 94.23 K, SO4-+-KCI-+D
2.02 MF acs | 0.25 | 5.85 | 93.89 KCI--ED
2.33 | 4.04 | 0.22 | 6.15 | 93.63 a
a 2.40 | 3.99 | 0.21 6.18 | 93.61 -
S™ | 3.58 | 3.90 | o14 | 7.98 | 92.92 2
3.72 |.3.95 )|2 0.18 | 7.54 1) 92.33
3.98:| 4.00 | 0.12 | 7.86 | 92.02 55
o 4.66 | 3.93 | 0.10 | 8.49 | 91.41 K Cl-E D+ Dies
e 4.58 | 3.93 | o | ssi | 149 KGEsDies
0 4.66 | 3.93 | 0.10 | 8.49 | 91.41 K Cla= Dis ee D
o 4.66 | 3.93 | 0.10 | 8.49 | 91.41 K Cl DyaaeeD
5.74 | 3.27 | 0.11 | 8.90 | 90.99 DaeDies
2 6.60 | 2.98 | 0.12 | 9.46 | 90.42 .
Or 7.46 | 2.66 | 0.13 | 9.99 | 89.88 f
8.91 2.23 | 0.14 | 11.00 | 88.86 Z
n 10.44 1.71 0.19 | 11.96 | 87.85 Cu Dag
n 10.44 | 1.71 0.19 | 11.96 | 87.85 Ci; 4D sa 50
d 10.44 | 1.84 0 | 12.28 | 87.72 Cug- Diss
n 10.44 | eel 0.19 | 11.96 | 87.85 Cig Dj oa
as 10.30 | 1.25 0.32 | 11.23 | 88.45 Cu, + D
Su eao.19, ora 0.68 | 10.42 | 88.90 Cu,+Cu; + D
m 10.19 0.91 | 0.68 | 10.42 | 88.90 Ca, Gin
b 10.03 | 0 0.54 | 9.49 89.97 Cu, + Cus

545

TABLE Ill.
The quaternary system: Cu SO4— Cu Cl, — K, SO, — K, Cl, — Hy O at 30°.
Ions Cu, K, SO, and Cl, and Mol. H, O in a quantity of
solution which contains 100 Mol. in all.

Poittty ee Cua) KG | SO, ch | H,O Solid phase.
| " |
:
m 10.19 0.91 | 0.68 | 10.42 | 88.90 Guy |: Cu, 4 D
8.93 | 0.94 | 0.78 | 9.09 | 90.13 Cup-+D
8.27 1.01 | 0.82 | 8.46 | 90.72 | fr
|
7.10 1.07 | 0.96 7.21 | 91.83 | é
l 5.98 1612 | 1.25 5.85 | 92.90 | Cus-++Dy1.6-+D
| 5.67 1.36 | 0.82 21 | 92.97

2.38 | 3.39 | 0.34 43 | 94.23
2.49 | 3.34 | 0.34 49 | 94.17

A 2.38 | 3.65 | 0.28 75 | 93.97 |

2 3.50 | 3.29 | 0.22 | 6.57 | 93.21

i 3.48 | 3.32 | 0.22 | 6.58 | 93.20

2 4.96 | 3.06 | 0.16 | 7:86 | 91.98

3 5.09 3.05 0.15 7.99 | 91.86

4.73 less | 0.97 5.09 93.94 Saturation surface Dy.;.¢.

In table III the compositions are indicated in the number of ions
Cu, K,, SO, and Cl, and molecules H,O, which are present in a
quantity of solution, which contains in all 100 molecules.

When a solution contains a ions Cu, 4 ions K,, c ions SO,, d ions Cl,
and w molecules of water, then is consequently

atb=c+d-ndwt+a+t+b=w+ce+d=100.
Leiden. Anorg. Lab. Chem.

546

Chemistry. — “The catalyse”. By Prof. J. Bousexen. (Communi-
cated by Prof. A. F. HoLieman).

(Communicated in the meeting of June 27, 1914).

1. It appears to me that, a summary having been given from
various quarters on catalytic phenomena, the time has arrived to
show briefly how the development of my ideas on this subject has
advanced and how the insight thus gained has been supported by a
deduction of one of my students.

I do this in the first place because in that historical account the
eradual elucidation of the phenomena is exposed, but also because
I imagine that a point has now been reached where the co-operation
of many is necessary in order to assist in completing the edifice of
the catalysis.

2. When working at my dissertation (1895—1897), when a large
number of fatty-aromatic ketones was prepared according to the
reaction of Frinper and Crarts, it struck me that when to a cooled
mixture of acid chloride and benzene finely powdered aluminium
chloride was added, this certainly dissolved rapidly, but that an
evolution of hydrogen chloride only took place slowly on warming’).

As aluminium chloride did not perceptibly dissolve in benzene,
I was then convinced that not the benzene but the acid chloride
might be the point of attack of the catalyst.

This question was afterwards taken up by me and solved in so
far that the synthesis of the aromatic ketones could be divided into
two stages: (a) The catalyst combines with the acid chloride: (b)
this compound is attacked by the aromatic hydrocarbon (Rec. 19
19 (1900) 20 102 (1901).

Although the course of the reaction was indicated therewith, I
was soon aware, however, that the catalytic action of aluminium
chloride remained in complete obscurity *).

In this I was corroborated by the observation that chloroform
and benzyl chloride suffered the reaction with benzene still far
better and more vigorously, whilst these substances did not combine

1) Afterwards | modified the preparation by taking the AICls in excess and then
adding drop by drop the mixture of acid chloride and benzene, because the reaction
then proceeded very regularly. By the research of OLIviER (Dissertation, Delft 1912)
it has been shown that the cause of this favourable result must be attributed to
the presence of free AIClg (see later).

2) PERRIER who had noticed this reaction course previously (Thése, Caen 1893)
was of opinion that this explained the catalylic action of aluminium chloride.

547
with aluminium chloride and the quantities of the catalyst necessary
for the reaction were much less than in the synthesis of the ketones.
(Ree. 22, 301 (1903)).

When it appeared that nitrobenzyl chloride, which does unite with
AICI,, was also attacked much less rapidly than benzyl chloride,
and further that the very reactive anisol, which also forms a molecular
compound with AICI,,
did so readily, the facts were such that | ventured the thesis that
the formation of compounds between the catalyst and the activated

did not react ad a// with CCl,, whereas benzene

substance had nothing to do with the actual catalytic action (Ree.
23,104 (1904)) and that, when the catalyst does not unite with one
of the substances present in the reaction, we are dealing with catalytic
action in its purest form (Rec. 24, 10 (1905)).

Thus by means of the inductive method, | came to the conclusion
that the formation of a compound with the catalyst did not give an
explanation of the catalytic action as such, and that with this the
theory of the intermediate products exploded.

2. I have also tried to demonstrate subsequently by means of the
deductive method that the formation of a compound of substance and
catalyst must necessarily lead to a partial paralysis of the latter
(Proc. 1907 p. 613; 1909 p. 418).

Hence, if we wished to arrive at a satisfactory explanation this
had to be looked for in what happened before there is any question
of a compound between catalyst and substance. When the catalyst
draws near to the activated substance a phenomenon ought to take
place partaking more of a disruption or a dislocation than of a union
(Gedenkboek vAN BeMMELEN p. 386, Rec. 29, 87 (1910)),.

I have then demonstrated (Proc. 1909 p. 419; also Rec. 32, 1
(1913); Chem. Weekbl. 7, 121 (1910); Rec. 29, 86 (1910)) that a
catalyst like AICi, exerts indeed a dissociating influence on the
chlorides which it activates; chloral was resolved into CO, HCl and
©,Cl,; trimethylacethyl chloride into carbon-monoxide, HCl, and
isobutene, ete.

But here it transpired also that even now the explanation was
not given, because the action had been too violent; instead of the
to be expected condensation products with benzene there were
obtained in similar cases, either the decomposition products or the
condensation products of these molecule residues with benzene. Thus,
from SO,Cl, and the benzene hydrocarbons were generated relatively
very small quantities of sulphones compared to large quantities of
sulphinie acid and chlorine derivatives; owing to too great an aciivily

Proceedings Royal Acad. Amsterdam. Vol. XVII.

548

the catalyst had disrupted the SO,Cl, into SO, and Cl, which were
now subsequently influenced catalytically (Rec. 30, 381 (1911)).

The catalytic action proper can, therefore, be no union, because
in that compound the catalyst is paralysed; it also cannot be a
dissociation because the substance is then too much attacked, hence,
it must be an intermediary influence.

I have called the latter a dislocation or disruption (Ree 80, 88
(1911) dating from Sept. 1909) in order to demonstrate that there
certainly does exist an influence, but that this should effeet neither
union or dissoeiation if it is to be considered as a purely catalytic
one. In order to more sharply confirm experimentally this result
obtained, the transformation of chloral into metachloral under the
influence of diverse catalysts was submitted to a closer investigation. *)

This system was chosen because it had been shown that:

1st it is an equilibrium between two substances, therefore a very
simple ease because we are only dealing with the transformation of
one substance into another one.

2nd this equilibrium is situated in a readily attainable temperature-
zone, whereas the properties of monomeride and polymeride differ
rather strongly, so that the specific influence of the catalyst may
come perceptibly to the fore.

394 That the monomeride itself is a supercharged molecule, so
that it was to be expected that the action of the catalyst would be
a pronounced one.

In fact it could now be demonstrated that the equilibrium
was attained rapidly only then when the activator was present in
small quantities and had not perceptibly united with one of the
modifications.

If the catalyst (pyridine) was retained (absorbed) in the colloidal
polymeride the equilibrium set in, but in the hquid phase of the
monomeride the reaction ceased.

If the catalyst combined with one of the components (the mono-
meride) the equilibrium was shifted in the direction of that component.

If, finally, the action of the activator was stronger still, the split-
ting products were obtained only.

About the same time, S. C. J. Outvier (Diss. Delft 1913, Proe.
1912 and R 88, 91 (1914) had finished a dynamic research on the
action of bromobenzenesulphochloride on some benzene-hydrocarbons
under the influence of aluininium chloride.

Whereas the researches had been as yet of a qualitative character
it could now also be demonstrated quantitatively that the retention

1) KR 32, 112 (1913).

549

of the eatalyst in the sulpho-chloride or in the sulphone caused a
partial paralysis, as the reaction proceeded much more rapidly the
moment a small quantity of the catalyst in the solution was present
in the free state.

Also, could it be deduced sharply from the progress of the reaction
(Proe. 1913 p. 1069) that this could be explained satisfactorily only
then when the activating action was sought in) what happened
between benzene on one side and chloride + catalyst on the other
side before they had undergone chemical transformation.

Hence, it was proved experimentally also here that the most important
stage of the catalysis is that which takes place before the union.

3. If we now consider what can be the significance of the
removal of the catalysis to the pre-stage of the reaction, it should
be remembered that in view of Ostwatop’s definition a catalyst should
be a substance unchanged in quantity and quality after the reaction.

Guided by this definition we may during the reaction assume all
kinds of material and energetic changes if only the condition is
satisfied that the catalyst remains unmodified before the beginning
and after the end of the reaction.

If now, however, we look for a further explanation, that is to
say, penetrate further into the mechanism of a reaction, we notice
that somewhere during the reaction a catalyst can no longer satisfy
that definition.

Hence, a catalyst can never remain unchanged during the entire
course of the reaction; an ideal catalyst exists no more than an
ideal gas or an ideal dilute solution, but for all that we have been
able to make excellent use of the notion.

Now, a substance will approach this ideal condition all the more,
the smaller the material or energetic displacements will be and it
is plain without any further evidence, that similar very small changes
will just take place on the approach of the catalyst to the bonds to
be activated.

When there the action ceases, we can understand that these
shiftings may be so small that they elude observation (so that for
instance, apparently a same equilibrium is reached under the influence
of diverse catalysts, which in reality cannot be the case.)

4. If now we want to get a concrete conception of these exceed-
ingly small actions, which in the catalysis are both satisfactory and
authoritative, we may consult the modern views on our atomic.
world.

550

It is supposed that the atoms consist of (or at least are populated
by) electrons and that they hold together by means of force regions
between these corpuscles; the catalytic action may then be deseribed
as a change of these force regions on the approach of the catalyst.
If this is so, we have in the pure photocatalysis the simplest
catalytic actions and the study of these phenomena will no doubt
much deepen our insights. *)

On penetrating further into the phenomena in general we are
obliged to resolve the substance into steadily decreasing units and
the same has happened with the special phenomena called catalytic;
here it will just be shown that what takes place in the atoms will
be of preponderating importance. But just as we have not been able
to find the ideal catalyst among the atoms, we cannot expect to
meet it among the electro-magnetic equilibria-perturbations, only
the limit of our insight in the catalytic phenomena has advanced
a step.

Il.

1. During this mainiy inductive development of my ideas my
pupil H. J. Prtxs had found a synthesis of chloropropane derivatives
and I advised him to couple this experimental subject with a survey
of the different cases in the reaction of FrispeL and Crarts. *)

With this, however, he did not content himself, but starting from
the “Principle of Reciprocity” he has endeavoured to furnish an
explanation of the catalytic phenomena in general, with the reaction
of Friepet and Crarrs as a special case.

The result of this is given in his dissertation (“Bijdrage tot de
kennis der katalyse’, Delft 1912) and supplemented with a few
subsequent articles (Journ. f. pr. Chem. N. F. 89, 425 (1914);
Chem. Weekbl. 11, 474 (1914).

In order to reproduce Prins’s intention in the simplest possible
manner, | will quote a few parts of his deduction, taking the liberty
to omit the, in my opinion, non-essential matter.

1) The simplest case is the photocatalytic change of a monatomic element.

2) The reaction of FR. and Cr. offers us already a great diversity of catalytic
reactions, because AICI; can form all kinds of compounds. Only in such cases
where it unites neither with the initial products nor with the end product, or attacks
this secondarily do we approach a case ef pure catalysis.

The number of these cases is very small, the chlorination of benzene is a very
appropriate example thereof; here the quantity of the catalyst is minimal indeed
(see further)

The axioms which are more particularly applicable to the cata-
lysis are:

“When... the one exerts an influence on the other, this latter...
is changed by the first...

“If in the calculation of one of these the change may be neglected
we may speak of a one-sided influencing, which, however, as such...
may not be considered one-sidedly (dissertation p. 4—5).

and subsequently :

“If we consider the possible relation of two substances (whether
element or compound) three stages are to be distinguished therein’.

“J. The stage of the relative inertness. In this stadium even
the catalytic influence is imperceptible, whilst there is no question
of a chemical compound.

“2. The catalytic stage’) in which occurs also the mutual acti-
vation. In this stage the catalytic actions are enacted.

“3. The reaction stage in which appears an intra- or extra-
molecular reaction”.

The catalytic stage forms the bridge between the inertness and
the chemical compound. In each chemical reaction all three stages
are gone through.

By varying the conditions we can, however, cause the influencing
to be confined to the second stage’. (Chem. Weekbl. 11, 475,
also Journ. f. pr. Chem. N. F. 89, 448 (1913).

2. Prins starts from the general thesis that on interaction, there
takes place a change in two conditions, which will be least powerful
the moment it begins to reveal itself.

This stage lies, chemically speaking, in the dissociation region
where the free energy of the entire system approaches to zero
and is called by Prins the catalytic stage.

In this catalytic stage there is really no question of a catalyst
in the sense of OstwaLp; we are dealing with a change of condition :
AZB which taken by itself can take place more or less rapidly.

Being in the catalytic stage does not at all imply, in my opinion, that the
changes must take place rapidly; this depends on the nature of the change
(chemically speaking on the nature of the atoms or atomic groups which in the
transformation play a role in the first place).

If, for convenience sake, we call A and B two molecules. one
of these molecules, in a reaction in which the other one (with its

1) In order to prevent confusion it would be better to speak of the activating
stage. (PRINS also points out that the word “activator”? expresses his ideas better
than catalyst).

552

specific atomic group) occurs as a component, will be a catalyst
in the sense of OsTWALp.

BSC A—>D

N N
A B

The above symbols represent this explanation from which we gather
that the change of the’free energy in so far as it concerns the catalyst
approaches in the pure catalysis to zero and wherewith we also wish
to express that the catalyst is in faet more a change of condition
than a substance. ,

In the positive catalytic action the equilibrinm A <> Bb will set in
much more rapidly than the reaction B—+C or A—D and thus
cause or accelerate the same.

Hence an ideal catalyst, according to this deduction and in connexion with
OstwWatp’s definition, is a substance which undergoes with one of the to be
activated substances (or bonds) such reciprocal action that in the latter

system the thermodynamic potential and chemical resistance simultaneously
approach to zero.

As it concerns here particularly the bond that is being activated,
the other moleeule wili also be more or less influenced; this we
notice immediately when we remember that intramolecular displace-
ments come under the same point of view.

Hence, we will obtaim the maximal catalytic action when, with
the catalyst (for instance Bb) we approach as closely as possible the
catalytic stage in regard to A as well as D.

The chlorination of benzene again presents us with a suitable
meaning example to elucidate the intention of this thesis.

Both chlorine and benzene are in regard to AICI, in the catalytic
stage; they are both rendered active without forming a compound.

As soon as we replace benzene by nitrobenzene the action ceases
at the ordinary temperature because A/C/, forms a solid combination
with nitrobenzene so that these two are, in regard to each other,
not in the catalytic stage and because AICI, cannot any longer
activate the chlorine simultaneously.

At a higher temperature the chlorination starts; we may assume
that the system A/C7,NO,C,H, is then again approaching the
catalytic stage.

It is, however, self-evident that a case like the chlorination of
benzene is rarely met with; as presumably somewhat similar cases
I mention: all ionreactions in aqueous solutions; the union of
hydrogen and oxygen and the decomposition of hydrogen peroxide

on or in platinum; the transformation: aldehyde = paraldehyde
under the influence of sulphuric acid ete.

Much more frequent will be the cases. such as in the chlorination
of nitrobenzene, where the catalyst is found, in regard to one of
the substances, a good long way over this most favourable stage ;
in that case it will have united with one of the components to a
more or less firm compound.

The sulphone formation from bromosulphone-chloride and benzene
under co-operation of A/C7, is an illustrative instance hereof:

The A/C/, is combined with the sulphone-chloride and is, therefore,
in regard to the chloride, already far removed from the catalytic
stage, at 25° it is however not completely paralysed, as according
to the course of the reaction it is still capable of activating the
second molecule (benzene).

The sulphone formed now also unites with A/C/, and now it
appears also from the course of the reaction that it keeps on activ-
ating the benzene, but is, however, no longer capable of influencing
the sulfone-chloride, for an excess of the latter exerts no influence
on the reaction velocity. (Otivirr and Borseken, Proc. 1913 1. ¢.).

From this case it is shown how complicated this reaction may
become when in the reaction mixture different substances are present
which paralyse the catalyst more or less, and that only a clear
conception of the catalysis enables us to interpret the observations
satisfactorily.

Represented symbolically, we thus have here (when we assume
that the HC/(D) does not interfere, which has also been proved by
OLIVIER) :

Rese Bees Cee 1)
ae ae
So

The A/C/, united to C (the sulphone) can no longer reach A (the
sulphonechloride), only the A/CZ, united to A itself can still activate
the S-C7 bond, but much less so than free A/C/,; only the benzene
(B) is still attainable for the A/C/,.

I want to observe here that the paralysis starts here, presumably,
from the SO,-group, because this occurs in the sulphonechloride as
well as in the sulphone.

These are just the cases, wherein the catalyst is united with one of the
starting products, but is not entirely paralysed thereby, which have
originated the theory of the intermediate products.

By removing wilfully from the most favourable catalytic stage

554

(for instance by lowering the temperature) similar coumpounds have
often been met with and if was imagined that the explanation of
the catalytic phenomena had thus been found.

Now, however, it is evident that the explanation is not given by
the formation of these compounds, but should be found before the
formation and that the best catalysts will be those whose dissociation
equilibrium extends over as large as possible a region of tempera-
ture and pressure, without any compounds being formed.

3. In this manner, ascending by the inductive method from the
special case of the reaction of Friepen and Crarrs (BorseKEN) and
descending by the deductive method from the general principle of
reciprocity (H. J. Prins), we have come to the conclusion that
the catalytic action is situated in the pre-stage of the chemical
wnton,

It is evident that with this result no explanation has been found
in the sense that now everything is completely elucidated.

Yet, in my opinion, owing to the sharper definition of the con-
ceptions the whole field is easier to survey (Prins le.) and the
special cases are more readily understood, also a fundament has
been given on which we can pursue our researches with a greater
certainly.

These in view of the further elucidation will have to move in
two directions.

Ist. It must be ascertained, as has been already done in some
cases (L¢.), in how far the change in velocity is connected with the
shifting of the catalyst and activated bonds in the dissociation region.

With this may be coupled systematic researches as to the most
suitable catalysts for specified reactions, (for instance on metals which
are in a rapidly setting in dissociation-equilibrium simultaneously
with N, and H, at a low temperature in view of the ammonia
synthesis; or on carbonates which in view of the ketone synthesis
from acids according to Sapatier and SeENDERENS must, at about
300°, be with those acids in the same favourable conditions).

2ed, Those catalytic actions must be investigated where very sraall
evergy shiftings are concerned; to this appertain in the first place
the photocatalytic phenomena.

The first series of researches are of a more direct practical result;
the second series, on the other hand, are of a more penetrating
nature, the object being to attack the catalytic phenomena in their
last recess.

Delft, June 1914.

ayaa)

Chemistry. — ‘Researches on the Temperature-coefficients of the
Sree Surface-energy of Liquids between — 80° and 1650° C.:
VIL. The specific surface-energy of the molten Halogenides of
the Alcali-metals.” By Prof. Dr. F. M. Janerr. (Communicated
by Prof. HaGa).

§ 1. Notwithstanding the original intention to publish the results
of the measurements concerning the temperature-coefticients of the
free surface-energy of molten salts at the same time as the deter-
minations of the specific gravities of the investigated salts at different
temperatures, and in this way to give completely all data, necessary
for the calculation of the temperature-coefficients of their molecular
surface-energy, — it seemed desirable on account of the present
precarious conditions, to resolve already now on the publication of
the results hitherto obtained, and relating to the change of the specific
surface-energies of {hose salts with the temperature of observation.
The present uncertainty about the moment, when the now stopped
experiments, necessary for the determination of the specific weights,
again may be resumed in future, makes it perhaps desirable to
publish already now the available data of the free surface-energy of
some forty salts, and to draw the attention on this occasion to some
general conclusions, relating to these measurements.

§ 2. In this connection it is perhaps of interest to mention here
also some details concerning our original tentatives, to reach the
proposed aim by means of the method of capillar ascension-measure-
ments, — notwithstanding the fact, that these experiments finally
had to be given up because of reasons already formerly explained ');
these details doubtlessly can be of use for later investigations to
be made in this direction.

Originally the investigated salt was introduced into wide tubes of
heavily fusible /ena-glass, provided with rounded bottoms ; the tubes
were heated in a bath of a molten mixture of potassium-, and sodium-
nitrate, either by means of gas, or better by electrical current. The salt-
mixture was filled into an iron cylinder, outwardly lined with thick
asbestos ; its wall was provided with two diametrically opposed,
narrow windows, which were closed by glassplates, fastened by
means of asbestos-covered iron-frames. Through these planeparallel

1) F. M. JAr@rr, These Proc. Comm. I. (1914).

556

windows the desired observations were executed by means of a
telescope; the beight of ascension in the capillary tubes was read
upon a perpendicularly divided seale. The liquid salt in the surround-
ing bath was continually stirred; an arrangement was made to
prevent as much as possible the annoying currents of hot air cireu-
lating before the windows.

In all these experiments it was stated very soon, that the investi-
gated salts, when melted in the glass-tubes and on cooling again
solidifying therein, made the tubes in most cases crack ; or at least
they appeared on renewed heating to get soon unsuitable and badly
damaged, thus a substitution of the tubes by new ones being necessary
after each experiment.

After many attempts, the tubes were arranged finally in the fol-
lowing way, to prevent this effect. AB (fig. 1) is a tube of Jena heavily
fusible glass, which has a conieal nar-
rowing at a, and a sideway tube e
with stopeock d; the wider tube ean
be closed at its upper end by means
of a stopper h, provided with the
stopcock C. Just above the round
bottom of the tube 5, a small plati-
num crucible 7’ of about 1 cem.
volume, hangs between three strong
horizontal platinum-wires ; they are
either melted into the glasswall of
the tube, or they can be fixed to a
platinum-ring, supported by three
elevations in the wall of the tube.
If in the last mentioned ease the

tube 6 at the same time is arranged
in such a way, that e.g. just below
e the two parts of it can be put
together by means of a ground col-
lar, it will thus be possible eventu-
ally to take the platinum-ring easily
from the tube, and to restore it again
after thoroughly cleaning the different

parts of the apparatus. In every case
the platinum-crucible 7’ needs to be
fixed into the tube as centrally as
possible. The narrowing at a is ground

557

conically ; the piece 4 (also conically shaped, ground and enlarged)
of the heavily fusible, capillary glass-tube, can just be fixed into it;
the capillary tube thus has the form represented in fig. 1, and it is
cut to such a length, that it can be easily caught with a pincette
from above through the hole 4, while at its other end it reaches
just to a little above the bottom of 7, if 6 is caught by the collar
a. The enlarged part of is provided at its outward side with two
very fine, vertical canals, which thus have the function of capillary
connections between the spaces A and JA.

By means of a funnel with a broad and long stem, the erucible

T is now filled with a sufficient quantity of the finely pulverised
and dry salt; then AZ is put into the bath, and as soon as the
salt in 7’ is molten, the carefully cleaned capillary tube is lowered
very slowly into the apparatus, until 6 is lying just in the collar a;
immediately the liquid begins to rise then into the capillary tube.
Then both stopeocks C and d are closed, after the tube being put
in such a_ position, that the capillary tube will be just vertical ;
this may be easily controlled by means of a plummet. If now the
air is eliminated from A through C, it will appear easily to let the
liquid rise into the capillary tube, because the settlement of the
pressure-differences in A and B will oceur only very slowly by the
narrow canals in 4; in this way one can try to wet the walls of
the tube by the liquid salt, and to eliminate the air-bubbles even-
tually inelosed. A superfluous rising into the capillary tube can be
stopped at any moment by means of the stopcock d. Reversely, by
sucking at d, it will be possible, if necessary, to introduce air into
the molten salt through the capillary tube, or to remove the liquid
from it; also it is possible to substitute the air in AB by a neutral
atmosphere, e.g. by nitrogen or another gas, if desired. The experi-
ment being finished, the capillary tube 6 is removed first; the salt
will afterwards solidify in 7 without causing the cracking of the
olass-tube. In such a way several experiments can be made by means
of a single apparatus.

§ 3. Although this method of operating can be recommended in
such cases as in principle a very suitable one, the experimental
difficulties however appeared to be of a rather appreciable magnitude.

One of the chief difficulties was the elimination of the very small
air-bubbles from the liquid in the capillary tube, which appeared to
be transported into it, whenever the liquid begins to rise into the
narrow tube. Notwithstanding all care, this could not be completely
prevented, and the column of liquid then appears as if broken into

558

a great number of pieces. It is extremely difficult, again to eliminate
such transported air-bubbles, even in repeating the above mentioned
way of rising and falling of the liquid in the capillary tube for a
number of times. Almost quite impossible is the elimination of the
air, if the wall of the tube moreover is attacked by the molten salt,
— this wall becoming more or less rough by it: the air-bubbles
will then persist in sticking to the narrow canal.

Moreover the microscopical control of the glass-tubes proved
doubtlessly that the walls of it were attacked by the molten salt
almost always seriously te a more or less extent; this faet, in con-
nection with the just mentioned difficulties caused by the not
removable air-bubbles and the impossibility to determine sufficiently
the exact situation of the surface of the liquid in 7’, were the chief .
causes why these tentatives finally had to be stopped. In some cases,
e.g. in that of sodiumehromate, we could obtain rather reliable data ;
but e.g. with lithiumsalts, which will always attack the glass in a
high degree, and just so in the case of silvernitrate, only very un-
trustworthy numbers could be obtained. It appeared moreover to be
very difficult, to keep the temperature constant along the full length
of the capillary tube; this can soon be controlled by means of a
set of very small thermometers, placed within Z at several distances
from the bottom.

§ 4. After this experience we thought it adviceable to abandon
the said method completely. All numbers here given therefore are
collected after the method formerly described by us in detail’);
they relate to the purest salts. For the details of these experiments
the reader is referred to Comm. I of this series.

§ 5. Measurements of molten Alcali-halogenides.

This series includes the following salts: The Flwordes and Chlorides
of Lithium, Sodium, Potassium, Rubidium and Caestum, and the
Bromides and Lodides of Sodium, Potassium, Rubidium and Cuestium.
The preparation of the anhydrous bromide and iodide of lithium
gave hitherto no good results, because of the hydrolysis caused by
heating the crystallized, hydrated salts.

1) F. M. Jaraer, loco cit. 335—348.

Lithiumfluoride: LiF.

Maximum Pressure
Surface-tension
Bere = = = z in Erg.
: in mm. mer- ‘ , pro cm».
cury of 0° C. in Dynes

868.5 7.098 9463 249.5
897.6 7.021 9360 248.0
944 6.890 9186 242.3
984.6 6.770 9026 238.3
1029.4 6.634 8844 233.5
1065 6.525 8699 229.8
1116.5 6.323 8430 222.7
1155.5 6.170 8226 217.4
1208 5.976 71967 210.6
1270 5.700 7599 201.1

Molecular weight: 25.99.

Radius of the Capillary tube :0.05240

em: at 19° €:
Depth: 0.1 mm.

The salt melts at 840° C.; at 1150° it evaporates already rather
rapidly, and above 1270° so fast, as to make measurements
useless. The vapours show alkaline reaction.

Il.

Lithiumchloride: LiCl.

}
|

Maximum Pressure

| Surface-tension

henperetire | hau Se hes 32 % in Erg.

| in mm. mer- ; pro cme.

| cury of oo c. | Dynes |

— — al oe = =
611 | 3.928 5237 137.8
640 | 3.859 5145 135.4
680 3.786 5047 132.9
734.5 3.668 4890 128.8
775.5 3.580 4713 125.8
813.7 3.504 4672 123.2
860.1 3.410 4546 119.9
914.8 3.300 4400 116.1
967.8 3.199 4265 112.6
1021.9 | 3.082 4109 108.5
1074.6 2.976 3968 104.8

Molecular weight: 42.45. Radius of the Capillary tube: 0.05240

The salt melts at 608° C.; at 960

Gin: ath192 G.
Depth: 0.1 mm.

it begins to evaporate read-

ily, and above 1080° so fast, that exact measurements become
almost impossibie. The sublimed salt has a feeble alkaline reaction.

Ill.

Sodiumfluoride: NaF. |

Maximum Pressure
. Surface-tension
elas Ee 7 pl" eet eel z% in Erg.
: in mm. mer- : pro cm?.
cury of 0° C. in Dynes.
fo}
1010 5.685 71579 199.5
1052.8 | 5.570 7426 195.5
1097 5.445 7259 191.2
1146.7 5.290 | 7053 185.8
1189 5.136 6847 180.5
1234 5.019 6691 176.4
1263.2 4.922 | 6562 173.1
1313 4.761 6347 167.5
1357.3 4.628 | 6170 | 162.9
1405.3 4.480 | 5973 157.8
1456.4 4.330 | 5773 152.5
1497 4.220 5626 148.7
1546 4.070 | 5426 143.5

Molecular weight: 42.0. Radius of the Capillary tube: 0.05223 cm.
Depth: 0.1 mm.
The salt melts at 990° C. At 1360° C. appreciable vaporisation
sets in; at 1450° C. this occurs very rapidly.

IV.
Sodiumchloride: NaCl.

Maximum Pressure 7 :
Temperature << _ = ere eee es Surface-tensiony
ee in mm. mer pro em?
In 5 P= . | +
euny, of, ONG: in Dynes. |
802.6 3.580 4772.9 113.8
810.5 | 3.572 4162.2 113.5
820.8 | SE5O2 4735.5 112.9
832 3.520 4692.9 111.9
859 3.457 4608.9 | 109.9
883.2 } 3.401 4534.3 108.2
907.5 3.345 4459.7 106.4
930.6 3.285 4379.7 104.5
960.5 3.227 4302.3 | 102.7
1999.5 Deloe 4175.6 | 99.7
037 3.047 4062.3 97.0
1080 2.951 3934.3 94.0
1122.3 2.864 3818.3 91.3
1171.8 2.761 3681.0 88.0
| |

Molecular weight: 58.46. Radius of the Capillary tube: 0.04736 cm.
at 18° C. Depth: 0.1 mm.

The pure salt melts at 801° C.; at 1080° it begins to evaporate
already rapidly, at 1150° C. very rapidly. Between 801° and 859° C.
the coefficient of ~ seems to be about 0.57 Erg., and to increase
with rise of temperature. The mass shows in water afterwards a |
strong alkaline reaction. |

561

Sodiumbromide: NaBr.

| : z Sees
|

Maximum Pressure |
| Surface-tension

|
|
| Temperaiure = | zi Erg.
| | in mm. mer- : *
| | cury of 0° C. oe eMeS |
| | “De |
760.9 3.011 4015 105.8
809.5 2.928 3904 102.9
851.9 2.834 3778 99.6
896.8 2.737 3649 96.2
941.5 2.640 3520 92.9
984.5 2.556 3408 90.0
1029.4 2.449 3265 86.2
1073.5 2.384 3178 84.0
1116 2 302 3069 81.1

1165.7 2.214 2952 78.0

| Molecular weight: 102.92. Radius of the Capillar tube: 0.05240
| cm. at 19° C.
| Depth: 0.1 mm.

The salt melts at 768° C.; it begins readily to evaporate at
10002 C., and free bromine can be observed then. The sublimed
salt possesses alkaline reaction.

VI.

Sodium-iodide: NaJ.

Maximum Pressure

Surface-tension
ee sraneme|t fain Ere
: : " é pro cm2,
eirynet oie in Dynes
| |
705.5 2.438 | 3250 85.6
746 2.388 | 3184 83.9
815.5 2.291 | 3054 80.5

860.7 2.209 | 2945 17.6

Molecular weight: 149.92. Radius of the Capillary tube : 0.05240
cm. at 19° C.
Depth: 0.1 mm.

The salt, which melts at about 660° C, evaporates soon to a
high degree, and free iodine is observed. The sublimed salt
reacts somewhat alkaline.

562

VII.

Potassiumfluoride: KF. |

Maximum Pressure
y | Surface-tension
Tene |= ee
in mm. mer- | pro cm¢.
cury of 0 C. in Dynes
912.7 4.123 | 5497 138.4
961.5 4.024 | 5365 135.2
1015 3.898 | 5197 131.0
1062 3.790 5053 127.4
1097 3 701 4934 124.5
1146.5 3.564 4752 119.9
1185 3.450 4600 116.1
1234 3.336 4448 PLES
1275 3.225 4300 108.6
1310 3.116 4154 104.9

Molecular weight: 58.1. | Radius of the Capillary tube: 0.05002
em. at 18° C.
Depth: 0.1 mm.

The salt melts at 860° C. At 1140° C. it begins to evaporate
distinctly, at 1180° C. this goes on already rapidiy, while acid
vapours are set free.

VIII.

Potassiumchloride: KCl.

Maximum Pressure

Temperature es eee ee eee meetin
in ° C. in mm, mer- = : a
cury of 0° C. | in Dynes. pro cm*,
799.5 | 3.015 4019 95.8
827.1 2.957 3942 94.0
861.5 2.873 3830 91.3
885.1 2.819 3758 89.7
908.5 2.768 3690 88.0
941 2.697 | 3595 85.8
986 2.582 | 3442 | 82.2 4
1029 | 2.484 | 3311 | 79.1
1054 | 2.425 3233 | dee
1087.5 | 2.361 3147 | Tei?
1103.6 | 2.313 | 3083 IBIS
1125 PPA 3033 72.5
1167 2.182 2909 69.6

Molecular weight: 74.56. Radius of the Capillary tube: 0.04736 cm.
atgloanG,
Depth: 0.1 mm.

The compound solidifies after heating above its meltingpoint

during 4 hours, at 768° C. It evaporates at 980° already appreci- |

ably, at 1160 very rapidly. The vapours are acid, while the soli-
dified mass shows in water alkaline reaction. The valves of the

maximum pressure appear to decrease gradually, as a result of |
| continuous heating of the molten mass above 1100? C.

563

IX.

Potassiumbromide: KBr. |

Maximum Pressure |
Temperature | . 7 SUP AES et sion |
in® C. ha Gaia
in ; - ‘ p 5
ane 0G. in Dynes
775° 2.702 3602 85.7
798 2.642 3522 83.8
826 2.585 3446 | 82.0
859 2.504 3338 719.5
886.5 2.450 3266 71.8
920 2.376 3167 715.4

Molecular weight: 119.02. Radius of the Capillary tube: 0.04728
cm. at 15? C.
Depth: 0.1 mm.

The salt melts at 734° C. At 825° C. already a decomposition
under liberation of hydrobromic acid and bromine is observed;
| at 940° C. the salt evaporates so rapidly and decomposes to
such a degree, that further determinations seem to be useless.

Potassium-iodide: KJ.

Maximum Pressure H
Surface-tension
Homperstace = a7 Ha Erg.
? in mm. mer- : pro cm*.
cury of 0°? C. in Dynes

ceils 2.372 3162 15.2

764 2.274 3031 Teal

812 2.183 2910 69.2

866 2.106 2807 66.8

873 2.097 2795 66.5

Molecular weight: 165.96. Radius of the Capillary tube: 0.04728
Chiat 15S;
Depth: 0.1 mm.

The salt melts at 681.95 C. At 750° C. already it begins to
evaporate very appreciably, while iodine is set free. For again
higher temperatures the determinations can hardly have any
essential significance.

37
Proceedings Royal Acad; Amsterdam. Vol. XVII.

564

XI.

} Rubidiumfluoride: RdbF.

Maximum Pressure 7
Temperature ——— 2s

Surface-tension |

|
|

|
|
: : z in Erg.
° | by
| ee | in mm. mer- | a anees | pro cm?
| | cury of 0° (G, | ye |
= = = : —— 1 — a ———
| 802.6 3.630 4839 ee
| 847.2 3.461 4614 121.3
| 886.8 oroel 4436 116.7
| 936 3.220 4293 | 113.0
985.6 3.102 4136 108.9
1036.7 2.997 | 3996 105.2

1085.4 | 2.910 3879 102.2

Molecular weight: 104.45. Radius of the Capillary tube: 0.05223
cm. at 19° C.
Depth: 0.1 mm.

The salt melts at 765° C. At 1000° C. it begins already to
evaporate in an appreciable degree.

XL.

Rubidiumchloride : RbC/.

Maximum Pressure H ae
é cs urface-tension
Teepe rate . = ee apeaniienes
| : in mm. mer- . | pro cm?.
cury of 0? C. in Dynes |
o

750 PAs BY 3642 95.7
769.7 2.689 3585 94.2
828.2 2.540 3386 89.0
880 2.410 3213 84.5
922.7 ZEB 3084 81.1
933 2.278 3037 719.9
961.5 2.205 2940 Tiles
994 2.130 2840 74.7
1036.6 2.030 2706 | es
1088.5 1.900 2533 66.7
1150 1.749 2332 61.4

Molecular weight: 120.91. Radius of the Capillary tube: 0.05223
cm. at 19° C.
Depth: 0.1 mm.

The salt melts at 720° C.; at 950° C. it begins to sublime
already distinctly. Analysis gave: 29.25%, Cl and 70.75%, Rb,
proving satisfactorily the purity of the salt.

565

XIII.
Rubidiumbromide: Rb£Er.
Maximum Pressure S
: urface-tension
Peenealane wees cin Erg.
in mm. mer- . pro cm’.
cury of 0° C. zy Dynes
| ————————————————— ———— ——— SSS = =—™ —=
729.2 2,504 3338 87.7
7719 2.401 3201 84.1
831 2.301 3068 80.7
884.3 2.200 2933 ile’
943.5 2.084 2718 (Breil
985.7 2.000 2666 70.2 |
1041 1.900 2533 66.7
1121 1.724 | 2298 60.6 |
|

Molecular weight: 165.37.

em. at 19°? C.

Depth

: 0.1 mm.

Radius of the Capillary tube : 0.05223

The salt melts at about 685° C.; at 940° C. already it begins to subli-
me, while bromine and hydrobromic acid distinctly are observed too.

XIV.

Rubidium-lodide: RbJ.

Maximum Pressure 1

Surface-tension

ee a Bee.
‘ in mm. mer- é : pro cm”,
cury of 0° C. in Dynes, |
|
is} |
673.4 2.268 | 3024 79.4
721.8 2.165 2886 15.8
771.5 2.061 2748 PAE
822 1.956 2607 68.5 |
869 1.857 2476 65.1
918 Nalos 2344 61.6
968 1.663 | 2217 58.3
1016 1.578 | 2104 55.4 |

Molecular weight: 212.37.

Radius of the Capillary tube : 0.05223

em. at 19° C.
Depth: 0.1 mm.

The salt melts at 642° C. At 900° C. evaporation happens
already distinctly; at 1000? C. it is so fast, that the measure-
ments are influenced by it in a most troublesome way, the values
of H seeming to be increased by the heavy vapours.

566

XV.

Caesiumfluoride: CsF.

| Maximum Pressure H é
urface-tension
femperaiue | ai Erg.
; in mm. mer- : pro cm?
| cury of 0? C. in Dynes ,
| ° i |
| 722.5 3.116 4154 104.5
768.7 3.011 4014 101.0
825.6 2.872 | 3829 96.4
877.3 2.748 3664 92.3
929.7 | 2.624 3498 | 88.1
985 2.510 | 3346 84.3
1042 2.418 | 3224 81.3
1100 2.346 3128 78.9
|

| Molecular weight: 151.81. Radius of the Capillary tube: 0.05002
cm. at 18° C.
Depth: 0.1 mm.

The salt melts at 692° C. At 990° C. it begins to evaporate
distmcetly.

XVI.

Caesiumchloride: CsCl.

| Maximum Pressure H ;
| Temperature Suriace tension
| aa | ee
| in mm, OC. | in Dynes
|= : — |
| 663.7 2.660 | 3546 | 89.2
717 2.560 3413 85.9
7711 2.440 3253 81.9
829.6 2.315 3086 | dilotl
881 | 2.193 2924 Sea
934.2 2.075 2766 69.7
979 | 1.975 2633 66.4
1034.7 | 1.833 | 2444 61.6
1080 1.673 2230 56.3
| |
Molecular weight: 168.27. Radius of the Capillary tube: 0.05002
cm. at 18° C.
Depth: 0.1 mm.

The salt melts at 632? C. At 925° C. it begins to sublime; at
1000° C. the evaporation occurs already very rapidly.

XVII.

Caesiumbromide: CsBr.

| Maximum Pressure H erate ea
urface-tension
meuTuevalure | - | - z in Erg.
: | in mm, mer- % | pro cm2, +
cury of 0° C. in) Dynes |
i S.. |
a A ee ; |
657.7 2.439 | 3252 81.8
693.6 2.351 | 3134 | 718.9
7152.5 2.231 2974 14.9
807.5 2.132 | 2842 71.6
858.3 2.040 | 2720 | 68.5
915.8 1.950 | 2600 65.5
970.6 1.865 | 2486 62.7

Molecular weight: 212.73. Radius of the Capillary tube: 0.05002
cm. at 18° C.
Depth: 0.1 mm.

The salt melts at 631° C. At 900° C. it evaporates already
very rapidly, making the measurements very difficult.

XVIII.

Caesium-lodide: CsJ.

Maximum Pressure
Temperature e purlacetension
bl OG, : ara ae
mm. - : mG
cury of 0? c, | itt Dynes
653.6 2178 | 2904 | 73.1
713 2.050 2733 68.8
768 .2 1.955 | 2606 65.7
821.4 1.860 | 2480 | 62.5
879 1.762 | 2349 59.2
926 1.684 | 2245 56.6
980 1.600 2134 53.8
1030 1.520 | 2026 tl

Molecular weight: 259.73. Radius of the Capillary tube : 0.05002
emi aulsouG:
Depth: 0.1 mm.

The salt melts at 620° C. It begins to sublime appreciably
at 825° C.

568

§ 6. The temperature-cocjicients of the specific surface-energy
of the molten alcali-halogenides.

During these measurements, it became clear, that the shape of
the curves, which illustrated the dependence of % and ¢, was in
most cases much nearer to that of straight lines, than was the
ease with most of the hitherto investigated organic liquids. However
it must be remarked, that notwithstanding this, also in the case of
molten salts, the y-curves could evidently belong to every one of
the three formerly discerned possible types, while in the case of
occurring dissociation a more rapid bending towards the temperature-
axis could be stated, just as in the analogous cases formerly studied.
Because of the much greater values of the maximum-pressures
however in the here studied cases, those deviations from straight
lines come much less to the foreground. As a consequence, in thirty
cases of the about forty investigated salts, the dependence of y and
¢ could be expressed with sufficient accuracy by dimear expressions ;
for the remaining cases a quadratic expression in ¢ with three con-
stants appeared to be adapted to this purpose to a really sufficient
degree.

If ¢, is the meltingpoint of the salt, then x, above this melting-
point, can be calculated from an equation of the form:

A%=a—b(t—t)+ct—t,)’,
in whieh «@ corresponds to the value of y, at the meltingpoint. In
the following table the corresponding values of ¢,, a, 6 and ¢ for
every one of the investigated halogenides are resumed :

Formula of ates | |
the Salt. fs in°C. | i | b | e

| LiF s40 | 255.2 | 0.126 | 0

| Licl 608 140.2 | 0.076 0
NaF 990 201.6 | 0.106 0
NaCl 801 114.1 0.071 0
NaBr 768 106.5 0.069 0
NaJ 660 88.2 0.053 0
KF 858 143.2 | 0.087 0
Kel 780 97.4 0.072 0
KBr 7134 88.8 0.070 0
KJ 681 78.3 0.064 0
RbF 765 132.0 0.131 0.00012

R6éCl 720 98.3 | 0.086 0

| RobBr 685 90.7 | 0.069 | -0

| RbJ . 642 80.3 0.065 0

| CsF 692 107.1 0.088 0.00004
CsCl 646 91.3 0.077 0

| CsBr 631 83.6 0.063 0
CsJ | 620 91.6 0.056 0

569

Specific Surface-Energy
in Erg pro cm?.

760

rere
700" 750" 800° 850" YOU" 950° 100 190 TU 150 10 Ti Ta TW Ta Tere —‘emperature

Fig, 2:

Specific Surface-Energy
in Erg. pro cm2.

600° 650 100" 750 800" 850" 900° 950° 0w W050 morse 7200" +“ Temperature

Fig. 3.

Specific Surface-Energy
in Erg pro cm2.

650° 700° 750° 800°850°900' 950" 000°1050 100 1150°/200° Temperature
Fig. 4.

Specific Surface-Energy
in Erg pro cm2.

650° 100° 150° 800° 850° 900° 950" wer ese”—S heMperature
Fig. 5.

§ 7. From these data it can be deduced in the first place, that
in general the temperature-coefficients of the specific surface-energy
x of these salts appear to be smadler than for most organic liquids.
While in the last mentioned cases these values are oscillating between

0.09 and 0.18, —as the following instances may prove once more:
Acetic acid: 0.118. | Guajacol : (OISEL,

Benzene: 0.136. Resorcine- Dimethylether : 0.105.
Diethylmalonate: 0.102 Hydroquinone Dimethylether: 0.109.
Anisol: 0.114. Pyridine : 0.125.

Phenetol: 0.102. a-Picoline: 0.128.

Anethol: 0.094. Chinoline : 0.104.

— the values of 06 for these salts are situated between 0,05 and
0,09, being thus about of the order of magnitude of the coefficient
for e.g. ethylalcohol: 0,086. Only in the case of some fluorides some
numbers for 6 were found, corresponding in some degree with those
for organic liquids. (if : 0,126; RbF : 0,181; NaF : 0,106). If
attention is drawn to the much higher temperatures of observation
in the case of molten salts in comparison with those of the organie
liquids, it will be hardly permitted to conelude to a principal differ-
ence in this respect. in the behaviour of both classes of liquids; on
the other side however just with respect to these much higher

571

temperatures, the enormously high absolute values of % with these
salts, which may occasionally be more than three times that of
water, must be considered as very remarkable. In connection with
the data given above, we can moreover generally conclude:

1. The temperature-coefficient 6 of the specific surface-energy
decreases continually in the case of the four halogenides of the same
alcali-metal, with increasing atomic weight of the halogen-atom. This
rule holds evidently quite accurately in all the cases here considered.

As to the absolute values of y of these salts, attention can more-
over be drawn to the following general rules:

2. At the same temperature t, the values x for the same halogenide
of all alcali-metals, will decrease gradually with increasing atomic
weight of the alcali-metal.

3. At the same temperature ¢ the values 4, will gradually. decrease in
the case of the four halogenides of the same alcali-metal, with increas-
ing atomic weight of the halogen-atom.

These relations however do not possess a simple additive character.

Generally speaking, the Z-compounds appear to deviate more
from those of the other aleali-metals, than these from each other;
the A-, Rdb-, and Cs-compounds approach each other more, than
each of these elements do the corresponding Na-compounds, while
in the series of the first mentioned three alcalimetals, the compounds
of K and Rb appear to have the nearest analogies to each other,
Probably the liquid lithium-salts imay possess a higher degree of
molecular complexity, than the salts of the other aleali-metals.

Groningen, Augustus 1914. Laboratory for Inorganic and Physical
Chemistry of the University.

Chemistry. — ‘Researches on the Temperature-coefficienis of the
free Surface-energy of Liquids at Temperatures between
— 80° and 1650° C. VIII. The Specific Surface-energy of
some Salts of the Alcali-metals.” By Prof. Dr. F. M. Janenr.
(Communicated by Prof. H. Haga).

§ 1. As a sequel to the data published in the foregoing com-
munication, which related to the /alogenides of the aleali-metals,
the results of the measurements made with a number of salts of
the alcali-metals, which belong to some other series, are communicated
in the following pages. These measurements include the following
objects :

572

The Sulphates of Lithium, Sodium, Potassium, Rubidium and
Caesium; the Nitrates of Lithium, Sodium, Potassium, Rubidium and
Caesium; the Metaborates of Lithium, Sodium and Potassium; and
the Molybdates, Tungstates and Metaphosphates of Sodium and
Potassium.

With the exception of rubidiumsulfate, which evidently contained
some potassiumsulfate, all salts were chemically pure; the sulfates,
molybdates and tungstates were those commonly used in this laboratory
for the calibration of the thermoelements, and just the same was
the ease with lithiummetaborate. For the method and practice of the
measurements etc., we can refer to the foregoing communication.

§ 2.
I.
|
| Lithiumsulphate: Li.SO,.
Maximum Pressure 11
Temperature ¢ es ae ee | Suc eee

inne G: ae

: : pro cm?.:

E cro Oc. | in Dynes

|
ie} |

860 | 6.361 8481 223.8
873.5 6.342 8455 223.1
897 6.303 8403 | 221.8
923 6.256 8341 220.2
962.5 6.169 | 8224 | 217.4
976.8 6.146 8194 216.4
1001.2 6.099 8132 214.8
1038.5 6.027 8035 | 212.3
1057 5.987 7982 211.0 |
1074 5.953 7936 209.8
1089.5 | 5.923 | 7897 | 208.8
1112 5.879 7838 | 207.3 }
1156.5 | 5.791 7720 | 204.2 |
1167.5 | 5.766 7687 203.4 |
1183.5 eye TET 7649 202.4
1192.2 | 5.718 7624 | 201.8
1214 5.675 7566 | 200.3

cm. at 16°
Depth: 0.1 mm.

The meltingpoint is 852° C.; the salt appears to be stable up

| oe
| Molecular weight: 109.94. Radius of ane Capillary tube 0.05240 |
|

to rather high temperatures. |

573

Il.

Sodiumsulphate: Na,SO,.

Maximum Pressure .
Sui face-tension

petupera ure laa: yin Erg. |

: in mm. mer- é procm’. |

cury of 0°C. ie Dyes |

900. 6.285 8379 194.8 |
945 6.247 8329 | 189.3

990 6.209 8278 188.2 |
1032 6.149 81¢8 186.5
1077 6.088 8116 184.7

Molecular weight: 142.07. Radius of the Capillary tube: 0.04512
Ciipeat, 1628:
Depth: 0.1 mm.

The salt melted at 884° C. The molten mass, if brought into |
water, Shows an alkaline reaction, if the temperature of the |
molten salt has been above 1100° C.

ll.

Potassiumsulphate: K,SO,.

1070.2 4.080 5439 143.7
1103 4.048 5397 | 142.6
1145 3.989 5318 | 140.6
1199 | 3.878 5171 | 136.7
1247 3.762 | 5016 132.7
1305.5 | 3.651 4868 128.8
1347 3.578 4770 126.2
ile 7fil ets) | 3.529 4705 124.6
1400 3.468 4623 122.4
1439.5 3.393 4523 119.8
1462.5 3.344 4458 118.1
1490.4 3.286 | 4381 116.1
1530.3 | 3.228 | 4304 114.1
1586 | 3.130 | 4173 110.7
1656 3.020 4026 106.8

Molecular weight: 174.27. Radius of the Capillary tube: 0.05240
cm. at 19° C.
Depth: 0.1 mm.

The salt melts at 1074° C., and does not dissociate appreciably
up to 1550° C.

Temperature

Rubidiumsulphate: Rb,S0,.

IV.

Maximum Pressure 1

Surface-tension

in ° a x in Erg.
in mm. mer- : pro cm*.
cury of 0° C. in Dynes |
°
1086 3.760 5013 132.5
1112 3.681 4907 | 129.7
1144.7 3.611 4814 ies
1195 3.520 4693 | 124.2
1234.5 3.452 4602 | 121.8
1289 3.368 4490 | 118.9
1343.8 3.286 4381 116.0
1396.8 3.223 4297 113.8
1414.6 3.200 4267 | 113.1
1482 3.138 4183 110.9
1545 3.079 4105 108.9

Molecular weight: 266.97. Radius of the Capillary tube: 0.0524

cm. at 18° C.
Depht: 0.1 mm.

The salt melts at 1055° C. At about 1400° C. it begins to
evaporate somewhat faster, and sublimes against the colder parts
of the apparatus. It appears to contain some KjSQ4; analysis
gave: 37,45 % SO, and 62,56 % Rb, instead of 36 %, SO,

and 64°, Rb.

Caesiumsulphate: Cs,SQ,.

Temperature

Maximum Pressure H

Surface-tension

insos.

i L : ro cm?

} Segoe oe | cangoaces, 910g
fo}

1036 3.170 4226 111.3
1063 3.080 4106 108.2
1105 2.988 3984 105.0
1165 2.869 3825 100.8
1221 2.764 3685 97.3
1274.5 2.691 3588 94.7
1331.4 2.607 3476 91.7
1372 2.552 3402 89.8
1423 2.482 3309 87.4
1470 2.427 3236 85.5
1530 2.354 3138 83.0

Molecular weight: 361.69. Radius of the Capillary tube: 0.05223

cm. at 18° C.
Depth: 0.1 mm.

The salt melts at ca. 1015° C. At 1325° C. it begins to evaporate
in an appreciable degree; at 1440° C. very rapidly, and at nigher
temperatures it sublimes in a rather troublesome way.

Specific Surface-Energy
in Erg. pro cm?.

850° 900° 950° 100° 050° 102° 1507 200° 12501300 1950 14001950 1500 15307600 7650 770" +~Temperature

Fig. 1.

VI.

Lithiumnitrate: L7NO3.

|
| | Maximum Pressure :
Temperature ers So ee Sunlace tension
Dasccetee | 0 Er
in mm. mer- | : *.
cury of 0° C. in Dynes | |
358.5. | 3.334 | 4445 | 111.5
| 403 3.260 4347 109.1
418.2 3.240 4320 | 108.4
445.3 3.169 4225 106.0
492.5 3.069 4092 102.3
| 555.3 2.956 | 3941 99.0
| 609.4 2.872 3829 96.2

Molecular weight; 68.95. Radius of the Capillary tube : 0.05002
cm, at 18? C.
Depth: 0.1 mm.

The salt melts at 254° C. to a very thin liquid. The values
of y are evidently szmadler than in the case of the sodium nitrate.
At 600° C. already a decomposition, with oxygen and nitrous
vapours setting free, can be stated.

VIL.
Sodiumnitrate: NaNO3.
= = As “a
Maximum Pressure H ;
Temperature pe ss —— a See
ingonG:
is j in mm. mer- | <p yes pro cm?
| cury of 0° C.
———————— os 7 SS 7 —— ——— =

32195 | 3.580 4713 119.7
355 3.534 4711 118.1
396.5 3.466 4621 115.9
426.5 3.412 4549 114.2
465.7 | 3.341 4454 111.8
51a 3.253 4337 108.9
559 | 3.162 4216 105.9
601.6 | 3.086 4114 103.4
656.3 | 2.966 3954 99.4
693 | 2.889 3852 96.8
738.2 2.793 3723 93.7

Molecular weight: 85.01. Radius a the Capillary tube: 0 05002 cm.
at 18° C.
Depth: 0.1 mm.

The salt melts at 312° C. At 700° C. already it distinctly
gives off nitrous vapours and oxygen; the solidified mass gives
in water a strong alkaline reaction.

Potassiumnitrate: KNO3.

Maximum Pressure
; | Surface-tension
ceupe yale > eG EJs ea ee
: in mm. mer- . | pro cm’,
Guryioh Onn) as Dynes |

— ~~ — | — —
380. | 3.300 4400 110.4
436 3.168 | 4223 106.0
480.1 3.073 4097 102.8
534.3 | 2.942 3923 98.5
578 | 2.841 3788 95.2
628 | PS 7E%) 3646 91.6
675.4 | 2.623 | 3497 87.9
(PANG 2.506 3341 | 84.0
771.6 2.391 3188 80.2

Molecular weight: 101.11. Radius of the Capillary tube 0.05002
cm. at 18° C.
Depth: 0.1 mm.

The salt melts at 339° C. At 760° C. already a decomposition, ana-
logous to that observed in the case of the sodiumsalt, can be stated.

IX,
| Rubidiumnitrate: RbNO3.
| ane ee a PAs
Maximum Pressure H :
Temperature | __ ao ee ah Le aia
TEE : ;
es in mm. mer- | Carre pro cm?.
cury of 0? C. | Meals
| 326.5 | 3.215 | 4286 107.5
376 3.110 | 4146 104.0
428 2.982 3976 | 99.8
480 | 2.871 3828 96.1
oes 2.763 3684 | 92 8
578 2.653 | 3537 | 88.
| 625 | 2.556 | 3408 | 85.6
| 676.2 2.429 | 3238 | 81.4
| 726.2 2.316 | 3088 | riley
| |

Molecular weight: 147.46. Radius of the Capillary tube: 0.05002
cm. at 18° C.
Depth: 0.1 mm.

The salt melts at 304° C. At 650° C. it begins to decompose,
setting free oxygen and nitrous vapours.

Caesiumnitrate: CsNO3.

| | Maximum Pressure H

Temperature ¥ Surface-tension
id gs z in Erg.
| NOUS | se rae ite 3 pro cm?.
| | cury of 0° C. in Dynes
|
| ° |
| 425.5 2.743 3657 91.8
459.7 2.636 | 3514 | 88.2
5il 2.500 3333 83.7
576.5 2.366 3154 | 79.2
602 2.277 | 3036 76.3
686.4 | 2.162 2882 1a

Molecular weight: 194.82. Radius of the Capillary tube: 0.05002
cm. at 18’ C.
Depth: 0.1 mm.

The salt melts at 414° C.; just as in the case of the solubi-
lities, also in the situation of the meltingpoints of K-. Rb-, and
Cs-nitrates an evident irregularity can be stated. At 600° C.
already the molten salt begins to decompose.

or
cot hy
(eo oF)

Specific Surface-Energy
in Erg pro cm?. =

Temperature

Fig. 2.

XI.

Lithium-Metaborate: LiBO,.

Maximum Pressure H
Temperature |—— s Surtace-lensiea
ree (Cx ae a ae
in mm. mer- . :
cury of 0° C. in Dyes
fo}

879.2 7.442 9922 261.8
922 7.379 9838 259.7
967.5 7.279 9704 256.2
1011.5 7.190 9586 253.1
1054.5 7.108 9476 250.3
1097.3 7.034 9378 247.7
1149.7 6.912 9215 243.6
1198 6.800 9066 239.7
1249 6.638 | 8850 234.2
1309.3 6.399 | 8531 225.8
1355 6.252 8335 220.7
1408 6.022 | 8029 Zen
1457 5.750 | 7666 203.1
1520 5.445 7260 192.4

Molecular weight: 49.99. Radius of the Capillary tube: 0.05240
cm. at 19° C.
Depth: 0.1 mm.

The salt melts at 845° C. At 1200° C. it begins to evaporate
appreciably; the vapours show alkaline reaction (LZ0). At 1300° C.
the volatilisation of the £/,0 occurs already rather rapidly; the y-¢-
curve descends by this dissociation far more rapidly, than in
the beginning.

Sodiummetaborate: NaBOs.

Molecular weight: 66.0.

Radius of the Capillary tube: 0.05002
cm. at 18° C.
Depth: 0.01 mm.

The salt melts at ca. 965° C. At 1230? C.it begins toevaporate |
distinctly; at 1350° the evaporation goes on rapidly.

XIII.

Potassiummetaborate: KBQ,.

3829 | 96.6

Maximum Pressure 7
Surface-tension
Temperature -| yin Erg. |
i x Bll : pro cm?, |
cury of 0° C. oes Dynes |
va 3i ae i
992 | Bere) | | 4901 | 123.5
1036 | 3.341 | 4454 112.3
| 1091 | 3.062 | 4083 103.0
1142 | 2.872 |

Molecular weight: 82.1. Radius of the Capillary tube: 0.05002
cm. at 18°? C.
Depth: 0.1—0.3 mm.

The salt melts at about 946° C. The measurements were diffi-
cult by the great volatility and high viscosity of the substance.
The obtained values cannot be considered therefore as being
highly accurate.

wo
(06)

Proceedings Royal Acad. Amsterdam, Vol. XVII.

Specific Surface-Energy
in Erg pro cm?,

SCO* 830° CO* 950° 1000" 1050" T100° 7150" L200° T250°7500 FEO°F400" 450° F300 950 16000" Temperatu re

Fig. 3.
XIV.
Sodiummolybdate: Na.MoO,.
| Maximum Pressure | ,
Temperature | es SUrTaCe ener
fav SG 1m oto: pty
In mm, mer- - 50
cury of 0° C. in Dynes
698.5 6.091 | 8122 | 214.0
728.5 5.975 | 7967 | 210.0
751 5.921 | 7893 208.1
7771 5.828 7170 204.9
818.8 Heol 7675 202.4
858.5 5.657 71542 199.0
903.8 5.552 7401 195.4
948 5.436 7247 191.4
989.5 5.330 7106 187.7
1035 5.224 6966 184.1
1078.5 5.141 6854 181.2
1121.5 5.070 6760 178.8
| MARKO 4,998 6654 176.1
1212 4.947 6595 174.6
Molecular weight: 206. Radius of the Capillary tube; 0.05240 cm.
Depth: 0.1 mm.

The salt melts at 687° C. to a colourless liquid.

581

XV.

Temperature

Potassium-Molybdate: K,Mo0,.

Maximum Pressure

|
Surface-tension |
x in Erg.

in ° C | inmm. mer- |, | 3
| Giinys of 0°57 mene Dyn | LW Ate
fe}
930.6 4.310 | 5746 150.5
977 | 4.218 | 5626 147.3
1021 4.158 5543 145.2
1105 4.021 5360 140.7
1143 | 3.960 5280 138.6
1189.3 | 3.868 5156 135.5
1273 3.714 4950 130.0
1286 | 3.676 4900 128.8
1356 I) Bevesss Mel ci 123.6
1438 3.364 4483 118.0
1452.8 3.330 4440 116.9
1522.3 3.205 4273 112.5
Molecular weight: 238.2. Radius of the Capillary tube: 0.05240 |
cm, at 18° C. |
Depth: 0.1 mm.

The salt melts at 919° C.; at 1400°C. it begins to decompose
very slowly.

XVI.

Sodiumtungstate: Na,Wo0,.

: = |

Remmperatiire Maximum Pressure | Surface-tension

corr. on i = 5 | pee |

ray, | atm mers | in Dynes | > proemé |

710 Budg2m | 7909 | 993.3.) ||
719.5 5.909 | 7878 | 202.6
741 5.863 7817 201.0
788 5.718 7103 198.2
834 5.686 7580 195.2
879 5.579 7438 191.5
932 eS ii 7355 189.5
985.3 5.364 7151 184.2
1038.5 5.280 7040 181.4
1080.5 5.186 6913 178.3
1133 5.073 6762 174.6
1181.4 5.010 6679 172.4
1231.5 4.880 6506 168.0
1281.8 4.755 6339 163.8
1331.5 4.663 6217 160.6
1390.5 4.494 5991 155.0
1450 4.405 5872 152.0
1516.5 4.265 5686 147.3
1559 4.171 5560 144.0
1595 4.129 5508 142.6

Molecular weight: Radius of the Capillary tube: 0.05113
cm. at 16° C.
Depth: 0.1 mm.

The colourless, perfectly anhydrous salt melts at 694° C toa
very clear, somewhat viscous liquid, which however at higher
temperatures soon becomes much thinner.

38*

582

XVII.

Potassiumtungstate: K,W0,.

Maximum Pressure ina :
Temperature Suriac ees
in CG: ? pro! ree
in mm. mer- ‘ .
cury of 0° C. in Dynes

925 4.611 6147 161.0
969 4.410 5879 154.1
1012.5 4.305 5739 150.2
1051.5 4.173 5563 145.9
1097 | 4.056 5409 141.9
1138.8 | 3.943 5257 138.0
1183.2 3.832 5109 134.1
1230 3.720 4960 130.3
1284 3.558 4744 124.6
1322.4 | 3.449 4598 120.9
1366.5 3.379 4505 118.4
| 1408.5 | 3.259 4345 114.3
| 1458.2 3.135 4180 110.0
| 1489 3.076 4101 107.9
| 1520.3 3.010 4013 105.6

Molecular weight: 326.2. Radius of the Capillary tube: 0.05201
cm. at 17° C.
Depth: 0.1—0.2 mm.

The meltingpoint of the salt is 921° C.; even at 1500° C. the
compound does not sublime appreciably.

— —————e

Specific Surface-Energy
in Erg. pro cm?.

700

650° 700" 750" 800° 850° YOO" 950" 10001050 M0 H50° 1200 1250" 100° 13501460 14301500 19501000"

Tempe-
rature

Fig. 4,

583

XVIII.

Sodium-Metaphosphate: NaP03.

Maximum Pressure
Temperature _ | Surface-tension

in °C. | ASE

in mm. mer- : pro cm-.

cury, of 02a: in Dynes
827 5.730 7639 197.5
871.4 5.648 7538 194.8
927 52553 7403 191.6
1014 5.406 ALO2S | 186.7
1098.5 5.254 7004 181.6
1181 5.109 6811 176.6
1264.5 4.939 6584, 170.9
1317 4.814 6418 | 166.7
1434 4.511 6014 | 156.2
1516.5 4.254 5671 147.5

Molecular weight: 102.04. Radius of the Capillary tube: 0.05140
cme ablboaG:
Depth: 0.1 mm.

The salt melts at about 620° C. At 1200° C. it begins to eva-
porate considerably, and sublimes readily at higher temperatures.

XIX.

Potassium-Metaphosphate: KP0O,.

Maximum Pressure
Surface-tension
Tonperfute At nee cae =) EE = x in Erg.
, in mm. mer- ; pro cm?.
cury of 0? GC in Dynes
fe}
897 4.506 6007 155.5
942 4.395 5860 151.8
995.7 4.346 5793 149.0
1036 4.233 5643 146.1
1082 4.137 5515 143.0
1120 4.060 5413 140.3
1167 | 3.957 5275 136.8
1205.2 3.859 5145 133.5
1250 3.842 5122 130.2
1288 3.650 4866 126.3
1344.5 3.538 4717 122.5
1372 3.422 4562 118.5
1412.5 3.310 4413 114.7
1496.5 3.043 4057 105.5
1536 2.894 3858 | 100.3

Molecular weight: 118. Radius of the Capillary tube: 0.05140 cm.
Depth: 0.1 mm.

The salt melts at about 820° C.; it begins to evaporate readily |

at 1400° C,, and sublimes fast at higher temperatures,

584

§ 8. The Temperature-coefficients of the Specific Surface-energy
In connection with what was said in the foregoing communication
about the calculation of xy, at any arbitrary temperature ¢, lying
above the meltingpoint ¢, of the salt investigated, we only need to
resume here the corresponding values of ¢,, a, 6, and ¢, for each salt:

l |
Formula of |

eal entree eee | GPa Oe c | Remarks.
| - Tasso, 852° 224.4 | 0.067 0
| NaoSO4 884 196.3 0.140 0.00042
KySO, 1074 144.5 0.066 0
| RboSO4 1055 135.0 | 0.087 0.00007
| CsySO4 | 1015 113.1 | 0.087 0.00006
LiNO3 254 118.4 | 0.063 0
| NaNO; | 312 120.7 | 0.063 0
KNO3 339 112.9 | 0.075 0
| RbNO; 304 109.4 | 0.075 | 0
CsNO3 | 414 92:0 | 0.084 0 |
LiBO, 845 264.8 0.082 0 Decomposes
above 1320° C.
NaBO, 965 201.6 0.159 0
| KBO, 946 136.6 0.310 0.00053
Na,Mo0, 687 215.1 0.121 0.00009
Ky Mo0, 919 152.5 0.066 0
Na, WO, 694 204.4 0.068 0
KiWO, 921 158.2 0.083 0
NaPoO; 620 209.5 | 0.059 0
Only up to 1275°
C.; then the curve
KPO3 820 161.2 0.069 0 bends more ra-
pidly to the tem-
perature-axis.

In connection with the general rules, given in § 7 of the foregoing
communication, we can make the following remarks with respect
to the data given above.

Although in these cases also, the value of yx, at the same tempe-
rature ¢ appears gradually to decrease with increasing atomic weights
of the aleali-metals, whose corresponding salts are investigated, we
see that in the series of the nitrates, the lithiumsalt represents an
exception to this rule, because its y-t-curve lies under that of the
sodiumnitrate. It is of interest, that just in this series of the aleali-
nitrates also other deviations of the normal arrangement are found:
so with respect to the solubilities and the meltingpoints. About the
relative or absolute values of the temperature-coefficient 4, nothing
of general application can be put to the fore: evidently no simple
relations will be found here, where the structure of the salts is already
more complicated than in the case of the halogenides of the alcali-metals.

: Lab. for Inorg. and Physical
Groningen, August 1914. : J J 5 a
: ze Chemistry of the University.

Bd
Chemistry. — “A crystaliized compound of isoprene with sulphur
diowide’. By Mr. G. pé Brui. (Communicated by Prof. P. van
’ ROMBURGH).

(Communicated in the meeting of June 27, 1914).

As is known from the patent literature’) unsaturated hydrocarbons
with conjugated double bonds combine in different circumstances
with sulphurous acid. Thus, crude isoprene on shaking with an
aqueous solution of that acid yields a compound separating in the
form of white flakes.

When I mixed isoprene, prepared according to Harrigs’s method *)
(from ecarvene) and which had been purified by fractionation, the
fraction from 384° to 38° being collected separately, with an equal
volume of liquefied sulphur dioxide and left this mixture ina sealed
tube at the temperature of the room, I obtained after one or two
days a considerable quantity of a crystallized product. As a rule the
mixture soon turns brown, but sometimes it remains colourless.

Beside the erystals is always formed a viscous, white mass which
on drying gets hard and brittle. In some experiments no crystals
were deposited, but on pouring the contents of these tubes into a
small flask it instantly solidified owing to the formation of a large
number of crystals.

The crystalline product may be readily recrystallized from ether.
By repeating this operation a few times a pure, white product is
obtained melting without decomposition at 62°.5, Presence of moisture
is not necessary for the formation of the crystals, anyhow exactly
the same result was obtained with tubes filled with sulphur dioxide
dried over sulphuric acid, and dry isoprene.

The analysis gave the following results :

0.2016 grm. of the substance (burnt in a close tube with lead

chromate) gave: 0.3384 grm. CO, and 0.1107 grm. H,O

0.1612 gm. of the substance gave 0.2814 grm. BaSo,

OE iObmGs pa ah 233 3 3» O:3156" 5 59

Found: 45.77 °/,C.6.10°/, H. I. 23.97 °/, 8. Il. 24.35 °/, S.

Theory for C,H,SO,: 45.46 °/, C. 6.06 °/, H. 24.29 °/, 5.

Determination of the molecular weight by means of the lowering
of the freezing point ih benzene: O5491 grm. of substance in
23.806 germs. of benzene gave a lowering of 0°.835. Molecular
weight found: 138.

1) D. Par. B. 59862, kl. 120, Gr. 2, 18 Aug. 1910.
2) Ann. 383, 228 (1911).

586

Calculated for C,H,SO, : 132.

Hence, the crystallized compound is formed from one mol. of
isoprene and one mol. of SO,,.

The substance is soluble in water. The aqueous solution has a
neutral reaction.

If a solution of the compound in carbon tetrachloride or ether is
shaken with a solution of bromine in the same solvent, the colour
of the bromine is not discharged; bromine water, however, is
eradualiy decolourised. With dilute alkaline potassium permanganate
a reduction sets in at once.

As to the structure of this compound I do not as yet venture
to pronounce an opinion. In connexion with Tnieve’s theory the
occurrence of a compound of the formula CH, — C|CH,| = CH — CH,

| SO, |
would not be improbable.
Utrecht. Org. Chem. Lab. University.
Geophysics. — “7Vhe treatment of frequencies of directed quantities’.

By Dr. J. P. vAN DER STOK.
(Communicated in the meeting of June 27, 1914).

1. The frequency-curves of barometric heights, atmospheric
temperatures and other meteorological quantities assume different and
peculiar forms, which can be considered as climatological charac-
teristics and, as the number of available data increases, it is desirable
to subject these curves to such a treatment that these characteristic
peculiarities are represented by climatological constants.

If we choose for this purpose the development in series-form, the
first question is, what treatment is to be chosen for each special
case, in conformity with the distinctive features of the quantities
under consideration and the limits between which they are com-
prised. The purpose of this investigation is to inquire, what form
is to be chosen for frequencies of wind-velocities independent of
direction, and of direction without regard to velocity. Furthermore,
to state in how far the observed series of quantities may be regarded
as normal- or standard-values, and the problem may be stated also
in this way: what is the best form for frequencies of directed
quantities assuming the form of linear quantities, and further, how
to integrate the expression

587

hh' : :
eS(h.9) RdRdO
Ed toe ere (Lt)

J (R.A) =? [BR sin (9@—B) — a}? + h? [R cos (AQ—Bf) — 6}?

i.e. the standard-value of directed quantities, on the one hand with
respect to @ between the limits 2a and zero, on the other hand
with respect to R between the limits o and zero.

Both problems were treated in previous communications ')”), but
it may appear from the following that now a more principal, and
therefore more complete, solution can be obtained than seemed
possible a few years hence.

2. If we wish to develop a function of one variable in an
infinite series of polynomia

n=
[2 (a) =A, G;, .
n=0
Opa =F aaat a a2 . . ans
the quantities a@ can be determined so that — as in the Fourimr-
series — for the assumed limits, @ and 6

if Dh thd = 0

for all values of m different from 7.

The constants A, are then given by the equation :

A, (. daz =(rio U, da.

The values of the constants a@ are defermined by the n equations :

[o dz = 0, fe Pale = 0G +. | OE iS ey (2)

every integral being taken between the assumed limits.

By partial integration we have:

1) The treatment of wind-observations. Proc. Sci. Kon. Akad. v. Wet. IX,
(684—699).

2) On the Analysis of Frequency-curves according to a general method, Proc.
Sci. K. Akad. Wet. X, (799-817).

588

| UR Gi —— ais

x x

| U, « dx = a P,— Ff > =u. da

0 0

x
{v. ui dz =x ~,—22 9, + Ys Ps = |. dx, ete.
‘ 0

By (2) it follows from these equations that the imposed conditions
are fulfilled when, in the development

| Un at de = x" —p,—n 1 —p,...(—1)—1 n(n—1) 20 (—1)rn! nts (8)

y, be given such a value that this function, as also its (2—1) first
differential-quotients, become zero for «= and «= «and that then

= Apy si ;
U,, =a and fee et (=) ain cae remem Cs)
aun
8 B

This simple method of determining the terms of the required series
was indicated in 1833 by Murpny as a new method of coming to
zonal harmonies ; in THomson and Tait’s “Natural Philosophy” it is
mentioned in article 782.

The method, however, is by no means restricted to the calculation
of zonal harmonics but can easily be generalized and applied to other
circumstances than those mentioned above.

Instead of a complete polynomium we can also consider separately
even and uneven polynomia; polynomia multiplied by an exponential
factor as e-” or e-* may be used, and instead of dz we can take
vdv (plane) or a*dzv (space) as the element of integration, whereas
for v also quantities of another kind, e.g. siz @, may be substituted.

3. If the limits are + 1 and —4J, it is rational to put:

Pn = C (a? — 1)" UF = (6 (z* — 1)

C’ being an arbitrary constant.
Putting

589

nl
C=
(2n)!
U;, becomes
ee ee eae eee oth. (S)
2(2n—1) 2 4.(2n—1)(2n—3)

the well known form (but for a constant factor) of the zonal har-
monie funetion and, a to (4):

eae nin! Qr+1(n!)!

OR nS - -- 1)" dx ————

(2n)L J — n+ 12 ny!
—l
; 1 . in ; ‘ :
utine; = Bees find, if by P, the commonly used form of
an!

zonal harmonies is denoted,

D»\!
= _(2n)- U,
LY tere nt
22 nInt
from which
4
vad 9,
TER Oh = =
5 2n+-1
—1l
If the limits are + © and — o it is rational to choose for ,
dn
Oy == (C7 lth, == (GF =. OH
Pn n dian
Putting
C (1)
aa an

U,, assumes the form :

| n(n — 1) 2 n(n—1) Yun —2 Yn a)
G=ee|| gt — = qn—2 4 ant - 4

ral -
CSG. (Oe = ami 219)
ye )
eisai siete =— SH nm uneven
( a! (6)
In—1 |
9
,
Sie a ave
genoo’ ( ) (m even)
On ! =
2,

and, by (4):

+ x +a
~ 1? !
U2d nt 2 n: Vy
0h) = er dx = — uw.
n On an
-— o 0

The series (6), proposed by Bruns ') and CHARitpR *), is in mathe:
maties known as Hermirn’s function and might, if applied to
analysis of frequencies, be called the gv, function, as proposed by Bruns.

It is the most appropriate form for quantities as atmospheric and
watertemperatures, barometric heights ete., moving between un-
certain limits, and also for wind-observations if generalized for
application to functions of two variaoles.

In either of the cases considered above the terms of even and
uneven power are separated automatically because

ae, +o
| v+1 dx = 0 and fo e—? dv =0.
hese 1 =

If, however, the limits are 1 and O or w and O, then such a
separation does not take place and we must either maintain the
complete polynomium or consider both eases separately.

4. Considering the even polynomia separately for the limits 1
and 0, every polynomium U2, contains only » constants and the
development (5) takes the form:

| U2, 02” da = a2" —~, — An a2 ~, + 2? n(n—1) a4 —|, — (7)
0
(— 1)! 22-1 hn (n—1) ... 2 @? Gn (— 1)" 2”. nl Gna
where
x eb rt
= { Wey (ihe “GPS =) P, td@... Prt = | Pn vda
0 0 0
az ze
| Us, da =(— 1) 2”. ut Pn wdea .
0 0
Putting
lez,
A=-— —
Xv da

) Wahrscheinlichkeitsrechnting tind Kollektivmasslehre. 1906.
2) Researches ints the theory of Probability. (Comm. from the Astron. Obsery,
Lund.). 1906,

we find
Wa Nar WA or eM seun renee ag 4c. | ((9)
whereas for g,, as the simplest expression, we must take:
Pn = Ca?! (2? — 1)”.
Assigning to C the value:
1
(4n—1)(4n—3)... 2n +1)
the zonal harmonic function, as given in (5), is again found also for
the limits 1 and 0.
In the case of uneven polynomia
Uentt = C Ar amH(e? —1ye.. 2. . 2, (9)

which for
1

(4n-+1) (4n—1). . ,(2n+8)

again leads to the expression (5).

s 1
Giving C' the value Bape obtain from (8) as well as from (9
- a"!

the zonal harmonic function in the form as commonly used.
No more as for the limits 1 and 0, the development (7) for the
limits a and O leads to new expressions; we have to put

Pr C a7 e—2

for even as well as for uneven functions, and by the formulae

— Aye 1 H
i — = 5 ee : (A = 2)n gen+ti ]
on an" az
(—1)" } o x (10)
Uon4+1 = Sonik ene? (A — 2) aen+1 |

we find the same expression as in § 3 for @, of formula (6), but by
an abridged calculation.

5. The problem, which form of development is the fittest for
frequencies of a quantity which assumes the form of a function of
one variable, moving between the limits 1 and O or w and 0, but,
as a matter of fact, must be considered as a function of two vari-
ables, is not solved satisfactorily in § 5, at least if we are not satisfied
by a merely formal representation.

A graphical representation of such a function is given by the
distribution of points in a plane about a given origin, ihe element
of integration is then, not dz, but 27RdR and the question must
be put as follows; to find a polynomium such that

592
| U, Um RAR = 0
for all values of m different from 2.
The development by partial integration then becomes:

| Us R2+1 dx = R2 —~,—2n R2n—2 —E, + 2?n(n—-1) R24 y,
-(11)

(Ds Ein (nD) erect yeep
where

gy, =] Uakdk, 9p, = 19,kdR etc.

if U%»,R dR = (—1) n! fotar.

If the limits are 1 and 0, then we have to put:
Gn = CR (R?—1)r

and

so that
U2, = CAn R2n (R?—1)".

1
Putting C= — we tind for the polynomium :
AL ”

a (2n)!

2n—1)!/
Oo», — R2n nC, ( : )
nt (n—1)!

2n—2))

* (n—2)!

R2n—-2 + ny

Vititmes go Cie, —— (112)

where "C, denotes the p'" binomium-coefficient of the x" power,
further :
1 1 1

. . . l
| U5, RAR = 2” (2)’f RdR=(2n)/ | R241 (F?—1)"dR= =

0 1) 0

nin!

2n+1-

This new function may be considered as a zonal harmonic general-
ized for the case of directed quantities and might be applied e.g.
to the distribution of hits on a target.

The analogy of (12) with the zonal harmonic function becomes

2n—1)!
conspicuous if the latter (5), by multiplication by ae be
m—1).
given the form:
2n—1)! ; —2! 7, (2n—4)!
Ge ak i wy an : : ge gn? oa Aen a) yi 4 selice
(n—1)! 2 (n—2)! 2 (n—4)!
The expression (12) satisfies the differential equation:

Vay
R + 4n(n 4-1) RU, =0.

aus ee
BE) ee ok

593

For uneven polynomia ¢, has to be given the same value as (9)
and then again the common zonal harmonie would result. As,
however, the quantities under consideration are essentially positive,
uneven functions ean be left out of consideration.

If the limits are o and O, then the same reasoning holds; it is
then rational to put:

Gn CR tems
Don = CA” BR e-RU'5n = C (A— 2)" RE

Putting

(—1y

On
a

the polynomium assumes the form:

TR 3 Den—? n*(n—1)? je. F ,
Von = R2" — n? R2N—2 + an Ren—4 — ,..(—-1)"n! . (18a)
and
ce oo
Y !
fo RdR = 2”. utfir hak ae :
0 0 S

In analogy with (12) the polynomium, by putting

liye
Ga eal
2"n!
may be written also:
Rn R2n—2 R2n—4
es Sa ES yee oes iC had as ° 2),
Seamer Ga ne

This new function (13) seems to be the proper form of development
in the case of directed quantities as wind-velocities, disregarding
direction; it satisfies the diff. equations :

aS oe poe
=
a? Usn
i
dk?

R -f- An RUt>, = 0

In applyine this development, a simplification may be obtained
pplymsg j

by a change of seale-value: writing 7R for R and putting

v to) to) c

+ (2R?- a a 4+ 4(n 41) RU» = 0

the second term with the coefficient A, will disappear as

U', = (R?—1).
Here J/° denotes the moment of the second order of the given
frequency-series,

594

6. In the same manner as in §5 in the case of a directed quantity
in a plane, the development appropriate for quantities in space may
be found, e.g. for distances of stars, disregarding direction.

The element of integration is then 47#?dR, and the development
(11) holds good if in the left member A?"+! is written instead of
22” and, at the same time for ¢@,

7 = {0 Rdk
0

so that
C
Cr — R An Pn and fr = C R2n+1 e—R’,
Vv
Putting
,_ (|)
Co Qn
U7. becomes :
n aon 1 n on 1 on—1
U' ne? Up —=R™ -C, =e R220, a ) R24
. (14
py CRED! es)
aly) 22m!

and

| U*on F2dR = (—1)r. 2”. nt firn RdR = (—1)" 2°—1 nln!

0 0

In applying this development a simplification may be obtained by
writing HR for A and putting:

Z 3
HT =o’
then A, = 0, because
Uo = 3),

7. Although we may expect @ priort that the Fourier-series is
the most appropriate form of development for frequencies of directions
(disregarding velocity), it seems desirable in connection with the
foregoing to show that, following the same method, we, in fact,
come to this result.

5G SU Ct evel las
then we may distinguish four different types of functions, namely :

Jes F,= U sinacos a F< Uscotae (en ie Usina

595
For F, the development holds good:

~.
[ese ada = gp, sin” a — 2n x, sin?” a 4

(Ca) 5 2n2 — IN 2o (= V)hor nN
where

ie 9) _ an} » 2
i | Uda j= | Y, sinacosada ete.
vu

Therefore, putting

1 d
————————
sin a cos a da
2m!
Ga = Cosme" a cose" a and) (Ci
(2n)!
. . . . T
we find for the limits = and OQ:
27. n!
pe sin a cos a A” Gy, = cos 2na.
(2n)!
In the same manner:
c 2° nn! car ; :
Fy — — A™1 sin"-1 @ cos?"—1 a = sin 2nea
(2n—1)!
2". n!
i sin at A” sin2”—! @ ¢0s2"+1 « = cos (2n + loa
(2n)!
2" .n!
th @n)! cos a A” sin?'+1 @ cos?”—1 @ = sin (2n + l)a.
an

8. The solution of the second problem, as formulated in § 1, can
be simplified by putting @6—PB=~y in form. (1), ie. by counting
the angular values not, as usual, from the North-direction, but from
NpE; this has, of course, no influence on the sums of the velocities.

It is, however, unfeasible to apply a similar correction for the
components a and 6 of the resulting wind, and the problem to be
solved comes to the development in series-form of the expression :

hh as
ef g—la—a)>—h'(y —b)2 Fi cos G6 = y

FL Risin O =a.

It appears from the first of the communications cited in § 1 that,
in following the usual method of developing, difficulties are ex-
perienced which practically are unsurmountable. In the second com-
munication however, it wes shown that the development (6) may
be extended to the case of two variables 2 and y, and that such a
function ean be developed in a series of polynomia of the form:

Proceedings Royal Acad, Amsterdam. Vol. XVIL.

596

F(«,y)=e—°-1"| Aoo U,+-A1.0U1+A0.1 Vit-A2.0U2+A11 Ui VitAoe Vo+et>. ](15)
where |’ represents the same funetion of (7) as U of (x) in form. (6).
The coefficients A are then determined by the expression:

Aa =ef fri ty) UnVm dedy = & Sam

—o— ©
n\m!\
2m+n

xv and y, Rsin@ and Rcos 6, then, by

Substituting again for
to @, all uneven polynomia vanish and,

integration with respect

because
sin Qn)!
in?" a i hie ( nyt
cos?” a 227 n'In!
0
we find
Ue Vom d@ —- an - (2n)! ! (2m)! ie . »--H? 2 (HR) pe —
x, cet 22(n-+4m) n!m! (m+n)! !
0 (17)
(HR 2(m—-n—1 ) HR)2(m-+n—2)
= mn ATES ) os --m-fn C, Ce y = (ie,
(m+n—1)! “(m+n—2)

i.e. the same expression as 13°, found in a different way.
As to the determination of the A coefficients, it is expedient to
first the case that a and 6 are equal to zero.

consider
It is then easily found that
(2n)! (2n)!
Smo= 5,1 At ET? —— 7 fe On ae
and similarly for the V funetion
(2m)! (2m) !
on= M" H? — */,)2 =
Suze am. m! re /s) 2m .m!
il
Mt = — M? = ——
2h? 2h?

The arbitrary constant H now can be given such a value that
P or Q=0; putting P=O, then H=A, and in the development
only the V funetions remain.

If a and 6 are different from zero, then it appears that (for P=0)

S,=Q4 10
r|s S,=3 QV 4+ 6hd7Q + hid!

15 Q® + 45 h2b7Q? + 15 A4b'Q + Ab!

ie) &

or, generally :

597

: (2m)! F _b2Qn—i
Son = f2n q2n at Qu 1 m( ES Adie
aril m! Qm ; 1
8
Awe hi bs (Qn—? : f2m §2m |\ - (18)
m
rei, = =p ee ——
kg 8 1 .3...(2m—1)

Although, therefore, in this case the U functions do not altogether
vanish, still the form remains the same as in (132) and (13’) because,
as appears from (17), the polynomium has the same value for all
terms where n+ m has the same value so that e.g. the terms with

A40 Ayo and Ao4
can be taken together.

In order to investigate in how far a given collection of wind-
observations may be considered as a collection of two independent
quantities depending on chance, we have, therefore, in the first place
to ecaleulate the constants a, 4,8, hand’ from the set of observations.

In the second place the development (184) has to be applied to
the frequency-series of the wind-velocities, thereby taking for H
either 2 or h’ so that the term J, remains.

A comparison between the A constants calculated in this way
with those determined according to (18) then gives an answer to
the question.

9. By writing in (15) AR sin 6 and hRcos 6 for x and y, multi
plying by RdR and integrating with respect to RA between the
limits 0 and zero, we obtain a development representing the fre-
quencies of the directions independent of velocity.

The even terms Uy, and Vo,, or the product Vo, U2, then give
rise to a series of terms of the type /, (§ 7) all of which have the
factor cos 2ne in common.

The even terms Us,41 Vo,41, produced by the product of two
uneven terms have sim @ cosa as a common factor and give rise td
terms with sin 2na, according to the functions /’, in § 7.

The uneven terms, analogous to /’, and /’,, assume a simpler form,
namely :

Uont1 = Ksmacos*"a and Von41 = K cos a sin” a
and therefore give rise to terms with sé (2n-++1) «and cos (2n-+-1) e,
whereas all non-periodic terms vanish, except in the first term
with A,.

A comparison with the Fourter-series thus produced and calculated
on the base of the five wind-constants with the Foukrer-series as
directly deduced from the observations of direction-frequencies, then

again gives an answer to the question.
39*

598

Physics. — “Some remarks on the values of the critical quantities
in case of association.” By Dr. J. J. van Laar. (Communi-

cated by Prof. H. A. Lorentz).

(Communicated in the meeting of May 30, 1914).

1. Though this subject was treated already very fully by me ina
paper in the Arch. Tryier') in 1908; and use was made afterwards
(in 1909) of the contents of this paper in my Treatises on the Solid
State *) — I wish to make a few remarks induced by a paper by
Prof. van per Waats in These Proceedings of April 1914 (p. 1076 et seq.)
which may contribute to the removal of the pretty large difference
found by him (p. 1081) for the volume value of CH, for methyl-
aleohol (2,12) and for ethylaleohol (2,76).

Van per Waats makes namely use of values of vz, RT, and pz,
of which he states (on p. 1078) that they would be exact by approxi-
mation. But it has appeared from the investigation made by me in
1908 that the “linear” dependence of the quantities RZ), and s of
the association factor 2: (1 + 8) cannot be assumed even by approxi-
mation.

Not only does this hold when (as v. p. W. assumes) the volume
of the molecules does not undergo any change on association ; when
in other words A/ = — */, 6, + 6, = 0 — but the deviation in question
presents itself to a much greater degree, when Ad is not = 0, as is
certainly the case for water *) and the alcohols.

In the cited TryLer article I started from the equation

——) J 2

in which @ represents the degree of dissociation of the double mole-
cules, so that to the original '/, double molecule are found '/, (1 — 3
double molecules and */, . 23 = @ single molecules, together ‘/, (1 + 8)
molecules.

1) Arch. Teyier (2) T. XI, Troisiéme partie (1908): Théorie .générale de l’asso-
ciation de molécules semblables et de Ja combinaison de molécules différentes.
(p. 1—96).

2) These Proc. of April 22, June 25, Aug. 31 1909; Nov. 24, 1910; Jan. 26
and June 23, 1911; resp. p. 765, 26, 120, 138, 454, 656 and 84. (See especially
the third paper, p. 127—130).

3) Already in 1899 I think I showed that the phenomenon of maximum
density at 4° C. can be explained in a very simple way by the assumption of a
negative value of ab, so that a double molecule would have a larger volume
than two single molecules. [Zeitschr. f. physik. Ch. 31 (Jubelband fiir van ‘t Horr)],

Doe

The quantity @ appeared to have been left unchanged by the
association, viz. =a, — the value for the case that all the molecules
are single — everything referring to a single *) molecular quantity
(e.g. 18 Gr. of H,O, 46 Gr. of C,H,O, ete.). For we have evidently
(the index 2 now refers, in distinction with my Trytur article to
the double molecules, the index 1 to the single molecules) :

1—p\? Je! AD 2B 7
a=|(— >-]% +2 - aa fh an ies
= a c) -

a, and a, = 4a,, so that we get:

=]
z
=
5
R
e

|
b

a=(1 — @fa, +21 B) Ba, + B?a,=a

1°

Further :
1—p 23 f
ps =, BSS OS , SS a
or ='/,6,+ 8(—‘°*/, 6, + 6,)="/, 6, + B Abd.
The equation of state used by van pur Waats (p. 1078) is identical
with ours, as VAN bDeR WaAAIS starts from 1 —.2 single molecules

and 2 double molecules, together 1 mol., while we started from
single molecules and (1— 3): 2 double molecules, together */, (1 + 6)
molecules. Accordingly we left the quantity of substance (viz. a
single molecular quantity, e.g. 18 gr. of water ete.) constant, and
varied the number of mo/ecules on association from 1 to '/, (1 + 8) —
and van ppER Waars left the number of molecules constant = 1,
while he increased quantity of the substance from 1 to 1+ 2.

If this is borne in mind, van per Waats’s v: (1 + 2) now passes
into v' (now just as with us referring to a single molecular quantity
of substance), and we get :

RT :(l+e) a,
P —

(i ene Gaens?
v—b, v

in which therefore 1:(1-++x) is identical with our (1 + 8): 2, v’
with our v, VAN DER WaAAtLs putting 4/—0, and therefore identi-
fying b with 6,.

2. As (, the degree of dissociation of the double molecules, is a
function of v, the dependence of the quantity @ on v will have to
be taken into aecount in order to find the values of the critical

1) In the cited Tryter article | made everything refer to a dowble molecular
quantity, but I think it more practical to continue to make the different quantities
refer to a single molecular quantity. Hence all the quantities have now been divided
by 2, resp. 4.

600

; f ; Op )
quantities in the determination of = = 0 and = = 0. The ealcula-
v v

tions relating to this are pretty laborious, and were carried out in
a separate chapter (§ 5 p. 25—34) in the cited Tkyuer article (ef.
also the above cited paper in These Proc. of Aug. 31, 1909, p. 127—130).
We refer to this article, and give here only the results of the caleula-
tions — again making everything have reference to a single mole-
cular quantity.
For vz was found:
2

mm
BE APES 3m? — Qn’ (2)
in which
m=1 + */,8(1—8) (1+9)* a
m=1 +4 */,8(1—8) (1+-y) + */8 1—8) 1884) (1+)
w hile
Ab
PU) eae Peer ss (5)

(p. 26 and 29 loc. cit.).
When Ab=0 and so also gy =O, as VAN DER WAALS assumes,
even then remains:

m=1 + */,8(1—8) =(1+8) (1 —*/,8)

3 1/ £ 2 2 9 a(’ (3°)
m— 1 4-9/6 (18) +) op) (hep) (an hea
through which for vz, with
3m*—2n = (1+ 8)? (1—’/,8),
is found:
(ear
"90 2a
VI oN Tas (2°)

In this the factor 3 must of course be replaced by a smaller one
(e.g. 2,1), when & is a function of v, and varies between 6, and 6,,
when v varies from o to 2%.

With regard to the factor of 3b; —— which according to VAN DER
Waats (referring namely to a single molecular quantity and not to
a 1+ times larger quantity) would remain constant = 1 (at least
by approximation) — we see immediately that this factor can differ
pretty considerably from unity. For @=0 (only double molecules)
and 3=1 (only single molecules) the factor is properly = 1, but

for B= 7/, it has the minimum value */,. And this deviation, which al-
ready amounts to 11 °/,, is still more pronounced when Ad is not =O,
but has e.g. a negative value.

For RT; we have found (p. 31 loc. cit.), again referring to a
single molecular quantity :

601

8 a, 2 n*(dm? —2n)

27 by i= 8 m®

RI, = teen c08 (5)

which with 44 =O passes into

8 2 1+ 8)(1—°/,6 + */,8°)? 1—*/,8
ee ale ( +B) ( /sf an me /4P) (52)
Nate ase (1—?/,8)
A 8
If 8=1 (single molecules), then RZ, duly becomes =
1
8
but for 8=0O (double molecules) RZ; becomes = 2 Xap

But it is again immediately seen that 7), certainly does not linearly
change with 2:(1-+8), ie. with van per Waats’s 1-2, as the latter
assumes on p. 1078 of his treatise.

For the remaining factor is indeed again =1 for 8=O and
B11, but it is 3456; 3125 = 1,106 for p= */,; = 1445: 1296 =
=e tor P= */,; and 1125 ; 1024-— 1099) for 6 = 7/,. The
deviation can therefore again amount to 9°/,, in comparison with
11°/, for vz, but in opposite direction. This deviation too is more
pronounced, when 4é differs from 0.

With regard to the value of pz, at last, we find:

I a (8m? —2n)? (4n —3m)

— » Oe OOM Ok 0 6
Pk 27 6; a m? (9)
passing into
1k @ (1—*/,3)? (1+ 8—8p* + °/,8°) ‘
Pk = 55755 X — Pace (GO
27 6, (1—’/,8)

when Ab=0. For
4n—3m = (1+) (1+8—36"+"/,6").
1
The factor of aia duly has the value 1 both for 8 =O and
a 1
pies but becomes == 4617 3 3125 — 1477 for §='/;; = 379:
oto — e430 fon) p 7/2; and —— 189. 128: — 76) for p=".
Accordingly the deviation from unity is very considerable — for
B='/, more than 54°/,. Hence there is no longer any question of

an approximate equality to as VAN DER Waals supposes he

a
a7 8”
may assume. (p. 1078 l.c.). And this amount can still increase for
Ab not = 0.

1) If it is taken into account that a = !/,d, b) =1/, by, RTk becomes as it

; a . A :
always did = 5? in which a and b, now refer to a double molecular quantity.
2

8
27

602

It is therefore self-evident that when the quantities s= RT}: peor
and 7: pz are caleulated, which occur in vAN Der WaAALs’s consi-
derations, no linear dependence on 2:(1-+ 8), resp. 1 -+ x is to be
expected there either.

3. Now
Ri wee ae ni?
= ee re
Pevk & 14+ 8° mn? (4n—3m)
is found for the quantity s, passing (with Ab = 0) into
8 2 \ (WIS ai Bom B*)* (7 )
= — — < = a a
3 1p (=, eb = see)
For 8=1 (all simple molecules) s becomes = s, = °/, (or =3,77,

when 6 varies with v), and for 8=O (all double molecules) s becomes
= °/, <2, hence twice the value. But here too we remain very
far from linear dependence.

For @='*/,; we find namely for the last factor in (7a) the value
384 :475 — 0,808; for B='/, the value 280: 360 = 0,803; and
for 8=7?/, the value 375: 448 = 0,837. Hence a difference of about
DO Aeon irae

On account of the importance of the accurate knowledge of the

value of the quantity s for associating substances, I have calculated
the following table.

2 S

B ae = ee Factor | ite X factor = S
0 2 haga | 2
0.1 1.818 | 0.903 1.642
0.2 1.667 | 0.847 1.412
0.3 | 1.5388 | 0.815 1.253
0.35} 1.481 | 0.805 1.192
o4 | 17420 | orent | 1.145
0.5 | 1.333 0.803 1.071
0.6 | 1.250 0.820 1.025
0.7 1.176 | 0.849 0.998
Oh |) Meili | 0.890 | 0.989 (min)
9 | 1.058 0.945 | 0.995
als 7a leit 1

603

Instead of a regular linear deerease with 2: (1)+ 8), 1.e. with
1+ 2, values are even seen to appear <4 in the neighbourhood
of B=1 (all the molecules single), with a minzmum at about B= 0,8
(accurately at 80,8015), and a horizontal final direction, Le.

d (ss
is) =°

On increasing association (3 from 1 to 0), s will therefore first
become somewhat smaller than s, (= 3,77 for “ordinary” substances),
and then (from @ = 0,7) s:.s, will become greater than 1, and increase
to 2 for =O, when the association to double molecules is perfect.

A straight line for s:s, (as VAN DER Waats thinks) therefore
replaced by a line that is pretty considerably curved downward
between the values 2 and 1 with a minimum close to 1, so that
s:s, at first decreases there instead of increasing.

What consequences this behaviour will have with respect to the
degree of assvcuttion B, caleulated from the value found for s for
methylalcohol, viz. 4,52, may appear from what follows.

As s:s, == 4,52: 3,77 =1,2, we should find about S=0,67 or
v=0,2 for B, according to the second column of the above table,
when we were led by a supposed linear dependence. But when we
also take account of the “factor” by the side of 2: (1+), we find
about B= 0,35 or c=0,5 from the last column for the value for

8 answering to the ratio s:s, = 1,2.

A difference, in fact, too large to be neglected. Instead of 0,8
single molecules to 0,2 double molecules, as vAN DER WaAats would
find with his linear dependence, we find more accurately 0,5 single
molecules to 0,5 double ones. The relation x: (1—a) has become
1 instead of 4.

4. The second quantity which plays a part in the cited paper by
vAN DER Waats, is the quantity 7%: pe, which may be put propor-
tional to the molecule size for non-associating substances. We now
find for it:

Lee 8 2 (1-8) U—*/,8+ */.8°)°

—— oak (Sa)

ap IP BL S83) (Sais oS)
which with 46 =O passes into

IL ip 8 2 n*
== by.

= pth Lees go) BAe)

Dk - Ri 1+. s (3m?—2n) (4n—3m)

We shall not discuss the course of this again, but solve from this

604

5
the required value of = Ok: By means of (7) and (8) we find easily :

8 Tienes 3m?—2n
6) = — b = : ran. eee 5. ((Y)
R : ie *) x m?* @)

or when Ab=0O:

8 Ty 1—'/.8
6b) = — 6. = : A ¥ ye ee Qa
One & Shae ue

When therefore the value of 8 has been found from (7) and (7a),
it can be substituted in (9) or (9a), and 8/p 6, is known.
According to van per Waaus, (0) would be = 6,52 : 1,2 = 5,43

for methylaleohol, whereas (for A= 0) the more accurate value
with 8= 0,35 (see above) would amount to 5,43 1,084 = 5,89.

This value is still larger than that found by van per Waats, and
would yield 7,55 5,89 = 1,66 for CH,, instead of 2,12. And when
4)=0 is assumed, the accurate value of (4) will be larger than
ihe approximate one for every value of 8, because 1 — */, is always
SS (eee ae

It is, however, easy to see that when not (7a) and (9a) are used
for the calculation resp. of 6 and (6), a value <1, e.g. 0,88 can
very well be found for the factor (8m*— 2n):m? in (9), through
which 5,48 would diminish to 4,78, so that 7,55 — 4,78 = 2,77
would be found for CH,, in good harmony with the value found
for ethylaleohol.

Now (8m? — 2n):m? becomes < 1, when

‘

>
ye Or) m2 <ain.
n

7
I.e. with a view to (3)
SA US iGES ie <Us ay etal ells GF) ==
> fh (ie) (loa) (aaa
must be, i. e.
BULB) CL Pee) On Bie pa —<e
< */, 8A— pi + @) =, 7, BE 8) C332) ies
or
(Se @) 7/5 PO SB) a
or also
6 — 8 =) 4 GS 8) 2) — 2) ere
If 8 were =O, then gy would have to be < 3—/ 10, i.e.
< — 0,162. If 8 were ='/,, then ~ ought to be < about — 0,25.
And if @ were =1, then g would have to be << —3+ V7, i.e.

605

< — 0,354. As now according to (4) y= (1-+ p) Ad: (v— 3), we
have also:
eae ae
b v—b
For 7}, with v = 26, the value g:(1 + 3) follows from this for
Ab:6. For gp resp. =0, ‘/,, and 1 we find therefore resp. the

values < —0,16, < —0,167 and < —0,177 from this. When
accordingly Ab:6 becomes smaller than about —‘/,, the value of
the factor (3m? — 2n):im’ can become <1. For a value 0,88 (see
above) it will therefore be necessary that — Ab:6 be about 0,2 —
a value which in view of the value for H,O (which has been found
of the same order of magnitude) is not at all impossible for methy]-
alcohol either.

At any rate it is seen from the above, that for associating sub-
stances (4) cannot be put simply proportional to (7% : pz) : (s: sy), but
that the factor (8m? — 2n):m* must be taken into account. Nor may
for the calculation of § from s:s, simply 2:(1+ 8)=1-+ <2 be
written for the latter ratio; another factor n° : m* (42 — 3m) must
be added to it, which factor amounts to about 0,8 (see the above
table) in the case AJ=O between p—O0,3 and ’=—0,5 or 0,6, which
differs too much from 1 to be neglected.

The error made by van DER Waats is according to § 2 owing to
this, that he believed he could assume values for R7,: (1 +2) and
pr, Which do not differ (at least differ little) from the corresponding
values for non-associating substances.

The calculation (given by me already in the cited TryiEr-article
in 1908) teaches something entirely different: for p, (with Ab = 0)
e.g. the deviation can amount to more than 54°/,.

The finding of a too large value for (7%: pg): (s:s,), viz. 5,43
instead of about 4,8 points out, that necessarily for CH,OH the
quantity 46:6 will have a pretty Jarge negative value, namely
about — 0,2, If 8 were about */,, then 6 would be = (1—8) */, 6, +
+ 8b,='*/,b, + °/,6,, and from

Ab = 3/50, by

b ah) “he b, + ape b, ES,
would follow 16:13 = 1,23 for-the ratio '/, b,:6,, i.e. the double
molecules would be about 1,23 times as large as two single mole-
cules — which is by no means impossible.

— 0,2

5. On this oceasion I will draw attention at the same time that
in § 7, p. 40—42 of the cited Tryrer-article also the quantity

606

T dp rips
fell *) for associating substances has been calculated by me.
: Pp ¢ k
When the heat of dissociation g of the double molecules may be
put — 0, we find for 7 (see formula (28) loc. cit.) :

n
4n—3m’

or when Ab=0O:

(LB) Seater aie)
1+ 8— 38 + 7, 8
in which the factor of /, both for @—O and for B=1 again
assumes the value 1. For 8 = 1/, the value is, however, 16:19 = 0,84,
which would make the normal value 7 descend to about 5,9. As_
J for methylacohol is found > 7, namely = about 8,6 (ef. Kurnen,
Die Zustandsgleichung, p. 142, where the value 3,75 >< 2,30 is given),
the factor of /, would have to be about J,2 instead of 0,84; i.e.
Ab not =0, and again negative or also the value of g (see the
full formula in Tryner, p. 42) would moreover have to be different

ik — Te x ’

from 0, and that positive.
Fontunivent sur Clarens, May 1, 1914.

Physics. — “On apparent thermodynamic discontinuities, im connection
with the value of the quantity b for infinitely large volume.” By
Dr. J. J. van Laar. (Communicated by Prof. H. A. Lorgntz).

(Communicated in the meeting of June 27, 1914).

1. One of the principal results of the foregoing series of commu-
nications ') has been this (cf. particularly II p. 926 and IV p. 464),
that the quantity b,, i.e. the value of for infinitely large volume
(hence in the ideal gas state) cannot possibly be = 4m as the classical
kinetic theory gives for it. With decreasing temperature }, approaches
namely more and more to &,. If in the ideal gas state 6, were
—4m, 6b, would have to be =4m also at very low temperature
(this kinetic result holds namely independent of the temperature),
while in the condensed liquid state with cubic arrangement e.g. of
the molecules, supposed to be spherical, 6, would be about = 2m’,
in which m’ is either equal to or smaller than m, so that then b,
cannot possibly become = /,.

1) These Proc. of March 26, April 23, May 29 and Sept. 26, 1914 (to be cited
as I—IY).

607

And yet, everything seems to point to this that actually a// sub-
stances at sufficiently low temperature approach to the type of the
mon-atomice substances with exceedingly low critical temperature, at
which the quantity 6 remains almost unchanged on diminution of
the volume from o to v,. Instructive are in this respect the tables
in I, p. 819 and III p. 1052, and also Porncaré’s and Kameruncu
Onnes’s remarks in the discussion of Nernst’s Report (Conseil Sotvay
German edition, p. 241 at the bottom to 242), where it was pointed
out that at very low temperature also the molecular heats of air
and hydrogen would probably approach to those of monatomic gases.

The above contradiction is now immediately removed by the

assumption that in the rarefied gas state 6 is not = 4m, but
simply =m (the real volume of the molecules, at most enlarged

by a certain sphere of influence), while also in the condensed liquid
state 5, is =m’, (m’<m) — in such a way that the idea of
immediate contact at vv, of the quasi-spherical molecules with
small, remaining intermolecular spaces without energy must be
replaced by the more rational view of a compact mass of molecules
without real interstices, unless they are considered to be the spheres
of influence belonging to the molecules, just as for the Jarge volumes.
This limiting state might however also be considered as a fictitious
state, which may be approached, but which can never be reached
entirely. But this is a question which may be left out of consider-
ation here.

The principal thing is that 6 always remains =m, and that on
diminution of the volume m, therefore, only changes in consequence
of the increased pressure under which the molecules are then, the
less as 7 is nearer 0, till at last both at v =v, (p=) and at
T =O the molecules will occupy their smallest volume /, =m’,
when the atoms or atomic groups inside the molecule have approached
each other as closely as possible.

2. Hence we attribute, as van per Waars did in his middle
period, when he drew up the so-called equation of state of the
molecule, the change of 4 with v entirely to a real change in con-
sequence of the changed internal pressure) — with rejection of

1) For a real diminution of the molecule on diminution of v or lowering of 7’
speaks also the form of the empirical relation b =f (v,7) found by us — see II,
p. 931—933, and III, p. 1051—1054. How little the later views of vAN DER
Waats and others — in order to make the original equation of state also applicable
to the condensed gas state and the liquid state — chi-fly by considering > as a
function of v and 7 (of whatever nature this variability may be) — have yet come

608

the so-called quasi change, which would be caused by the diminution
of the old factor 4 to about 2 in consequence of the partial over-
lapping of the ‘‘distance spheres’. We namely assume that the volume
available for the calculation of the pressure is immediately found by
subtracting the volume of the molecules m from the total volume 2,
always assuming that the kinetic energy of the moving molecules
and molecule groups, with the permanent gradual interchange of
the energy during the collisions, is continuously absorbed by the
surrounding medium (see I p. 809, and IV, p. 464 at the bottom),
and is finally after subtraction of the internal molecular pressure
observed as ‘‘external pressure”

It will be asked what part the so-called association or quasi-asso- |
ciation plays in these considerations.

Before answering this question I will first state clearly my opinion
about the difference between association and quasi-association, which
I hold in connection with the following considerations. We may
briefly express this difference in the following way.

Real association is quite individual and has a permanent character ;
it quite depends on the chemical nature of the molecules (whether
there are e.g. still free valencies or minor valencies present ete.).
Water, alcohol, acetic acid are associating substances — _ ether,
benzene, chlorobenzene ete. are non-associated substances.

Quasi-association on the other hand in consequence of the action
of the molecular forces, when two molecules get into each other's
neighbourhood, and which gives rise to the formation of temporary
“molecule aggregations’, ts entirely the same for all substances in
corresponding states, and of transient, albeit stationary nature.

This last form of association, which has been particularly studied
by van per Waats, is competent to explain why with the ordinary
kinetie view (which, when a// the active factors are taken into con-
sideration, must also lead to the truth) not 6, = 4mis found but less.
The theory which — evading the separate consideration of the moving

under the notice of many, may appear again from an article by A. Wout in the
Z. f. ph. Ch. 87, p. 1—39. This author thinks he can set everything right by an
equation of state of the wholly unjustifiable form

RT a c

in which a, b, and c are constants. That it is also possible to arrive among others
at the accurate values of the critical data by putting 6 variable with v in the
ordinary equation of state, does not seem to have occurred to him. Also von Jiipryer’s
many articles convey an impression of his not being at all in touch with the new
investigations in this department.

609

molecules, of their collisions and their temporary aggregations —
goes straight to its goal by imagining (see above) all the energy
absorbed in the surrounding medium, makes it further acceptable
that 4m would after all have to become simply m.

But that the theory of the quasi-association can only be of any
use in the rarefied gas state, in conjunction with the theory of the
colliding molecules, and that the medium theory can be left aside —
though there always remain constants undetermined (viz. the associ-
ation constants), as we shall immediately see; and that this theory
entirely fails for more condensed states — this is immediately to be seen.

For if one would apply the quasi-association theory to liquids, the
number of molecules associated to one molecule would theoretically
continually increase, so that finally — in the limiting state — the
whole liquid mass would have to be considered as one single asso-
ciated giant molecule, for which the equation of state of the substance
would then lose all its significance, as this is based on the joint
action of an exceedingly large number of molecules, and not on a
single molecule. What for larger volume can therefore be taken as
the equation of state of the whole mass of the substance, would now
have passed to the equation of state of a single giant molecule. But
in this the separate moleeules can again be taken as unities (real
association excluded of course) in consequence of the very slight
mutual distances (just as for a solid substance), and the equation of
state resulting from this will have analogous meaning as the original
one, which holds for the gas state. Only we shall then have to take
into account the continual change of the number of degrees of freedom.

The theory of quasi-association, applied to condensed states, would
therefore lead to great contradictions. While the molecules practi-
cally behave as single ones, the said theory would lead to an infinite
complexity in one giant molecule, with abolition of the original equation
of state.

While van per Waats, therefore, thought he could chiefly explain
the deviations of the liquid state with respect to the ideal equation
of state by the association theory, we see that exactly in this state
this theory would lead to contradictions. It may only be applied in
the rarefied gas state, though just there it is not necessary as an
explanation of the deviations from the equation of state meant by
vAN DER Waats, which would make their appearance not before
the liquid state, but which as we saw in the foregoing articles cau
be explained also without the assumption of quasi association. It is
indeed necessary, however, as we shall see presently, to explain
that then 47 can become m.

610

That with respect to the 4-values just liquids behave entirely
according to the ordinary theory with 6= f(v,7) — without quasi
association being taken into account — has appeared in my recent
caleulations with respect to Argon. In 1V p. 458 we saw namely
that the liquid values of 6 behave entirely according to the relation
b= (v) derived by me (if namely 6, = 6,: vz is only raised from
the value 0,286 obtained by extrapolation to 0,305). That the vapour
values of 6 exhibit deviations, and even become impossible, is to be
ascribed to the way of determination of the* vapour volumes at
lower temperatures — since it is no longer by direet observation,
but by application of the law of Boyin, which is not yet quite valid
then, as I have shown in IV p. 457.

3. Let us now proceed to examine the influence of the quasi
association in the very rarefied gas state, by which it will be proved
that the kinetic result 6, = 4m can no longer be maintained.

Abbreviated derivation. If in first approximation (this is permissible
for great v) we put the quantity 6 independent of the state of
(quasi) association (the quantity @ is always independent of it), the
equation of state for great v is:

po— 6) (ee) ee eee ee (C08)
when a fraction a of one single molecule associates to double mole-
cules, so that there will be 1—a single and */, double molecules,
together 1—'/, a. With very large volume the numbers of triple,
quadruple ete. molecules can namely be neglected with respect to
that of the double molecules.

In this « is given by an equation of the form (see for a justi-
fication of this and of some other assumptions the Appendix)

Ci (1 — x)? CL
SS Ss SS _ ‘
cr 1 ,v(1—’/,@) p
as the concentration c, of the single molecules = 1—«) : (1—’/,«),

and that of the double molecules c, = */,«:(1—*/,2).

In this it is supposed that also the specific heat does not undergo
any change in the quasi association, and that moreover the energy
change may be put = 0.

In the ideal gas state we have 7’: p= (v—6): R(A—"/,2), according
to (1), so that we can also write:

(l—a)?
7 e@

or also, as a will always be exceedingly slight with large volume,

C ;
=F (v—)),

and 7» may be written for v—b:

If we put:
pv - b') = RT,
in which 6’ is the value of 6 which would be found by leaving
the quasi association out of account — so the real value therefore
in the usual sense —, then by comparison with (1) follows:

v—b b b
v— = —=v( 1 — —}(l +2/,e) =vj 1——+ 1,2],
1-—'/,a v v ;

sO
v—b =v— 64+ 0.'/, 2,
thus
CTU Os ia) ee se og oe ee (3)
According to (2), however, v.'/,«®= R: C, when v approaches
to o and wv to O, so that we finally get;
y=! R
» = b — C he a eo te a (2)

in whieh 64m according to the kinetic theory of the perfectly
elastic collisions of the molecules, supposed to be spherical. And as
C’ — the association constant — will always possess a jinite value,
for else there would not be quasi association, we have always:
v< b, 1. @. b'< 4m (q.e.d.).

At the head of our paper we spoke of “apparent” thermodynamic
discontinuities, and mean by this what follows.

If there were no quasi association at all, i.e. if the association

constant C’ were absolutely = 0, so that there could not exist quasi
association at any volume, however small — then 6’ = 6 = 4mm.

But as soon as there exists quasi association ((C’ finite), however
slight it may be (according to (2) =O for v=o), immediately
6 (= 4m) is diminished by the finite quantity R: C, as v X */,7= » XO
is always finite, so that 6’ becomes < 4m.

There is therefore discontinuity — for at an association state = 0
for v=o, b’ can have the value 4m, and also possess all the values
<(4m. But this is only apparent, because the diminution of 4m
depends continuously on the value of the dissociation constant C,
which can vary from O to any finite value.

Now Cis not known, and this quantity, which depends on the
entropy constants, could only be determined by statistical-mechanical
way, when we knew ail the circumstances accurately and could
take them into account, which determine the quasi association. In

Proceedings Royal Acad. Amsterdam, Vol. XVIL.

612

default of this knowledge we can therefore only say that probably
2

ia
C will be such that 6’ = 4m — 7 will become about 6’=m,, in

which m,, represents the volume of the molecules with their immediate
sphere of influence (see § 1) — in harmony with the theory of the
absorption of energy and transmission through the intermolecular
medium (ef. also § 1).

If an analogous image is wanted: the old ballistic theory of
the rectilinear motion of the colliding molecules is in the same
relation to the modified theory, “in which the temporary mutual
influencing of the molecules is considered which will take place at
every impact, or (what comes to the same thing) to the medium
theory — as the consideration of the effect of a ray of light,
after it has passed through a narrow aperture without taking the
inflection into account, so that only that part of the space behind
the aperture would be affected by the light which is in the direction
of the ray — is in relation to the complete consideration of the light-
effeet with observance of the diffraction, in which therefore the
whole space behind the aperture is affected by the light, and of
which it is possible to determine the distribution of the intensity.

Appendia. Complete derivation’) of (A).
If a fraction x, of 1 mol. is temporarily joined to double molecules,
a fraction v, to triple molecules etc., we have therefore:
n,—1—2#,—2,... single mol. ; ,=%*/,2, double mol;
n, ='/, «, triple mol.; ete.
If further generally :
b=n,b, +n,b, + 7,6, +..,
then
= (1 —a, — 2, — 222) 0; Ey OF, Oe ee
or
OD me (Des ig) eg Onan) ere
In this 6, —*/,6,= A, 6 represents the change of +, always when
a half double molecule dissociates to a single molecule; 6, —*/, 6, = A,b
the change of 6, when one third triple molecule dissociates to a single
mol.; ete., so that we can also write:
b= b, — 2x, 4,b—a2x, A,b — ete. ee to (a
That a does not change in consequence of the association, is known.
For three kinds of molecules e.g. holds namely :

1) Already derived by me in 1908, but never published.

613

@=n,?a, + na, + n,’a, + 2n,n,a,, + 2n,n,a,, + 2n,n,a,, ;
meawnich @, = 40. , a; = 90. 0, — 20. — 3d, and @,; = 6a;,
so that we get:

a=—n,?a, + 4n,?a, + 9n,?a, + 4nyn,a, + 6n,n,a, + 12n,n,a,

= (n, 4+ 2n, + 3n,)?u, =a, ,
as n, + 2n, + 3n, = (1 —2,—a,)+2a,+2,=1

We may therefore write:
(» a 5) (CES bao REE. erties arr ()
v

in which 6 is given by («), and (see above)

C= =n =) Sy —— ol Giese a vaso to 64)

The following equations hold for the dissociation equilibrium of

ihe double, triple ete. molecules resp. (cf my alveady frequently

cited Teyler paper 1908: Théorie générale de association ete.,

p. 5, and also These Proc. of June 23, 1911 (Solid State VII), for-
mula (28)):

(l—a,—a,—...)? C 2 tt 5—%/RT ete eee RY

- pe Tas ee
= ere 3 e/ a pte

re ees MO Gea ea Ge ee
role? Wi a (p+4/o)?

or taking the equation of state (@) into account :

Bee ee By
(1 Uyg— Lye ) a C, Th oe b/ RT e— 9. 2Agb : (e—b) (y— )

af ic R
beep NN 7 papers tea)
(L—#,—#,—-. ) wee 2778 6 —WRT ¢ - 9. 3Agb : (v—b) (y —)?
1 a 78
is Ws, vv

. . . . ry . . . > . . . i . ry . . .

in which C,, C,, ete. are the dissociation constants resp. of the
double, triple ete. molecules; y,, y,, ete. the changes of the specific
heat in the dissociation, divided by R, viz. y, = (2k,—A,): R,
Y, = (38h4,—A4,): R, ete.; 9,, qs, ete. the heats of dissociation (energy
changes) 2(¢,))—(e2)o, 3(€,)> —(@,),, ete.; Ab, Ad, ete. the variations
of 6 already introduced above, which must now resp. be multiplied
by 2, 3, ete., the above equations referring to n-fold molecular
quantities, and not to a single quantity.

The first member contains the relations of the molecular concen-
trations, viz.

40*

é* (n,:2n,)? 2,7 (1—#,—a,—...)?
= = 7 Tt i

ce Dn Oe nO ile 's (2)

e,* _ (n,: &n,)? De (l—#,—2#,—...)*
== ry ?

cn Mae eaHey role Vion ald

ete. (for Yn, has namely been put 0).
For the dissociation constants C,, C,, ete. holds:
log C, = — ¥. + Ay + (log R — 1),
log C, = —y, + 4, + 2 (log R— 1),
etc., in which A,y, 4,7, ete. represent the variations of the entropy
constant, divided by A, viz. A,yj=(2(,),—(m;),): 4 Ap =
= (3 (,), — (1,).): KR, ete.

If we now put all the quantities y and g=0, which is allowed
for quasi association (otherwise we only think the terms referriny
io it included in the dissociation constants, e. g., CT? ¢ t/RI=
= C,’, ete.), then for large volumes, where «,, 2, ete. will be slight:

: S C, e— 4 2dgb :(v—b) (y—b)
ie vy Kh

1 y;
_— A e—4.3A3b : (v—b)(y — B)?

ne -

or as also Ab: (v—bd), A,b: (~—), ete. will be very small for large
v, and v may be written for v — b:

. R 1 ma

“itr m ee C, ai CLC) er mae
of which the first equation is identical with (2) of § 3.

We further see, what we have already immediately put in our
abbreviated derivation, that really for very large volume .,,.7,, ete.
may be neglected by the side of «,, and that therefore the consider-
ation of the dowble molecules suffices with disregard of the numbers
of triple and multiple molecules.

If we now again compare the equation (3) with (p+-¢/,2\v—bJ=RT
(the latter therefore without taking quasi association into account),
then (see also (@) and (y)):

v—b = y—b,4+2,4,b+2,A,6 +...
6 1—*/,7, — ?/,0,—--

hence with neglect of z, ete. by the side of w,:

v—b,—wx,A,b b, 4b ;
v — = ——. ——— ore + fre .

;

z —.
SR

615

b! = »—b,--2, 4,6 + v.*/

In this the infinitesimal quantity ,4,b (also when A4,/ is finite)
may be neglected by the side of 6, and the also finite quantity
Ho /s2,, and we get:

OO Ue eae,

identical with (3) of § 3. For v.'/,2, the value R: C.

, follows then

again from (), and the conclusions are further as in the cited paragraph.

Fontanivent sur Clarens.

Chemistry. “Ourrent Potentials of Electrolyte solutions’. By
Dr. H. R. Kruyr. (Communicated by Prof. Ernst Coney).

(Communicated in the meeling of June 27, 1914).

1. For a proper understanding of the reciprocal action between
electrolytes and colloids the knowledge of the capillary-electrie
phenomena is indispensable’). Researches on the influence of the
electrolyte ‘concentration in these phenomena have indeed been
earried out of late years; Pwrrin*) and Enissarorr *) studied the
electric endosmose of electrolyte solutions, Burron *) determined the
influence of electrolytes in various concentrations on the cataphoresis
whilst there already exists a vast material on the capillary-electro-
meter and the dropping electrode’). The recent investigations were,
therefore, chiefly concerned with the measurement of the phenomena
of motion in consequence of a supplied electric tension ; the reverse
phenomenon, however, namely the occurrence of an electric tension
in consequence of a moving electrolyte solution has been but little
studied "). The former investigations on these current potentials
(generally, though less accurately, called “Str6mungsstréme”) are
restricted to pure water. True, Crwonson’) states that electrolyte
solutions cannot produce current potentials, but from the quoted
treatises of Gourk pe ViILLEMONTEL *) it appears that the latter only
1) For full details of this problem see H. #RmUNDLICH, Kapillarchemie, Leipzig
1909 in very condensed form H. R. Kruyz, Aanteekeningen Prov. Utr. Gen. 3 June
1913 p. 9 and Chem. Weekbl. 10, 524 (1915).

2) Journal de Chimie physique 2. 601 (1904).

5), Z. f{. physik. Chem. 79, 385 (1912).

), Phil. Mag. [6] 11, 425; 12, 472 (1905) and 17, 583 (1909).

5) Detailed literature statements in Cuwo.son, Lehrbuch der Physik IV 1.

6) The most important investigations of recent times are those of CAMBRON and
Orrrincrr, Phil. Mag. [6] 18, 586 (1909); GrumBacH, Ann. de chim. et de
phys. [8] 24, 433 (1911) and Ruiry, ibidem [8] 30, 1 (1918).

7) |. ce. note 5.

8) Journ. de phys. [3] 6, 59 (1897).

616

investigated solutions of CuSO,, ZnSO, and NiSO, in the concentra-
tion of 10 grams per litre. Because current potential and electro-
endosmose are so to say each other’s reflected image *), one
may rather expect that the electrolyte concentration will make
itself felt in a similar manner in regard to those two phenomena.
As Euissarorr (I. ¢.) found that even exceedingly feeble electro-
lyte concentrations strongly diminish or suspend the electro-
endosmotic transport, we can only assume from the negative result
of Gourté pe Vitiemontée that in the concentrated solutions used by
him the potential is already lowered to about zero. Rufty’s result *)
have also confirmed this conclusion.

Grumpacn *), who investigated the influence of non-electrolytes on
the current potential, has not used pure water as comparison liquid
but a KCl-solution of the concentration 1 millimol. per litre and in
this manner obtained positiv results. In the investigation here
described I have made use in many respects of the experimental
methods mentioned in GruMBACH’s paper.

KEM

Yi);
CL

A i

—— SS SSP 5 & A
Bee, EI el

OW, We)

QO oO

f aR &

Q oO

=| iB;

Fig. 1.

*) Vel. SaxEn, Wied. Ann. 47, 16 (1892).
=) JE Os
) I ee

Vv
I
I

617

2. Apparatus. In tig. 1 the apparatus used is represented
schematically. The liquid serving in the experiment runs from flask
F into flask F, through a doubly bent glass tube Aap, which is
partly drawn to a capillary. Into the three-necked Wouter flask /,,
which is closed by means of rubber stoppers with copper wire
ligature, arrives also (1) a tube @ through which air can be pressed
and (2) an electrode #,. In the other flask /’, is found an electrode
&, and a thermometer 7. The electrodes are Ag-AgCl electrodes.
A silver wire is fixed into a glass capillary by means of CaiLLrret-
wax, The protruding end is electrolytically covered with AgCl
according to the indications given by JAHN *).

A constant pressure above the liquid in flask /’, is obtained as
follows: by means of a cycle foot-pump mereury can be pressed from
the reservoir /, into R,; the pressure thereby generated is read off
on the open mercury manometer. As owing to the transferring of the
liquid from /, to /', the pressure would diminish a little during
the experiment, it is kept constant by means of the arrangement
CD by turning the handle C.

The measurement of the potential differences between the electrodes
E, and E, was carried out by the compensation method of Pogary-
porFr-pu Bots Reymonp. A galvanometer could not be used as a zero
instrument because the strength of the current passing through the
instrument is exceedingly small in consequence of the enormous
resistance in the battery /F,. Hence, a capillary electrometer
(KEM in fig. 1) was used, which was fixed to the object table of
an ordinary microscope; the axis of the microscope was, of course,
placed horizontally. The readings were made using of an ocular-
micrometer, objective 4c (Reicnert) and Huyeens ocular 1.

The following serves to further explain the figure. S, is a key
for cutting off the short circuit of the capillary electrometer; A in-
diecates that this is connected with the earth. As working element
are used one or more accumulators Acc whose tension was determ-
ined by comparison with a Weston standard-cell, which was placed
in a thermostat at 25° (WNE). By O the different current inter-
rupters are indicated; by O, the electrodes #, and £, can be brought
into short circuit, which was always done during the time that no
observations were made. By Q, the current of the working cell is
twitched in; QO, annables to introduce at will one, two or four
accumulators as a compensation battery. QO, renders it possible to
take up in the circuit either the standard cell or the battery 1, /’,.

1) Zeitschrift f. physik. Chem. 38, special page 556 (1900).

618

In order to protect the Ag-AgCl-electrodes from the light, the
flasks /’, and /, are externally coated with a film of red gelatin
obtained by inserting them in a solution of gelatin to which a little
eosine had been added and which had just started to gelatinise.
Moreover, they were always protected from direct daylight.

3. Method and preliminary experiments. The measurements were
made a few minutes after the pressure had set in. A number of
measurements at different pressures were always made. When between
{wo measurements the liquid had to be pressed back from flask /,
to flask 7’, (for which at @ the connection with the pressure arrange-
ment could be broken off and an oil suction pump attached), no
measurements were executed at suction pressure.

From Grumpacn’s experiments we notice that the value of the
current potentials varies a little during the first days after the con-
struction of a battery /,F,. 1 repeated one of his observations, also
with the object of comparing the results obtained with his and my
own apparatus.

Table I contains the results of a series of measurements carried

TABLE I.
p iE E P| ae ae
em mercury) millivolts P cm mercury , millivolts | P
11 March = t= 14° | 622 | 253 4.1
61.2 271 4.4 SIe | 218 4.3
86.4 367 4.2 average 41
54.8 236 4.3 yj Mes March Le OS
70.8 315 4.4 82.2 310 | 3.8
average 4.3 85.2 323 | 3.8
12 March 1 1 ele 22 280 3.9
43.2 201 tel “eos | |) 1236 ll ene
57.2 240 4.2 average 3.9
68.1 | 280 41 16 March = t= 14°
average 4.2 | 86.2 | 341 | 4.0
13 March = t= 14° 70.2 | 284 | 4.0
85.2 | 350 4.1 58.8 240 | 4.1

73.2 | 302 | 41 | average 4.0

619

out with a solution of the concentration 1 m. Mol. AC/ per Liter.
The battery was filled March 11'". P indicates the pressure, E the
current potentials.

From this we notice that the apparatus acted splendidly. The
potential per em. mercury pressure has each day a constant value,
but varies the first two days. On the third day the terminal value
is attained.

4. Ieasurements. In this paper a series of measurements is com-
municated, the object of which was to ascertain the influence of
some solutions which differed in the valency of the cation. Therefore
solutions’ of the chlorides of A’, Ba’, and Al" were used. As
solvent was always used so-called “conductivity water”. The very dilute
solutions were made by diluting a standard solution. Ali measures
used in this investigation were carefully calibrated or recalibrated.

In order to shorten the time of these tedious measurements
they were all executed 20 hours after filling the cell. True, the
constant terminal value is then not yet attained, but the difference
is comparatively small and the error introduced is the same in all
measurements. Moreover, the inaccuracy caused thereby is without
influence on the tendency of the conclusions presently to be drawn,
in itself a good reason for proceeding to this measure of enormous
time saving. Moreover, several sets of flasks were used, in such a
manner however that, for instance, all the ACZ/ solutions were
measured in the same set. Finally, the sets were compared mutually
in which the solution of 100 a J/o/. (micromol ='/,,,, millimol) A C7
p. L. served as comparison liquid. With both apparatus was found
exactly the same value for the potential per unit of pressure.

In the subjoined tables, the concentrations in the first column are
given in « mols. p. L.; in the second column is found the current
potential #7 in millivolts per unit of pressure (ecm. of mercury) under
which the liquid was forced over. This value is always the mean
of two ov more measurements whose differences were of the order
of those in Table | (generally much less than those).

When in the tables no sign is indicated at the potential value,
the condition (as with pure water) is such that the electrode E, in
fig. 1 is negative. In the A/C/, solutions a change of poles took
place, hence the potentials following are indicated by ++.

The results of the tables If to [V are represented graphically in
fig. 2. Fig. 3 also gives the curve for A/C/, on a larger scale.

-300 -300

200

—200

= 100 —100

a
100 200 300

400 500 10
conc. Mol p.Li. conc. 4 Mol p.L,

+100

J
Fig. 2. Fig. 3.
TABLE II TABLE III
| KCI | BaCh
| = | |
Cone. | | Conc.
in yMol | Bi | in #Mol Pa
| P P
Dale | Puls
|
= = : —| a
0 about 350 | 10 139
50 102 | | 25 79
100 | 51 | 50 44
250 | 23 | | 100 25
|
500 | 12 | 200 9
1000 | 4 | 1000 1
40000 no exchange of
poles

621

0 about 350
| 0.5 52
1 | + #2
2 le se |
3 + 129 |
| 4 Le == 100 |
| 10 Hee ease |
| 100 Ib eectaves
500 ah 4A |

5. On considering these results we notice, of course, first of all the
great influence of the valency of the cation; as this gets higher the
capillary gets more strongly discharged at an equal concentration. This
had also been observed by Enissarorr when measuring the electric
endosmose and may be noticed with Risry from his experiments with
uni- and bivalent ions. The latter has observed a change of poles only
onee, namely with copper nitrate and that only at a high concen-
tration’). In the case of A/C/, about 0.8 uw mol. or about O.1 mg.
per liter appears to be sufficient to lower the current potential from
about 350 mV. to zero. It seems remarkable that this charge reversal
does not take place with AaC/, (see Table II) neither with ZnSO,
or CuSO, (Rifty) nor with substances with a univalent cation.

Still more striking is the fact that according to Exissarorr, the
electro-endosmotic transport requires, in a glass capillary, 100 micro-
mols of Al: to be reduced to 0 without a reversal occurring, whereas
the same investigator, although attaining the zero point, with a quartz
capillary, at about the same concentration as required in our research
{he found 1.6 @ mol. $ Al, (SO,),| could not even then notice a

reversal of the transport direction. This creates the impression that

1) The exact concentration cannot be made out from his experiments. In any
case, however, it lies above 900 « mol p. L.

622

in that research secondary influences come to the fore; perhaps the
powerful electric field in which the measurements are executed is
not without influence on the capillary itself. Only the quadrivalent
Th-ion was capable of causing a charge reversal.

The results obtained here are in harmony with the general theore-
tical points of view. The electric double layer in the capillary, in
the case of pure water consists of 'OH-ions at the side of the glass
wall and ‘H-ions at the side of the liquid in consequence of the
selective ion adsorption of the glass wall which always adsorbs the
‘OH-ion more strongly. From the electrolyte solutions the cations are
absorbed more eagerly than the anions so that the charge gets lowered.
If this adsorption for KCI, BaCl, and AICI, is such that solutions of
the same molecular concentration are absorbed about equally, it is
conceivable that the three times more active Al-:-ion requires a much
lesser concentration than the K'-ion in order to attain an equal
potential reduction.

If once the capillary is charged reversely the adsorption of the
Cl-ion, which carries a charge now opposite to that of the capillary,
seems to predominate. The positive charge now soon attains (at 3 j mol.)
a maximum value, and than decreases, but only slowly, because the
discharging ion is univalent here.

In agreement with the theory are also the resalis of Ruiry '), for
instance that the salt of a heavy metal has a stronger discharging
action than that of a lighter one (Cu and Zn, at least in the small
concentrations). A cation of a heavy metal is known to be adsorbed
more strongly than that of a light one.*)

Moreover, the behaviour in the case of CuSO, and of Cu(NO,), is
in agreement with investigations as to the adsorbability of those salts *).
The influence of the anions is also observable in Rusry’s results and
appears to have an effect corresponding with that in the ease of
AICI, just described.

The question whether the organic cations also behave according to
the theoretical expectations is being considered. Several other solutions
of electrolytes in water as well as in mixed solvents *) will be
investigated.

Utrecht, June 1914. van ‘ Horr-Laboratory.

MHL @

2) Morawitz, Koll. Beih. 1, 301 (1910).

5) Freunpuicu and Scuucui, Z. f. physik. Ghem. 85, 641 (1913).

*) Of these have also already been measured a few series in connexion with
the researches of Kruyr and van Dury, Koll. Beih. 5, 269 (1914).

623

Chemistry. — “Electric charge and limit value of Colloids’. By
Dr. H. R. Kruyr. (Communicated by Prof. Ernst Coney).

(Communicated in the meeting of June 27, 1914).

1. The present conception as to the relative stability of the sus-
pensoid system and the way in which it may be suspended has been
developed according to the following train of thoughts.

Harpy *) and afterwards burton *) have undoubtedly established
the fact that this relative stability falls and stands with the electric
charge of the suspended particle. Indeed, the permanently suspended
particle that exhibits a vivid Brown’s motion, has a cataphoretic

oF : Volt—. re
mobility of the order 2—4 uw per second and per eM. ;if by addition
e.M.

of an electrolyte one diminishes the relative stability, this velocity
also decreases and therefore, the electric charge of the particle has
evidently decreased also. The ‘iso-electric’” point, where that charge
seems to have become zero, coincides with the moment of the small-
est stability. Since the research of Wuitney and Ossr *) we know
moreover, that with the repeal of the stability (the coagulation) is
coupled a combination of the coagulating ion with the particles, and
by Freunpiicu’s *) researches we arrived at the knowledge that these
phenomena are described quantitatively by the equation of the
adsorption-isotherm.

From these elements is built up the theory that the particle owes
its charge to the selective ion-absorption in its boundary layer and
loses it by tke selective adsorption of the oppositely charged ion of
the coagulating electrolyte. As specific properties of the adsorbent are
usually of but very subordinate influence on the order of the charac-
terizing quantities in the adsorption, the action of diverse electro-
lytes on all capillary-electric phenomena ought to exhibit the same
order, which the researches as to the electro-endosmotic phenomena
compared with those of the coagulation of colloids have indeed
confirmed.

It now occurs to me that the researches on the current potentials,
particularly those which have been communicated in the preceding
paper, are capable of furnishing us not only with a new proof of
that equality of order, but also demonstrate that the influence which

1) Z. f. physik. Chem. 33, 385 (1900).

2) Phil. Mag. [6] 11, 425; 12, 472 (1906) and 17, 582 (1909).

8) Z. f. physik. Chem. 39, 630 (1902),

) Zeitschr. f. physik. Chem. 73, 385 (1910) and 85, 641 (1913),

624

electrolytes exert on the charge of a glass capillary is quantitatively
the same as that exerted on the colloidal particle during the coagulation.

2. As regards the order of the ion-actions, it has been pointed
out in the previous paper that the ions discharge more strongly,
when their valency is higher and that the heavy metals exert more
influence than the light ones of equal valency. It is well-known
that the limit values for the coagulation of suspensoids just exhibit

the same peculiarities.

3. In order to make a quantitative comparison it should be first
observed that the limit values for KCl and BaCl, in the same sol.
are generally in the proportion of about 60: 1. In contact with
either of these solutions the charge of the particle thus gets equally
diminished. We may, therefore also expect that the charge of a glass
capillary will be lowered by a solution of KCI to the same extent
as by the sixty times weaker BaCl, solution. Hence, when from the
tables 1 the preceding paper we calculate the charge in concen-
trations of KCl and BaCl, in the said proportion, those should be
equal if the idea as to the limit value just revealed is a correct one.

The caleulation of the charge is possible according to the theory
developed by Hetmno.rz'). The current potential is sequel to the
electric double layer formed at the wall of the capillary and is
related to the electric moment J/ as follows.

w
f= WP 6 S|) Sea
y)

in which w represents the specific resistance and 1 the constant of
the internal friction whilst P represents the pressure employed. For
comparison purposes we can consider the electric moment of the double
layer just as well as the charge ¢ per unit of section, as it is in
inverse proportion therewith.

We write equation (1):

If now we indicate the quantities relating to a BaCl,- solution
with the index /, those relating to the 60 times more concentrated
solution of KCl with the index /, then on the strength of the above
considerations we must get

EN Mb ef ie
al wy \PJe wx

(! Wied. Am. 7, 337 (1879).

625

As we only have in view very dilute solutions, we may put
Hy = 7 (namely = yu,0). From this follows

or in words: the relation of the current potentials of two electrolyte
solutions whose concentrations are related as in the limit values of
colloids are inversely proportional to the specific resistances of those
solutions.

Meanwhile attention should be called to the fact that by limit
values in this connexion we must not understand the concentration
y of the electrolyte added. From this a part is withdrawn by
adsorption and hence, to the setting in end-condition appertains a
lower concentration, which we will call x. In the experiments as
to the current potentials we may probably identify the total con-
centrations with the equilibrium concentrations as the adsorbing
surface (the glass walls) is so small: only in the ease of the exceedingly
weak AICI, solutions a doubt may arise. But in the colloid systems
that difference may not be neglected. These y-values themselves

Fig. 1.1)

ae
1) In Fig. 1 on the axis of coordinates should be read in stead of
mm m

626
have been determined only for As,S,') and HgS, *) and for electro-
lytes not used here.

The proportions are :

With As,S, XNH,Cl : XUO(NO;). —= 82
» Hg,S ~xNH.Cl: XBaB, = 29.

The proportion chosen 60:1 is, therefore, a rough approximation,
but a comparison with y-values of other sols (P¢, Aw ete.) renders
it probable that it represents the average.

The relations between charge, adsorption and limit value are
elucidated schematically in the above figure. In the upper half of
the figure is drawn the charge ¢ of the capillary in dependence on
the concentration of the traversing liquid, so that J, I], and III stand
for uni-, di- and trivalent cations respectively. In the lower half is
given, with the same concentration axis, the correlated adsorption
of the electrolyte as a downward directed ordinate. If now y,, ¥%,
and y, indicate the relation of the limit values for uni-, di- and
trivalent cations, respectively the correlated downward directed ordinates
must sbow the proportion 1:13 :3 and the upward directed ones
equal values.

4. For verification of this relation appeared suitable :

(a) 10 uMol BaCl, — 600 uMol KCI.

6) 25 uMol BaCl, — 1500 «Mol KCL.

It would not do to simply take the specific conductivity powers
as being proportional to the concentrations because in the so strongly
diluted BaCl, solutions the conductivity power of water could not
be neglected. Hence, I have made a direct measurement of the
relation of the specific resistances by fillmge m1 Wuwatstonn’s bridge
a vessel of arbitrary but fixed capacity with the liquids used.

The relation of these resistances was in the pair (@)

o, 4680
— = —_—_=—19
wk 247

and in the pair (¢)
oy 20 70n
wr 99.9

K ,
The values of P are obtained from the research communicated
in the preceding paper.

!) Freunpuicu, Zeitschr. f. physik. Chem. 73, 385 (1910).
*) Freunpiicu en Scuucut, ibidem 85, 641 (1913).

627

As the relation of the potentials for (a) we obtain +4* or 14; as
the relation of the resistances: 19.

From the combination (4) we obtain for the potentials = cr 26,
for the resistance 28.

This agreement undoubtedly tells much in favour of the above
mentioned theory. With concentrations somewhat larger than 60 the

agreement might be better still.

5. The material of Rifry') is only once suitable for testing the
relation (2).

For so far his measurements have been executed with solutions
of salts other than chlorides his measuring electrodes were non-
reversable ones and his results are therefore useless for quantitative
verification. | have only been able to find one combination of
chlorides where concentrations have been measured which are com-
parable with limit values: they are KCl and HCl. For As,S,-sol
these limit values have been determined to 50 and 31 mMol p. L.
respectively °*).

Now from his experiments Rifry has calculated the potential at
the capillary wall in certain units for 0.01 n. KCl as 3.1. We can
use this figure again for comparison purposes at it is directly propor-
tional to the charge.

In the case of HC] he determined for 0.005 7 : 3.39, for O.OLO 7 : 2.8,
For the comparison with 0.01 2 HCl we must know the potential at
the concentration #4 x 0.01 = 0.0062. This, | have interpolated by
assuming that the logarithms of the potentials are directly propor-
tional to those of the concentrations, after I had first convinced
myself that this interpolation") formula was quite satisfactory in the
longer series stated in Rigrys paper. We then find 3.2 which is
again a splendid agreement.

6. Quantitative comparisons with the trivalent cation are difficult
to draw, because the y-values thereof are either not known or uncer-
tain. From the treatises cited on p. 648 we, however, get the
impression that the z-values diverge very little from zero, as is also
expected from Table IV of the preceding communication, because a
complete discharge takes place already at a concentration of 0.8 u mol.

7. A no less striking parallelism between charge and limit value

1) Ann. de chim. et de phys. [8], 30, 1 (1913).

2) Frevuxpuicu, Kapillarchemie (Leipzig 1909) Table 81. True, those are 7- and
not y-values, but with these univalent ions, this cannot have any serious influence,

8) To this formula should only be attached the significance of an interpolation formula,

Proceedmes Royal Acad. Amsterdam. Vol, X VII

628

is furnished by the shape of the curve found for the current potential
with AICI, solutions. This line is absolutely connected with the
so-called irregular series.

From what is stated in § 3 in connection with Table 1V (fig. 3,
respectively) of the preceding paper it follows that the concentration
at which the battery- shows an exchange of poles, is also that of
the zero-charge of the capillary, whilst its positive charge goes up
to about 3a mol. and thence lowers without however reaching zero
again. An AICI, solution will consequently have first a discharging
and therefore a coagulating effect on a negative sol. ; at higher concen-
trations it will render it a positive sol and only at a much higher
concentration it will again reverse the charge and cause coagulation.
But therewith are described exactly the phenomena which, for instance,
have been observed by Buxton and Taneur'), when they coagulated
mastix with AICI, and indigo or Pt with FeCl,. The lower non-
coalescent, the lower coalescent zone, the upper non- and coalescent
zones, they can so to say be read off from the figures of the preceding
communication.

One is accustomed to attribute the phenomenon of the irregular
series tO a special action of the hydrolytically resolved hydroxides
of the coagulating ion. In connection with the preceding arises a doubt
whether to Al(OH), ought really to be attributed a preponderating
significance. For it does not seem probable that the AICI, which is
present in such a small concentration, can cause a reversal of charge
in the capillary. Much more acceptable seems the following idea. A
strongly discharging cation unloads the capillary at such a small
concentration that the small anion-concentration cannot prevent a
complete reversal of charge. Of this the anion-concentrations are
capable in the case of Ba and K- because there the charge gets
nearer the zero value only at so much larger concentrations.

Hence, the afterzone phenomenon will occur, as soon as the dis-
charge by the cation is already very large at small concentrations—
and is favoured by a feeble action of the anions. This strongly dis-
charging action of the cation may arise from its higher valency or
from its strong adsorbability. The fact that irregular series were
observed, for instance, also with strychnine nitrate, new fuchsin,
brilliant-green, auramine and_ silver nitrate *) is quite in harmony
with this argument. For here we are dealing with strongly adsorb-
able cations and because they are univalent the equivalent anion

1) Z. f. physik. Chem. 57, 64 (1907.

629

concentration present is still proportionately three times less than
with AICI,.

A start has already been made with investigations to get a proper
insight, particularly in this question of the irregular series.

8. Finally it should be pointed out that the previous considera-
tions also give an explanation of the fact often stated by us that in
the ease of Al-salis we can determine the limit value much more
accurately than with salts of uni- or bivalent metals. Two tubes with
As,S, sol. which contain Al in concentrations situated 1°/, above
and below the limit value, respectively exhibit after shaking a quite
clear and a turbid fluid respectively. In the case of bivalent cations
we must, so as to make quite sure, take the difference somewhat
Jarger and very much so for a univalent ion. It is self-evident

ae de
that the cause lies in the fact that ae charge, ¢ concentration of
coalescing ion) for Al is > for Ba and this again > for K-.

Utrecht. June 1914. van ‘Tt Horr- Laboratory.

{November 7, 1914).

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.

PROCEEDINGS OF THE MEETING
of Saturday October 31, 1914.
Vou. XVII.

Doce

President: Prof. H. A. Lorentz.
Secretary: Prof. P. Zeeman.

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Zaterdag 3i October 1914, Dl. XXIID).

ChE) ANF ah ao IN ae SS).

G. van Rignsperk: “Jn the nerve-distribution in the trunk-dermatoma.” (Communicated
by Prof. C. WinkixrR), p. 632.

Ernst Couen and W,. D. Herperman: “The Allotropy of Cadmium” IV. p. 638.

Ernst Conen and W. D. Herperman: “The Allotropy of Zine.” III, p. 641.

Ernst Conen and J. C. van pen Bosco: “The Allotropy of Antimony”, I. p. 645.

A. P. N. Francuimonr and H. J. Backer: “The Coloration of some derivatives of Pi-
erylmethylamide with alkalies”. p. 647.

A. P. N. Francutmonr and H. J. Backer: ‘“z-Sulpho-propionic acid and its resolution into
optically active isomerides”’, p. 653.

Miss H. J. Former: “A new electrometer, specially arranged for radio-active investigations.”
Part I. (Communicated by Prof. H.-Iaca), p: 659.

A. Suits: “The metastable continuation of the mixed crystal series of pseudo-components in
connection with the phenomenon allotropy”. If. (Communicated by Prof. J. D. yan pER
WaAats). p. 672. %

A. Smits and S$. C. Boxnorst: “On the vapour pressure lines of the system phosphorus”. IT.
(Communicated by Prof. J. D. van pER WaAALs), p. 678,

A. Suits and A. H. W. Aten: “The application of the theory of allotropy to electro-motive
equilibria.” III. (Communicated by Prof. J. D. van per Waats). p. 680.

¥. E. C. Scurrrer: “On gas equilibria, and a test of Prof. van per Waats Jr.’s formula”, I.
(Communicated by Prof. J. D. vAN per WaAAts), p. 695.

W. Reivers: “Equilibria in the system Pb—S—O; the roasting reaction process”. (Commu-
nicated by Prof. S. HooGrwerre), p. 703.

Proceedings Royal Acad. Amsterdam, Vol. XVIL.

632

Physiology. — “On the nerve-distribution in the trunk-dermatoma’.
By Prof. G. van Ruyperk. (Communicated by Prof. C. WINKLER).

(Communicated in the meeting of September 26, 1914).

We know as a result from the researches on the segmental skin-
innervation, made after the method of the so called “remaining
aesthesia’”’, first introduced by Snerrincton, that from a definite
zone on the skin (the dermatoma or root-area) stimuli may reach
the spinal cord along each separate dorsal root of the spinal cord.
Such investigations, however, do not teach us anything about the
manner in which the sensibility in each of these root-areas is
provided for by the peripherical cutaneous nerves. A few experi-
ments made on dogs have enabled me _ presently to offer the
following conclusions concerning exclusively the dermatomata of
the trunk.

In a dissertation by O. NAnricn’), written under the direction of
ELLENBERGER, the nerves providing the skin of the dog are described
with elegant accuracy. It is shown therein, that the skin of the

Fig. 1. Cutaneous nerves of the dog, according to NAuricu. —0O1 = Th. 1, first
thoracic nerve, dorsal branch. rl = first thoracic nerve, lateral branch. rl = Th. 3,
third thoracic nerve, ventral branch, ul = L. 1, first lumbar nerve, dorsal branch,
q =nerve of the large subcutaneous muscle.

1) O. N&uricw. Die Gefiihlshezirke und die motorischen Punkte des Hundes,
Ein Beitrag zur vergl. Anatomie und Physiologie. Inaug. Diss. Ziirich 1907.

633

trunk is innervated by means of the perforating branches of the
intercostal and lumbar nerves.

If Th. 3 is taken to be the most cranial and L. 4 to be the most
caudal nerve of the trunk, it will be found that from Th. 3 to
Th. 7 each nerve-root is sending three perforating branches to the
skin: a dorsal, a lateral, and a ventral branch. The dorsal nerve-
trunk generally supplies two main branches: a medio-dorsal and a
dorso-lateral one. The lateral nerve invariably supplies two branches :
a latero-dorsal and a latero-ventral branch. The ventral nerve-trunk
usually consists of one main trunk, which may be said to be medio-
ventral. From Th. 8 to L. 4 the medio-ventral branches are wanting:
their place is taken by the latero-ventral ones.

The different points, where the dorsal, lateral, and ventral nerves
enter into the skin, may be interconnected by lines. This having
been done, it becomes evident that the dorsal branches, going in
a cranial-caudalward direction, perforate the fascia continually at
a greater distance from the mid-dorsal line, whilst the lateral trunks
on the contrary come forth more dorsalward. A correct insight into
the relations of these nerves is offered by Fig. 1. From Fig. 2 it
may be seen moreover, that the skin of the trunk can be divided,
according to a superficial scheme, into three zones as regards its
peripherical nerves: a dorsal, a lateral, and a ventral zone.

rt dyrsales dM
yok
Framt laterales dda tntercostalest >

. cum M pectoralts dorsaltsve
} Ss Ash

>
Ss
J
Q
nn
S
&
JA &
ast! >

~ Netut hunger pest W axill)

B . cul cruris

_ anterior,
Se

Fig. 2 Extension-zones of the dorsal, lateral, and ventral nerve-branches of the
skin of dogs, according to NAuricu.

I. The first question I now put to myself was the following: are
the perforating dorsal, lateral, and ventral trunks, which belong when
42*

634

prepared macroscopically, to one intercostal resp. to one lumbar
nerve, unisegmental or pluri-segmental nerve-canals. For whilst it
is admitted almost generally that the intercostal nerves are uniseg-
mental courses, Ersier') believes “he has sufficient grounds for
stating that delicate nerve-plexus, situated on the inside of the ribs
always connect two intercostal nerves. This being so, an interchange
would oceur here between nerve-fibres of a different segmental origin.
Concerning the nerve-distribution of the root-areas, this question
may be formulated as follows: Do the nerve-fibres of each separate
dorsal root of the spinal cord reach the skin-area belonging to that
root along one single dorsal lateral or ventral perforating nerve-
trunk, or along several ones?

In order to solve this question, I made the following experiment.
After the afore mentioned method of Samrrinctron, the dorsal (and
ventral) spinal nerve root of a segment on one side of the spinal cord
of some dogs was “isolated”, usually between three cranial and as
many caudal roots, which were cut through extradural. This being done,
the isolated root-area, corresponding to the isolated root, was
demareated against the two insensible zones, corresponding to the
sectioned roots. Situation, form and extension of the sensible root-
area once being well defined, the skin was entirely cleft both in the
cranial and in the caudal insensible zone by a slit passing from
the mid-dorsal to the mid-ventral line. This of course could be done
without narcosis. Immediately after this, a search was made for
the perforating skin-nerves, and at least three successive ones of
these in cranio-caudal direction, in the dorsal, lateral, and ventral
skin-area, were prepared free, as much as possible avoiding any
lesion of them. Next to this, by means of the induction-current,
these nerves were stimulated to ascertain whether they conducted
painstimuli. Invariably the result was, that for each skin-area such
was only the case with these branches that belonged to one point
of entrance. lrritation of the other branches, even with the strongest
induction currents (the bobbin being entirely pushed in), never
produced any symptom of pain, if slippings of the current were
avoided. This result was wholly confirmed by a contra-experiment.
If, after careful determination of the dorsal, lateral and eventually
ventral branches, which were conductors of pain-stimuli, these branches
were cut through, the sensibility in the isolated root-area proved to
be destroyed entirely and irrevocably.

1) P. Etster. Ueber die Ursachen der Gefleclitbildung an den peripheren Nerven.
Verh. d Anatom. Gesellsch a. d. 16e Vers. in Halle. 1902. S. 200.

635

Thus it results that the trunk-skin of the dog forwards its stimuli,
destined for a definite segment of the spinal cord, only by means
of one set of peripherical skin-nerves. This means that in those
nerves only fibres belonging to one posterior root have their course,
and that consequently the perforating skin-branches are segmental
nerve-canals.

II. A second question, necessarily presenting itself, is the following
one: what separate portion within the dermatoma is innervated by
either the dorsal or the lateral (ventral) peripherical branches ?

To investigate this, the above-mentioned method was partially repeated
once more. With dogs, where a nerve-root had been isolated, the
peripherical branches entertaining its sensibility were sought for and
prepared free. After this the conduction was successively interrupted,
either provisorily or lastingly, in one or more of these branches.
To obtain a lasting interruption of the conduction, the branch was cut
through. For a provisory interruption the branch was enfolded by a
piece of cottonwool, drenched in a 5°/, solution of stovaine. The
conduction .once interrupted, the root-area was tested to ascertain
whether a portion of it had become insensible, and if so the confines
of the insensible area found in this manner were determinated.

Fig. 3. On a dog a root-area (Th. 10) has been isolated between two
insensible zones. After this, three cutaneous branches belonging to the dorsal
perforating nerve-trunk, are successively cut through. The dotted portion
of the root-area then becomes successively insensible, until finally the whole of
its dorsal part has lost sensibility.

a. Interruption of the conduction in the joint dorsal cutaneous
branches.

636

After this operation the entire dorsal portion of the isolated
dermatoma was found to have lost sensibility. To make the ventral
demarcation of the area that has been made insensible in this way
rightly understood, I may add the following: For a long time I had
been struck by the fact that after a carefully performed root-isolation,
the demarcation-lines of the isolated root-areas showed at a definite
point a distinct bent. The origin of this bent is, that at some
distance from the mid-dorsal line of the body, both the cranial
and the caudal demarcation lines of the root-area, change their
direction somewhat cranialward. In the cranial demarcationline this
bent is always found a little more dorsalward than in the caudal
demareationline. Now it is remarkable, that the ventral limit of the
insensible zone, originated by the sectioning of the dorsal nerve-
branches, is invariably found to be a straight line, connecting the
cranial with the caudal limit just above this bent. This line therefore
goes in a cranio-caudal direction. At the same time however it
deviates slightly in a dorso-ventral direction. Consequently the
latero-ventral nerves supply within the root-area the innervation of
a zone extending to a point somewhat above the alleged bent in
its demarcation-lines.

6. If the conduction is interrupted in the joint latero-ventral
branches, the entire ventral portion of the root-area becomes insensible.

Fig. 4. The same as in ig. 3, only for branches of the Jatero-
ventral trunk. (The isolated root-area is probably in the main Th. 12.
Its closer definition was neglected in the necropy.)

If we compare the demarcationline found in this way, with that
found after interrupting the conduction in the dorsal branches, it
becomes evident that the ventral boundary of the dorsal area does

not coincide exactly with the dorsal boundary of the ventral area,
but that a reciprocal overlapping occurs, although it be only a
slight one. It is shown thereby that the bent, found in the demar-
cationline of the root-area, is situated exactly at the point where the
dorsal and latero-ventral portions of the dermatoma meet. The cranial
direction of this bent indicates that the latero-ventral portion must
be lying somewhat more cranialward than the dorsal one. This fact
has been stated previously by Bok"), when he found in 1897 a
“discrepancy” of the dorsal and ventral dermatoma-areas on the
human trunk. In the experimentally defined dermatoma this discre-
pancy finds its expression in the alleged ‘bent’. Similar conditions
have been observed clinically by Eicuuorst’), after transversal lesions
of the spinal cord in the trunk-area.

ce. Interruption of the conduction in separate minor branches of the
dorsal and Jatero-ventral nerves.

The conduction may be interrupted in the separate minor branches

of the perforating nerves as well in the dorsal as in the latero-ventral
portion of the root-area. When this operation has been performed it
becomes evident, as long as only the larger branches were subjected
to it, that each of these supplies the innervation of a small zone,
extending equally into the cranial and into the caudal boundary of
the root-area, and for the rest demarcated by lines going in a
cranio-caudal direction. The whole root-area therefore is divided
into a series of small areas, lying alongside of one another in
dorso-ventral direction. The skin-area of the medio-dorsal branch
adjoins the mid-dorsal line, the dorso-lateral branch on the other
hand extends over an area, adjacent to the lateral portion of the
dermatoma, more ventralward than that of the medio-dorsal branch.
A similar ordination is found likewise to exist for all skin-areas
corresponding to the various latero-ventral branches.
Whenever very thin branches are cut through, either no insensi-
bility ensues, or else an irregularly insensible spot is found some-
where within the root-area. From the fact that in many cases, after
the sectioning of such small branches, no insensibility is found, we
may conclude that the areas of extension of the separate branches
of the cutaneous nerves must overlap one another to a certain degree.
I have not been able however to determine the extension of these
overlappings.

1) L. Bouk, A few data from the segmental anatomy of the human body.
Ned. Tijdschrift v. Geneeskunde. 1897. I p. 982—995, and 1897. II. p. 865—379.
(Compare especially p. 366 et seq.).

2) H. ErcHaorsr, Verbreitungsweise der Hautnerven beim Menschen. Zeitschr.

f. Klin. Medicin. Bd. XIV. S. 519. Berlin 1888.

638

Ill. Finally my attention was given to the nerve of the subcutaneous
muscle. NAnricn') testifies that by irritation of this nerve, in addition to
contraction of the cutaneous muscle, also pain-symptoms are brought
forth, whilst after the sectioning of this nerve, the sensibility of the
skin had diminished. I have not been able to verify this latter fact. It
is not to be doubted moreover that e.q. an isolated root-area, if either
the isolated root or the peripherical branches have been cut through,
becomes entirely and completely insensible, whilst the nerve of the
cutaneous muscle remains intact. It is therefore probable that this
nerve does not contribute to the sensibility of the skin. Nevertheless
I can confirm the statement of NAurica, that after its having been
cut through, irritation of the central end proves painful. It may be
that the muscular sensibility plays a part in producing these symp-
toms of pain.

Chemistry. — “The Allotrepy of Cadmium.” 1V. By Prof. Ernst
Courn and W. D. Her.peErMAn.

(Communicated in the meeting of September 26, 1914).

The electromotive behaviour of Cadmium. LI.

1. Up to the present we have only directed attention to the
electromotive behaviour of @- and y-cadmium; the 8-modification has
not been mentioned hitherto. It will be treated in the following lines.

2. It may be remembered that a number of cells constructed
according to the scheme:

Cd Guinea | Cd-amalgam
electrolytically : fee 12.5 percent
cenosied cadmium sulphate | py een
had an E.M.F. of 0.050 Volt at 25°.0, whilst the E.M.F. of others
was only 0.047 Volt at the same temperature. (The cells were
reproducible within 0.5 millivolt).

3. Now we were struck by the fact that when constructing a
large nuniber of these cells we often got cells which had an E.M.F.
of 0.048 Volt at 25°.0.

The E.M.F. of cells which originally had an E.M.F. of 0.050 Volt
at 25°.0, spontaneously decreased till the value 0,048 Volt was reached.
After this their E.M.F. remained constant.

4. The conclusion was plain that the cells giving 0.048 Volt might

1) L. c. p. 95—96,

639

contain /-cadmium, those giving 0.047 Volt ecadmium, whilst those
giving 0.050 Volt have y-cadmium as a negative electrode.

5. If this were really the case, it would be possible to construct
a transition cell by combining a cell with a@-cadmium with one
containing B-cadmium,; the E.M.F. of this combination would be zero
at the transition temperature of the change v-cadmium 2 p-cadmium.

6. However it is impossible to carry out an exact determination
of the transition point in this way, as the E.M.F. of the combination
is (at 25°.0) only (0.048—0.047) = 0.001 Volt and the reproducibility
of each of the cells is only 0.5 millivolt.

7. In order to ascertain if the E.M.F. of the B-cells has a real
significance, experiinents may be carried out on the following lines:

At temperatures above the transition point of the change «-cad-
mium 2 #-cadmium (which we found in the neighbourhood of 60°
by dilatometriec measurements) the E.M.F. of a@-cells must be higher
than that of p-cells. After cooling the cells below the transition point
mentioned, the contrary will occur.

8. Our experiments in this direction were carried out in the
following way:

We constructed a large number of Hurnrr cells’); one of these,
the E.M.F. of which had been originally 0.050 Volt at 25°.0, had
an E.M.F. of 0.047 Volt (at 25°.0) after having been kept for 4 weeks
at 47°.5. After this time it remained constant.

We combined this cell (N°. 7) with
another one (N°. 22) the E.M.F. of
which was 0.048 Volt at 25°.0. The
two cells AB (N°. 7) and CD (N°. 22)
were connected by a siphon H,
which contained the same solution
of cadmium sulphate as was present
in the cells. (Fig. 1).

The lateral tube E of the siphon
was closed by a rubber tube F, in

which was put a glass rod G. The

little apparatus was brought into a
Fig. 1. thermostat which could be kept at

will at 25°.0 or 64°.5.
9. We measured the E.M.F. between the cadmium which had
been electrolytically deposited on the platinum spirals A and C

1) Proceedings 17, 122 (1914),

640

against the common amalgam electrode B. (12.5°/, by weight). It
is absolutely necessary to use a common electrode as the cadmium
amalgam of 12.5 percent by weight does not form a heterogeneous
system at 64°.5; its E.M.F. is then a function of its composition. The
use of the #vo amalgam electrodes B and D might give rise to
serious mistakes, if there were only small differences in their com-
position.

The absolute E.M.F. of our amalgam electrode against cadmium
in A and C does not play any role in our measurements.

10. The determinations of E.M.F. were carried out by the Poe-
GENDORFF compensation method. The resistances used, had been checked
by the Physikalisch-Technische Reichsanstalt at Charlottenburg—
Berlin. The same was the case with the thermometers used. Our
two standard elements (WesToN) were put into a thermostat which
was kept at 25°.0. We used as a zero instrument a Deprez-D’ ARSONVAL
galvanometer, which was mounted on a vibration-free suspension
(Junius). The readings were made by means of a telescope and scale;
0.02 millivolt could easily be measured.

The determinations were continued during several days, until the
E.M.F. of the cells had become constant.

Our table I shows the results.

GAs elves ale

Temperature 25°.0.
E.M.F.
Cell 7 0.04741 Volt
Cell 22 0.04815 _,,

Temperature 64°.5

Cell 7 0.04029 Volt.
Cell 22 0.03979 __,,

After having brought the cells to 25°.0, we found:
Celli 0.04741 Volt.
Cell 22 0.04806 __,,

The table shows that at 64°.5 there has taken place an inversion
of the poles and that the cells regain their original E.M.F. at 25°.0.

A second experiment with two cells (n°. 4 and 8) newly con-
structed, gave the following results:

641

AM Nasa a8 JN

Temperature 25°.0,
E.K.
Cell 8 0.04757 Volt
Cell 4 0.04839 _,,

Temperature 64°.5.
Cell 8 0.04737 Volt
Cell 4 0.04633 _,,

After having brought the cells to 25°.0, we found:
Cell 8 0.04776 Volt
Cell 4 0.04789, .

11. From table II it may be seen that we are here at the limit
of measurement obtainable in working with cells of so small an
E.M.F. the reproducibility of which is 0.5 Millivolt.

12. From the inversion of poles which has been observed, we
may conclude that the value 0.048 Volt at 25°.0 really has signi-
licance and is to be attributed to the presence of $-cadmium.

13. As to the bearing of the existence of different modifications
of cadmium on the E.M.F. of the standard cell of Weston, we
refer to our paper “On the Thermodynamics of standard cells”
(sixth communication), published some months ago ').

Utrecht, September 1914. van “Tt Horr- Laboratory.

Chemistry. — “The Allotropy of Zinc.” I. By Prof. Ernst
Couen and W. D. HeLperMan.
(Communicated in the meeting of September 26, 1914).

1. In our first communication on the allotropy of zine’), we
summarized the earlier literature on this subject as follows: as long
as half a century ago various investigators tried to solve the problem
whether zine might be capable of existing in different allotropic
modifications. As late as 1890 Le Cratetimr proved that this metal
does really show a transition point in the neighbourhood of 350°.
Monkemerer found this point at 321°, Brnepicks at 330° (melting
point of pure zine 419.°4) whilst the measurements of Max Werner

i 1) Chemisch Weekblad 11, 740 (1914). This paper will be published before long
in the Zeitschr. f. physik. Chemie.
2) Proceedings 16, 565 (1913).

642

(who found 800°), published some weeks ago, agree sufficiently with
those of Le Cuarruimr. We shall discuss in a subsequent paper the
differences which exist amongst the results of the investigators mentioned
above. Whilst Brenepicks mentions a second transition point (at 170°),
Max Werner was unable to find this point. The question as to
whether it really exists or not, may be left open for the moment.

2. Since writing the above we became acquainted with the paper
of Le Verrier’), which has been summarized by one of us’).
Le Verrter found that the specific heat of zine varies greatly between
100 and 140° and that there oceurs an absorption of heat within
this interval of temperature of O—8 calories. This result indicates
that there exists here a transition point. Mr. G. pe Bruin is carrying
out a systematic investigation in this direction.

3. Brnepicks and RaGnar Arpt have recently published *) a new
investigation of this subject. In his first paper BrnEpicks pointed out
that ‘‘beziiglich der Frage, ob die fiir das Zine. puriss. Merck
(garantiert frei von Kisen und Arsen in Staben) gefundenen Angaben
auch fiir das absolut reine Metall gelten, bedarf es ebenfalls weiterer
Versuche”’.

That there was no reason to suppose that this sample contained
impurities may be coneluded from the authors’ words: “Jedoch ist
es im Hinblick auf die Wichtigkeit der Reinheit dieses Produktes
fiir seine Verwendung fiir analytische Zwecke sehr wahrscheinlich,
dass die Menge von Fremdkérpern zu vernachlassigen ist’.

4. However Brnepicks writes in his most recent paper: “Es ist
deshalb hier eine Revision der einschlagigen Verhaltnisse vorgenomen
worden, die zu ziemlich unerwarteten Ergebnissen gefiihrt hat. Namlich,
dass iiberhaupt keine Allotropiebeweise fiir Zink z. Z. vorliegen”.
He adds: “ Abgesehen wird dabei zuniachst von derjenigen Andeutung
von Allotropie, die neuerdings von EK. Courn und W. D. HeLpEermMan
durch spez. Gewichtsbestimmungen gefunden wurde”. We shall
revert to this point later.

5. The method followed by Brnepicks and Arpi to discover
possible transition points was the same as used formerly by BEnepicks,
viz. the determination of the electrical conductivity of the metal at
different temperatures.

Whilst he found in his first determinations (working with zine.
puriss. Merck) transition points at 170° and 330° respectively, he
was not able to find them when he used ‘Zine KaHLBaum”’ which

i) C. R. 114, 907 (1892).
2) Ernst Conen, Proceedings 17, 200 (1914).
5) Zeitschr. f. anorg. Chemie 88, 237 (1914).

643

only contained 0,0047°/, of Cd., 0,0033°/, of Pb., 0,00045°/, Ke,Cu).

But working with the same material to which 0.52 per cent by
weight of Cd, resp. 0,5 per cent of Pb. or 0,5 per cent of Cd--0,5
per cent of Pb had been added, he found several transition points
which grosso modo agreed with those found formerly by Brnapicks a.o.
On account of these results Benrpicks and Arvr conclude that the
transition points found by Brnepicks in his first investigation are to
be attributed to impurities in the metal used and that zine which
is pure does nof show transition points.

6. In the first place it may be pointed out that the curves which
form the basis of the authors’ conclusions, are so roughly defined,
that it is almost impossible to conclude anything from them. For
example, from a consideration of the curve 2 in Fig. 2 (which refers
to pure zinc), one might arrive at the conclusion that a break ')
exists at 150°.

7. However, a more serious objection to the method followed,
may be pointed out. Our recent investigations on the allotropy of
metals have shown that the changes in these substances take place
very slowly even at high temperatures. These retardations can only
be removed by special means (inoculating in contact with an electro-
lyte, repeated changes of temperature etc.). We may call to mind the
fact that we were able to heat cadmium 95 degrees above one of
its transition points without any changes occurring. It will be necessary
to give special attention in future to these phenomena, which play
also a role in ‘thermal analysis” and which may falsify its results.

Benepicks and Arpr did not make any provision to eliminate these
phenomena. On account of what we know now about these hyste-
resis phenomena it was to be expected that any transition point, if
it really existed, would only be found under favourable circumstances,
or by a systematic elimination of the retardations mentioned above.

8. Moreover it may be pointed out that Benepicks and Arpt made
the supposition “dass die betreffenden Metalle nicht geniigend rein
waren” (viz. the zinc. puriss. Merck, used by Brnepicks in his first
investigations and by Le Caaretier among others). We think that the
opinion put forward by Brnepicks in his first paper (see above § 3) “dass
die Menge von Fremdk6rpern zu vernachlassigen ist’’, is the just one.
As we were told by Messrs. Merck at Darmstadt their ‘Zinc. puriss.
Merck (garantiert frei von Hisen und Arsen in Stiben)” contains only
small traces of cadmium. We carried out an analysis of this material

‘) Whether this point really exists or not may be left open for the moment.

644

following the method described by Myzius?). In 100 gr. of this metal
we could only detect small traces of cadmium (lead and iron). We
think that the explanation of B. and A. which is based on the
presence of large amounts of impurities falls to the ground.

9. That it is not the presence of foreign substances which give
rise. to the strongly marked change of the mechanical properties of
zine at higher temperatures (which fact has been the starting point
of Brnepicks’ investigations) is evident from the fact, that this change
may also be observed in the purest zine (Zink ‘Kahlbaum”, comp.
§ 5). We bave been able to confirm this result repeatedly ourselves.

10. Finally some remarks, made in a note by Bengpicks and ArpI
may be considered here.

In the first place they believe, on account of an investigation con-
cerning the quenching velocities of metals, carried out by BENEDICKs *),
that “eine besonders grosse Abkiihlungsgeschwindigkeit nicht zu erzielen
ist” when the method is followed which we used. (1 kilo of zine
was chilled in a mixture of solid carbid dioxide and alcohol). It
may be pointed out that the velocity we used has been greatly exag-
gerated; we got the same results by using water or air of room tempe-
rature. We also carried out some experiments with carbon dioxide
and aleo hol in order to vary the external conditions of our experiments
as much as possible. In our researches on the allotropy of copper
and cadmium we also used water or air as a cooling medium.

14. Secondly Benwpicks and Arpr raise the question as to whether
there has not taken place an ‘Auflockerung der Oberflache” of our
preparations when we washed them with dilute hydrochloric acid.
By this operation a change of density might have occurred.

They have however overlooked two facts: in the first place the
recent investigations of JouHnsron and Apams*), which prove that the
density of any substance is independent of its state of division.
Moreover they have not taken into account the results of our inves-
tigations on cadmium‘), where the same difficulties would have
occurred. The reproducibility and reversibility of the phenomena
prove that the disturbances, mentioned by BrNepicks and Arpi really
do not occur.

We hope to report shortly on the real transition points of zine.

Utrecht, September 1914. van “t Horr-Laboratory.

1) Zeitschr. f. anorg. Chemie 9, 144 (1895); Myxius, ibid. 74, 407 (1912).

2) Journ. of the Iron and Steel Institute 77, 153 (1908).

3) Journ. Americ. Chem. Soc. 34, 563 (1912).
4) Proceedings 16, 485 (1913).

645

Chemistry. — “The Allotropy of Antimony.” I. By Prof. Erxst
Conen and J. C. van pen Boscn.

(Communicated in the meeting of September 26, 1914).

1. The following modifications of this metal were known hitherto:

a. The so called metallic antimony, a bluish-white solid with
metallic lustre. It is very brittle at ordinary temperatures and is
said to crystallize in the hexagonal system. Only this modification
is found in nature.

6. Black antimony. This form has been prepared by Stock and
Siebert’) in three different ways, the best method being by rapid
cooling of the vapour of ordinary metallic antimony. This black
modification is converted by heating into metallic antimony. Its colour
and density change slowly at 100°; at 400° the conversion occurs
instantly. This form seems to be metastable at ordinary temperatures.

c. Yellow antimony was first prepared by Stock and Gu?TTMANN *)
in the year 1904, by the interaction of antimony hydride (at —90°)
with air, oxygen or chlorine. Even at — 50° this form is meta-
stabie: it is converted by heating into the black modification.

d. Explosive Antimony. Ernst Conrn, Rinckr, StRENGgRs, and
Cotuins*) proved that the explosion which occurs when this body
is pounded, pressed or scraped, is to be attributed to the transformation
of an allotropic form called by them 3-antimony, into the ordinary
modification (metallic antimony ; ¢-antimony). Hitherto no investigation
of the connexion between these different forms has been carried out
as it is very difficult to procure sufficiently large quantities of them.

2. The investigations described below deal with the question
whether the metal known hitherto as “metallic antimony” is to be
considered at ordinary temperatures and pressures as a metastable
system, as is the case with the metals we have already investigated.
Our experiments will prove that this is really the case.

3. A kilogram of antimony (KaniBaum — Berlin) which contained
some hundredths of a percent of impurity, was melted and poured
into a cylinder of asbestos paper, which was surrounded by a mixture
of aleobol and solid carbon dioxide. The chilled metal so obtained
was used in all experiments.

4. It was powdered in a mortar. We determined its density at
25°.0 using two pycnometers as described by JoHNnsron and Apams‘),

1) Ber. d. d. chem. Ges. 38, 3837 (1906).

2) Ber. d. d. chem. Ges. 37, 885 (1904).

8) Zeitschr. f. physik. Chemie 47, 1 (1904); 50, 292 (1904); 52, 129 (1905).
4) Journ. Am. Chem. Soc. 34, 563 (1912).

646

The difference between any two of these determinations never exceeded
three units in the third decimal place.
Our thermometers had been compared with a standard of the

Phys. Techn. Reichanstalt at Charlottenburg — Berlin.
We used toluene as the liquid in the pyenometer; its density had
KO

fe a0. ad
been determined in four experiments to be d =e, 0.8603.

Two different parts (A) and (/) of our material gave the values
25°.0 6.6900 (A) and
4° 6.6897 (£).

5. The samples (A) and (2) were now heated separately during 4 x 24
hours in an aqueous solution of potassium chloride (10 gr. KCI on
100 er. of water), using a reflux condenser, the boiling point of the
solution being 102°.5.

The metal was then washed with dilute hydrochloric acid, water,
aleohol and ether, and dried iz vacuo over sulphuric acid.

Its density was now
25°.0 6.6744 (A)
4° 6.6803 (E);

Consequently the density has decreased by 13 units in the third

ad.

decimal place.

6. After having heated (A) and (/) for a second time (6 x 24

hours) in the boiling solution, we found:

25°.0 6.6784 and 6.6765 (A)
“4° «6.6789 and 6.6778 (E).
The density had undergone no further change.
7. The experiments described in §§ 4—6 show that the antimony
after chilling is present in a form which changes at 100° with a
measurable velocity.

In order to investigate if there exists here a transition tempera-
ture as in the case of the other metals which we have hitherto
studied, we carried out some dilatometric measurements, using the
electric thermostat which we described formerly. *)

8. The material which was put into the dilatometer consisted of
small pieces of the metal mixed up with fine powder and a part of
the metal from the pyenometers. (500 grams). The paraffin oil used
had been heated for some time at 200° in contact with finely divided
antimony. There was no evolution of gasbubbles.

9. At temperatures below 119° there occurred no change of the
meniscus at the jirst heating (the bore of the capillary tube was

1) Zeitschr. f, physik. Chemie 87, 409 (1914).

647

1 mm.), not even when the heating was continued for 48 hours.

On the contrary, the dilatometer having been kept at 15° during
a month, the change was:

At 101°.8 in 2 hours, + 74 mm.; ie. + 37 mm. per hour

a OO ORR Te Ar so> = 20, oe ells A Re ac

NOON el 5 BO Pre ala ha ae,

From these data one might conclude that there exists a transition
point in the neighbourhood of 101° which is in perfect agreement
with our density determinations (§ 4—6).

10. Guided by the experience gained in the case of cadmium and
copper‘), we now earried out some experiments with antimony
whose previous thermal history had been changed between wide limits.

After having kept the dilatometer for 50 minutes at.150°, the
meniscus fell during a certain time at the constant temperature of
96°.0; after this it became stationary and then began to rise. From
these observations one would conclude that there is a transition
point below 96°.0 and that, in consequence of the heating at 150°,
the transition temperature had thus been lowered. This experiment
proves, that at 96°.0 there are present at the same time more than
two modifications.

11. The dilatometer was now kept at 225° for 12 hours. After
this there occurred at 94°.6 (at constant temperature) a marked fall
in the oil level (569 mm. within 48 hours), while in the experiment
described in § 10 there took place a rise of the meniscus at the
same temperature.

12. The phenomena deseribed above show that meta/lic antimony,
such as we have known it hitherto, is also a metastable system
which consists of more than two allotropic forms.

We hope shortly to report on the modifications which play a
role here.

Utrecht, April 1914. van ‘t Horr-Laboratory.

Chemistry. — “Vhe Coloration of some derivatives of Picrylne-
thylamide with alkalies’. By Prof. A. P. N. Francumonr and
H. J. Backrr.
(Communicated in the meeting of September 26, 1914).

In a previous communication (Fee. trav. chim. 1913, 82, 325 ; Abstr.
Chem. Soc. 1914, ii, 84) we described the spectrographie investigation
of the coloration which picrylalkylnitramines undergo by alkalies. It
was shown, that the absorption spectrum of picrylmethylnitraimine
C,H, (NO,), N Me(NO,) after addition of alkali gets a certain ana-

1) Proceedings 17, 54, 60 (1914).

43
Proceedings Royal Acad. Amsterdam. Vol. XVII.

648

logy with that of picrylmethylamide C,H, (NO,), NHMe, and that the
latter spectrum is not much changed by alkali.

We then concluded, that the coloration of picrylalkyInitramines
with alkalies had a similar cause as the colour of nitranilines (wid.
Francumont, Rec. trav. chim. 1910, 29, 298, 313), which is ascribed
by Hanrzscu (Ler. 1910, 48, 1669) to an action between the nitro
and amino groups attached to the benzene nucleus. The coloration
of the nitramines would thus be produced by nitro groups of the
nucleus reacting with the base, the nitro group attached to nitrogen
playing only a secondary part.

In order to test this hypothesis, we have now examined several
derivatives of picrylmethylamide, compounds of the formula Pier.
N Me X?). For X we have chosen the nitroso group, the organic .
acyl groups COCH,, CO,Me, CO,,Et and finally the phenyl group
as example of a negative group being no acylgroup. The compounds
investigated were thus picrylmethyInitrosamine Picr. N Me(NO), pieryl-
methylacetamide Picr. NMe(COCH,), methylpicrylmethylaminoformiate
Picr. N Me (CO,Me) and the ethylester Picr. NMe (CO, Et), and picryl-
phenylmethylamide Pier. NMe Ph.

In the first place it should be observed that, like the nitrogroup,
also the acyl groups NO, COCH,, CO,Me, CO,Et strongly diminish
the colour of the picrylmethylamide. Compared with this deeply
yellow coloured amide, the nitramine, nitrosamine, acetyl derivative
and both the urethanes are only palish yellow.

These differences are clearly shown by the absorption curves.
Both the absorption bands of pierylmethylamide at = 2390 and 2875
(see curve 15) disappear wholly; the acyl derivatives give for the
concentrations examined, only a continuous absorption in the ultra-
violet (curves 3, 5, 8, 10), just as it was found for the nitramine
(Rec. trav. chim. 1913, 32, 332).

It must be admitted, that the presence of acyl groups in the
aminogroup of picrylmethylamide so strongly diminishes the basie
properties of this group, that it loses the power to act with a nitro-
group, and thus to produce colour.

If this hypothesis is correct, it must be possible to prevent this
reaction also by addition of a strong acid combining witlr the
amine group.

Indeed, picrylmethylamide dissolves perfectly colourless in strong

1) In this paper Pier. means the group 2, 4, 6-trinitrophenyl.

649

sulphurie acid. The absorption bands disappear wholly from the spec-
trum, and only a modest continuous absorption in the ultraviolet remains
(compare curves 14 and 15). For a concentration of 0.0002 gram-
molecules per litre and an absorbing layer of 100 m.m. the beginning

il
of the absorption is repelled by the sulphuric acid from — 2150 to

3400. This decoloration of picrylmethylamide by sulphuric acid is
just the reverse of the coloration of the nitramine with alkali. In
the first case the nitro groups of the nucleus are deprived of the
opportunity to combine with a basic group, in the latter case this
opportunity is on the contrary given.

The reaction with alkalies seems to be the same for the acylderi-
vatives now investigated as for the pierylalkylnitramines, the only
difference being that they want a little more alkali for the red

coloration. Formerly we found (Rec. trav. chim. 1918, 32, 332),
that a solution of picrylmethylnitramine containing an excess of

1
alkali gives two bands at A 1975 and 2350. At nearly the same

places two bands are shown by the alkaline solutions of the acetyl
derivative (curve 6) and the urethanes (9 and 11), though one of
the bands is only represented by a flat part of the absorption curve.

The anomalous curve given by the nitrosamine with alkali (4)
will be discussed separately.

Pierylphenylmethylamide, the last derivative of picrylmethylamide
we examined, exists in two forms of the same dark red colour but
of different melting points, 108 and 129°. Hanrzscu (Ber. 1910, 98,
1651) calls the two forms homochromo isomerides, whilst BitMANn
(Ber. 1911, 44, 827) regards them as polymorphous forms.

As Hawnrzscu has already observed, the spectra of the two forms
are completely eqaal (curve 12). It was now found, that the «and 8
forms in presence of alkalies also behave in the same way (curve 13),
so that the two forms when dissolved seem to be wholly identical.
The broad absorption band of the amide at 2350 becomes by addition
of alkali a little deeper and is somewhat displaced to larger wave-
lengths. At the same time it undergoes a division into a flat part at
2070 and a feeble band at 2400. This agrees with the behaviour
of the other compounds with bases.

Finally we have examined the coloration of 1,3,5-trinitrobenzene
with alkali, since here only the nitrogroups of the nucleus can act
with the base.

Whilst trinitrobenzene only absorbs continuously (curve 1), addition

43%

650

of alkali produces a broad band from 2040 to 2300 (curve 2). Its
centre is at about the same place as the centre of the two bands,
which show the picrylmethylamide derivates in presence of alkalies.

In the previous publication (l.c.) we mentioned a remarkable
decomposition of the alkaline solution of picrylmethylnitramine. After
a day it gave the spectrum of potassium picrate, being hydrolysed in
this way: Pier. N Me NO, — Picr. OH + Me NH NO,.

An analogous decomposition takes place, though more slowly, with
the acetyl derivative and the two urethanes. In a few days the spec-
trum of their alkaline solutions is perfectly the same as that shown
by potassium picrate (curve 7).

With picrylmethylnitrosamine this decomposition proceeds very
quickly, much more rapidly than with the nitramine. During the few
minutes required for the spectrographic examination its alkaline
solution is already partly decomposed. ;

The anomalous absorption curve (4) is apparantly due to a super-
position of the spectrum of the potassium compound of the nitro-
samine with that of potassium picrate. From the three bands shown

1 : 2
by this curve at A 2000, 2400 and 2900 the latter is undoubtedly

caused by the presence of potassium picrate, which gives a band at
about 2880. In the spectrum of the potassium compound of the nitro-
samine there may be expected two bands at about 2000 and 2350,
in analogy to the observations made with the other derivatives of
picrylmethylamide. The former band is indeed present, whilst the
second band, likely with assistance of the flat band shown by
potassium picrate at 2500, is transferred to 2400. Two hours after its
preparation, the alkaline solution of the nitrosamine was again
examined; it then showed the pure spectrum of potassium picrate
curve 7).

The results of this investigation may be expressed as follows.

The coloration of picrylmethylnitramine by alkali has the same
cause as the coloration of other derivatives of picrylmethylamide by
this reagent.

For the nitramine, the acetyl-, carboxymethyl- and carboxyethyl-
derivatives, which altogether only have continuous absorption for
ultraviolet rays, show two bands at about 2000 and 2350 after addition
of alkali. Picrylphenylmethylamide has already of itself an absorption
band, which, however, by alkali is divided into two parts at 2070
and 2400.

Logarithms of the thickness of the layers in mm. of 0.0002 normal solutions.

Fig. I.

651

16 18-2000) 22) 5524-26) 28-3000) 32, 34 36-38 4000 42

Reciprocal wavelengths.

1. 1,3,5-Trinitrobenzene. 2. id. + KOH. 3. Picrylmethylnitrosamine. 4. id.
+ KOH. 5. Pierylmethylacetamide. 6. id. -+-KOH. 7. Picric acid + KOH,
8. Methyl picrylmethylaminoformiate. 9. id. -- KOH. 10. Ethyl picryl-
methylaminoformiate. 11. id. + KOH.

Logarithms of the thickness of the layers in mm. of 0.0002 normal solutions.

Vig.

Bane

el etl ge ic i
Pee ere ee ae
Heyl

2 AZ

Bee

A
Zoe
eS

Za
eee

If.

18 2000 22 24 26 28 3000 32 34 36 38 4000 42
Reciprocal wavelengths.

12. Picrylphenyimethylamide (z & @). 13. id. +- KOH. 14. Picrylmethyl-
amide in sulphuric acid. 15, Pierylmethylamide,

653

The nitrogroup attached to the nitrogen atom of the nitramine
is evidently not essential for the reaction.

Further, the spectrum of trinitrobenzene with alkali, though much
differing from that of the other alkaline solutions, has yet its absorption

1
in about the same part (> 18002500 )

We may thus conclude, that in all these cases the coloration is
produced by a reaction of the base with one or more nitrogroups
of the nucleus.

Finally it bas been shown, that the presence of a strong acid, as
well as the introduction of acyl radicals, completely expels the absorp-
tion bands of picrylmethylamide.

Cheniistry. — ‘“a-Sulpho-propionic acid and its resolution into
optically active isomerides’. By Prof. A. P. N. Francuimont
and Dr. H. J. Backrr.

(Communicated in the meeting of September 26, 1914).

Already in 1902 a great number of diverse chemical and bioche-
mical methods were tried by the first of us to separate the e-sul-
phopropionic acid CH,(SO,H)CHCO,H prepared by him ') from pro-
pionie anhydride and sulphuric acid, into the two optical isomerides
that one might expect according to theory. Not a single one, however,
had given the desired result, although sometimes strychnine
salts with a different rotating power were obtained, but after their
conversion into ammonium salts these always appeared to be inactive.

As Swarts *) had stated that he certainly had obtained from
fluorochlorobromoacetic acid strychnine salts with varying rotating
power, but had not succeeded in isolating the optically active acids.
and as also Poncuer*), who tried to effect a separation of bromo-
chloromethanesulphonie acid by means of cinchonine, only obtained
rotating ammonium and barium salts, but no acids, it appeared as
if with such simple acids the tendency to form racemic mixtures
or compounds was very great and likewise the velocity of conver-
sion. This was provisionally also assumed in the case of «-sulpho-
propionic acid (methylsulphoacetic acid) and the experiments were
discontinued in consequence.

Still with lactic acid (methyloxyacetic acid) Purpim and Watknr *)

MD) TRE, Cl abe, Cla, Gls WAS Zo joo Ad (akststs)\
2) Bull. Ac. Belg. (3) 31. p. 25 (1896).

3) Bull. Soe. ch. (3) 27. p. 438 (1903).

4) J. ch. Soc. 61. p. 754 (1892).

and with ebromopropionic acid (methylbromoacetic acid) RaMBERG *)
had obtained decided results, but on the other hand, Por and Reap *)
did not sueceed in resolving the chlorosulphoacetie acid. The
question now arose whether perhaps the sulphogroup created the
difficulty, i.e. causes the rapid racemisation. This became less
probable after Pope and Reap *) had succeeded in splitting the
chloroiodomethanesulphonie acid and had found that the optically
active acids thus obtained were not so readily transformed into the
racemie mixture. Hence, the investigation of sulphopropionie acid
was at once again taken in hand.

Both ehlorosulphoacetic acid and methylsulphoacetic acid (¢-sulpho-
propionic acid) are dibasic and thus can form acid salts. Moreover,
ihe two groups that cause the acid reaction, have a different com-
position, the one being a carboxyl- and the other a sulphoxyl-group,
and of different strengtb, so that as the sulphoxyl is stronger acid,
salts will presumably contain the carboxyl-group in the free and the
sulphoxyl-group in the combined state.

Whereas, previously; chiefly the neutral and mixed metallic salts
and ihe neutral strychnine salt had been experimented with, the
acid strychnine salt was now employed and the desired result was
obtained at once.

a-Sulphopropionic acid itself was hitherto only known as a viscous
syrup, whilst sulphoacetic acid had been obtained in crystals;
therefore we have tried also to obtain «-sulphopropionie acid in a
crystallized condition.

A dilute solution of the acid prepared by decomposition of the
barium salt with the theoretical quantity of sulphuric acid was
concentrated by partial freezing and draining by suction. The strong
solution was placed in vacuo first over sulphuric acid and then
over P,O,. The viscous residue was kept for a day in an ice safe
at about 0°, when gradually large crystals were formed. The acid
thus obtained contains one mol. of water and is exceedingly hygro-
scopic. In order to determine its melting point a little apparatus
was constructed, consisting of two tubes communicating with a
transverse tube, one of which contained P,O, and the other the
«-sulphopropionie acid. After the apparatus had been evacuated and
sealed, it was allowed to stand for a few days. The m.p. of the
a-sulphopropionie acid was then found to be 100°.5, therefore, higher
than that of sulphoacetie acid, which is stated to be 84°—86°.
~ 1) Ber. d. D ch. G. 33. p. 3354 (1900).

2) J. ch. Soc. 93. p. 795 (1908).

3) J. ch. Soc, 105. p. 811 (1914).

655

An acid strychnine salt was obtained by evaporating an aqueous
solution of the acid with the equimolecular quantity of strychnine
on a steam-bath until crystallisation set in. The large erystals that
had separated were purified by repeated crystallisation from water ;
their composition then was C,H,O,5 + C,,H,,O,N, + H,O. They,
however, proved to be not the acid strychnine salt of the inactive
(racemic) c- ulphopropionie acid, but of the dextrorotatory acid. On
heating, they are decomposed at about 250° with evolution of gas
and formation of a brown liquid.

As in the case of all other compounds described here, the rotating
power was determined in aqueous solution with sodium light at 20°.
By concentration c is meant the number of grams of anhydrous
active substance per 100 ce. solution. The specific rotation [e] is
likewise calculated on the anhydrous substance. The molecular
rotation has, of course, the same value for the anhydrous and the
hydrated crystalline substance.

For the acid strychnine salt was found at c = 1.938,
any == — (Sine [41] = — TIA

By way of comparing, strychnine hydrochloride was also investiga-
ted and at c=1.297 was found: [a]= —- 30°.2 and | M]—-— 112°’).

The acid strychnine salt of @-sulphopropionic acid investigated is
therefore, presumably that of the dextrorotatory acid.

In order to obtain this acid, the acid strychnine salt was first
decomposed with the theoretical quantity of barium hydroxide *).
After complete separation of the strychnine by extracting the drained
off liquid with chloroform, the neutral barium salt was precipitated
by addition of alcohol. This salt is dwevorotatory.

For c=1.764 was found [«]=—4°.96 and [J |= —14°.4.

From this salt the active a-sulphopropionic acid was liberated by

1) This value agrees fairly well with the constant |J2]—— 114° found by Porr
and Reap for a somewhat different concentration. J. Chem. Soc. 105, p. 820 (1914).

2) The acid strychnine g-sulphopropionate can be titrated with baryta water and
a suitable indicator such as methyl-red which is sensitive to feeble bases. It may
also be titrated with litmus to violet-blue. If however, phenolphthalein is used which
is but little sensitive to weak bases such as strychnine, the colour does not appear
until also the second acid group combined to the strychnine has been neutralised
by the inorganic base. As the change in colour is fairly sharp, both with methyl-
red and phenolphihalein, the titration forms an interesting application of the
theory of indicators. Still more remarkable becomes the experiment, when
both indicators are used simultaneously. The methyl-red passes into yellow after
addition of a semi-molecule of barium hydroxide, the phenolphthalein then being
still colourless; so soon, however, one mol. bas been added, the violet colour of the
phenolphithalein salt appears, unaffected by the pale yellow colour of the methyl-red,

656

the theoretical quantity of sulphurie acid and its rotatory power
was then determined.

For c=0.645 was found [¢]=-+ 31°.6 and [7 ]=- 48°.7.

In another preparation was found for ¢=1.85, [@]=- 32°.0
and [J] = + 49°.2.

Therefore, it is the dextrorotatory acid, whose neutral barium salt
is laevorotatory.

It was now tried to obtain also this dextrorotatory acid in the
solid condition. The solution was, therefore, concentrated in vacuo
first over sulphuric acid and then over P,O,. The viscous mass did
not erystallize on cooling, but did so slowly after a trace of the racemic
compound had been introduced. The crystals are exceedingly
hygroscopic, melt between 81° and 82° and contain one mol. of water.

As the neutral barium salt of the dextro a-sulphopropionic acid
rotates in the opposite direction of the free acid, it became of
importance to investigate also the acid salt. For this was found
at c=0.776

[a] = + 18°.0 and [Af] = -+ 79°.8 or =2 X 39°.9%).

The acid potassium salt gave at c= 0.516 the valnes:

[eo] = + 23°.8. [MM] = 4+ 45°.7.

The acid metallic salts of dextro a-sulphopropionic acid are, there-
fore, dextrorotatory like the acid itself. The racemisation of dextro
e-sulphopropionic acid and its salts was also tried.

The aqueous solution, at c= 0.645, when heated for six hours
at 100°, suffered no appreciable racemisation, the rotation remaining
unchanged.

A solution of the barium salt at ¢ = 1.28 after being heated for
eight hours at 150° was racemised to the extent of 80°/,.

A solution of the potassium salt at ¢ = 0.64, which also contained
2°/, of free potassium hydroxide, was completely racemised after being
heated for eight hours at 180°. An excess of free base thus seems to
accelerate the racemisation *), although also the temperature, the

1) As the molecule of the acid barium salt contains two groups of the sulpho-
propionic acid, it may for the sake of comparison with the other rotations be
written more conveniently [IJ] = 2X 39°.9.

*) This would agree with the rule given by Rorue Ber. d. D. ch. G. 46. p. 845,
(1914), that active carboxylic acids, the z-carbon atom of which is asymmetric and
carries a hydrogen atom, are readily racemised under the influence of alkalies. He
tries to explain this by assuming that, owing to the base, enol formation takes
place in the molecule, thus causing the asymmetric carbon atom to disappear
temporarily.

657

concentration and the duration of the reaction may exert an
influence.

In the motherliquor, from which the acid strychnine salt of the
dextro-acid had deposited, there should still be present that of the
laevo-acid, this being more soluble. On addition of acetone a preci-
pitate was obtained which could be recrystallized from absolute
alcohol. Of course, it still contains a trifle of the less soluble salt
of the antipode, but yet in one of the preparations it was obtained
in a fairly pure condition.

For the rotating power at c= 1.658 was found [a] = — 27°.7
and {J/]=-— 135°. The concentration does not seem to exert a
great influence on the specific rotation, for, at e=8.424 was found
[a] = — 27°.4 and [M| = — 134°.

From this acid strychnine salt of the acid the neutral ammonium
salt was prepared. This gave for c=3.113 the values [a|=-+ 7°.9
and {J/|—-+ 14°.8. The neutral ammonium salt of the /acid is
therefore, dextrorotatory.

If to a solution of the ammonium salt is slowly added dilute
sulphurie acid, the dextrorotation diminishes, becomes zero and then
changes to a laevorotation, which finally remains constant, as soon as
all the erganie acid has been liberated. The rotation for the acid,
at c= 2.449, amounted to [@] = — 29°.8 and [MM] = — 45°.8.

Although we have not prepared the /-a-sulphopropionie acid in a pure
and solid condition, it appears from the experiments in quite a

d-acid l-acid
20 20 20 20
l4Ip | Mp [Ip IM]p
z-sulphopropionic acid C3H,O;S | + 32? | - 49.2 — 29.8 | =e
|
acid potassium salt C;H;0;SK | + 23.8 | + 45.7 | |
acid barium salt (C3H;0;S),Ba | -- 18.0 | + 79.8 |
acid strychnine salt leeueoes |
neutral ammonium salt
C3H,O;S(NH4), si Oneal 1428
neutral barium salt C;HjO;SBa| — 4.96 | — 14.4
|

658

satisfactory manner that a resolution has been effected of the racemic
a-sulphopropionic acid.

The specific and molecular rotations of the compounds investigated
are united in the subjoined table. It should, however, be remarked
that the values of the acid and its derivatives are less trustworthy
because the acid has not been quite pure.

It deserves notice that the molecular rotation of the @-sulphopropionic
acid (49°.2) is certainly somewhat stronger than that of the «-bromo-
propionie acid *) (44°.4) although the bromine atom (80) differs but little
in weight from the sulpho-group (81); still this may perhaps support
the view that the weight of the group influences the rotatory power.
If for instance, we compare with the rotation of a-ethylpropionic
acid?) (18°.2) we notice that both the rotation and the weight
of the group (29) are less.

More interesting seems the fact that the rotation of the neutral
metallic salts is much less than, and of an opposite sign to that of the
acid metallic salts and the acids themselves, particularly in connexion
with what has been stated at the commencement, namely that it
concerns here a dibasic acid with two groups of different ionisibility
which cause the acid functions.

Although the phenomenon that salts of optically active acids
possess a rotatory power contrary to that of the acids themselves
was observed previously, for instance with lactic and glyceric
acids, the example now found seems a more simple one, because
there are not present any groups that can react on each other, and
because it may be called highly improbable that in the circumstances
stated the carboxyl- and the sulphoxyl-group should react on each
other. Consequently, the rotation will, probably, be less dependent
on concentration, temperature, age of solution ete.

In conclusion, it may be remarked that the laevorotation of the
acid strychnine salt of the d-e-sulphopropionic acid as compared
with that of strychnine hydrochloride, amounts to about as much
Jess as the dextrorotation of the acid metallic salts.

+) RamBerG. Liebig’s Ann. 370. p. 234 (1909) gives[z] = 29°.0, whence [M] = 44°.4.

2) Scutirz & Marckwatp. Ber. d. D. ch. G. 29. p. 59 (1896) [z] = 179.85,
hence [J] = 18.2.

Physics. - - “A new electrometer, specially arranged for radio-active
L Oe
investigations’. Part I. By Miss H. J. Foumpr. (Communicated

by Prof. H. Haga).
(Communicated in the meeting of May 30, 1914).

Introduction.

In trying to find an accurate method for measurements of the
natural ionisation of air in closed vessels, radio-active radiation of
the elements, ete., researches in which very small ionisation currents
are to be measured, it seemed to me that the need is felt of an
electrometer, which, besides possessing a great sensibility of charge,
will also be able to measure very minute currents with accwracy.

As to the mentioned conditions, the latter is fulfilled by C.T. R.
Witson’s electroscope (the gold-leaf type), which owes this favour-
able quality to the very simplicity of the system; this namely renders
it possible to bring about the ionisation which is to be measured, in
the air contained in the apparatus itself, to avoid connecting wires,
together with electrostatic and other influences, the disturbance
caused by insulators being confined to that of a single one. In my
opinion this is the reason that this electroscope is generally preferred
for various measurements requiring great accuracy to say a sensitive
DoEzALek electrometer, which lacks these advantages, -notwithstand-
ing the fact of a much greater sensibility of charge of the latter ;
in consequence of this sudden changes in the natural ionisation of
air in closed vessels, for instance, the existence of which is accepted
by many investigators, cannot manifest themselves clearly when the
electroscope is used; moreover measurements of small currents will
take much time.

This has led me to construct an electrometer, the principle and the
method of working of which I shall discuss in what follows, and
which in my opinion ean supply the mentioned need. It appeared
from the results obtained, that with this apparatus currents can be
measured both very accurately and very sensitively; accordingly
it seems to me, that for these reasons the apparatus may be very
suitable for various radioactive researches requiring the above
mentioned qualities, as was also corroborated by experience.

Description of the principle of the apparatus.
In the figure a schematic representation of the arrangement is given’);
the apparatus consists of:

1) An accurate description of the apparatus will follow in a 2nd communication,

660

two separate spaces, viz. the
measuring space c: a flat brass

cylinder, and the ionisation space
J: a brass cylinder of volume
1 litre; the two cylinders are
insulated from each other by
ebonite.

In the measuring space is the
metal needle 6, supported in the
middle by a second metal needle
d, insulated by amber; 6 + d
together form the conductor, which

is charged by the ionisation current.

In ¢ is also found the very thin
aluminium strip a, which a few
mm. above / is fastened to a thin
metal rod with mirror, suspended
on a Wollaston wire, which is
fastened to a torsion head insulated
by means of ebonite.

Through a perforation in the amber and in the ebonite a rod /
can be brought in contact with the needle d.

In this way a, 6-+d, ¢, and f, can therefore be separately brought
in a conductive connection with a storage battery or with earth ;
e rests on a bottom plate, to which legs are fastened which support
the apparatus.

The charging of the apparatus before use.

In what follows we shall examine from the course of the lines of
foree, what state arises in the space c, and how this takes place,
when the system is charged: the lower cylinder f is of no
account as regards this, as it does not belong to the measuring
system proper.

The method of charging is founded on this that the two needles
a and b, which with untwisted position of a form an angle, let us
say of 30°, will sé// have this position with respect to each other,
when the system is in the charged state, in which latter case, however,
lines of force run between the different conductors.

We begin to charge a to a constant potential, e.g. to, + 20
volts, keeping 6 and c still at potential O volt. If for the sake of
simplicity we first imagine the state as it would be without the
presence of 6, the course of the lines of foree would be as follows:
lines of force would start from a, and end upon the bottom, the walls,

661

and the lid of c; in consequence, however, of the unequal distance
from a to those different parts of c, the potential gradient per unit
of length or the electric force, as also the density of the lines of
force, or the value of the tensions directed along the lines of
force in the space round @ would be of very unequal value ; how
great, however, the variation in different directions might be, yet
there would be complete symmetry in the course of the lines of
force with respect to the vertical plane in which the needle itself
is situated. The presence of /, however, disturbs this symmetry in
the following way :

1. The lines of force starting from @ in the direction of ) will
no longer end on c¢, but on 4; besides, on account of their diminished
length, therefore on account of the increased electric force, they
become there denser than before.

2. There will be inflection of lines of force ; some lines of force,
viz. those which, when not subjected to the influence of 6, would
run beside 6 from a to c, will pass into lines of force from a to }
under the influence of 0.

This disturbance caused by 6 will give rise to the formation of a
resulting electrostatic couple, acting on those halves of the side faces
of a, which are directed to the side of the acute angle between a
and 6, so that consequently @ is deflected to the side of 6, and the
angle between a and / will become such that the formed torsion
couple of the suspension wire will be in equilibrium with the
electrostatic directive couple.

In order to make @ return to the untwisted position, ¢ is charged
to a negative potential, which brings about the desired change; for

1. then the density of the lines of force between a and ¢ will
increase, which causes a slighter variation of lines of force on those
halves of the sides of @ which are directed to the side of the acute
angle between a and 0 ;

2. some lines of force between a and ¢/ will deflect and become
lines of force between a and c.

In case of a sufficient negative potential of c¢ the above mentioned
electrostatic resulting couple will be annihilated through this change.
The course of the lines of force has now become more symmetrical
(of course not quite), while @ returns to the untwisted position.

In this way e.g. a state of charge is realized for a= - 20 V.,
H=O V, == 3

For the sake of simplicity a whole number was taken for the
potential of c. the consequence of which is, that in the final state
the needle is only approximately in the untwisted position.

662

Measuring method of ionisation currents.

A quantity of vadio-active substance is placed on the bottom of
the ionisation cylinder /; the system is charged to the state : + 20 V.,
O V., —3 V.; f is then brought to a potential value, dependent on
the strength of current to be measured. While a, c, and / maintain
their potential values, 6 is insulated by breaking the contact with /;
the ions formed, let us say the positive ones, will then charge 6 to
a constantly increasing potential, with the consequence that the
number of lines of foree between a and 4 will decrease, and a
couple will be formed, which will cause the needles to slowly recede
from each other, and that the quickeras the current is the stronger
(to return later on to particulars of the motion).

Consideration.

It will be seen from the arrangement of the electrometer, how the
before mentioned advantages of the Witson-electroscope are. realized in
it; in the space / namely the ionisation current is directly carried to
the needle 4+ d, this needle being perfectly insulated by a single
piece of amber. The separation of ionisation space and measuring
space has, moreover, this advantage that the measuring system is
not contaminated with radio-active impurities, while the ionisation
space and the rod d, which can be removed, as regards the part
that lies in 7, can be easily cleaned.

As to the measuring system proper, the principle of it differs from
that of the quadrant electrometer; it has been thus chosen on purpose
that the lines of foree formed by the ionisation current contribute
as much as possible and as favourably as possible to the movement
of the needle a.

This is not the case in the quadrant electrometer; there namely
the movement is caused by the lines of force which run between
the quadrants and the rims of the needle, whereas the vertical lines
of force between needle and quadrants do not contribute anything to
the moving couple.

In my opinion it would not be possible to modify the quadrant
electrometer in such a way that, while maintaining the principle of
the quadrants, many lines of force are not retained at the same time
which in a measurement either give no movement, or will even
counteract the movement. The latter might be possible, if the flat
needle should be replaced by a horizontal wire, in which way a
large horizontal surface is, indeed, avoided, but on the other hand
the formed lines of force would act on the two sides of the needle,
when the latter is rotated. The advantage of the described apparatus

663

lies in this that the lines of foree between a and 6, which ave
subjected to a change on ionisation, will mostly arise on one side
of the vertical strip. This removes the last mentioned drawback, a
large injurious horizontal surface also being avoided. I think that
with this apparatus I have obtained a sensibility of charge, greater
than is possible with a DorezainK-electrometer, the same thickness
of wire given.

The realization of a greater sensibility of charge.

-The sensibility of the apparatus appeared to be capable of great
variation, the suspension wire being left unaltered, and that by
varying the state of charge, whereas, for the rest, the method of
charging and measuring remains the same. To make the system
more sensitive, a is not charged to + 20 V, but say to +32 V,
after which a negative potential value is imparted to ¢ such that a
has turned back to an almost untwisted position. The potential of
e will also be more strongly negative, of course, for this state than
for the state (+ 20.0,
e.g. (+ 32,0, —6) V.

In order to understand what causes this modification of charge to
bring about greater sensibility of charge, we must examine in the
apparatus 1. the variation of the potential sensibility. 2. the variation
of the value of the capacity; for these two factors together determine
the sensibility of charge.

1. The former is to be found from the curves I, in which examples
of some states of charge are given; to investigate the potential

3) V; the state of charge will then become

z
S
& 50
—
Ss
o
S
o
=
a 25
2.
fe
Q
0
ry) 30 Votts 20
Fig. 1.
44

Proceedings Royal Acad. Amsterdam, Vol. XVII.

664

sensibility & was increased every time by 2 Volts in potential
for every state separately. The state, as indicated over every
curve, always represents the initial state. All the measurements
following here were made with a provisional apparatus; the suspen-
sion consisted of a Wortaston wire 7m thick, and 97 mm. long.
(Seale distance 1.5 m.).

From these curves appears the greater potential sensibility of
the system for greater potential difference between a and 6; for the
state (+ 32.0, —6) V e.g. a displacement of almost 700 mm. was
fuund for 2 V potential increase of 4; for (+8.0, —2) V it amounted
to +500 mm. for 20 Volts. The state (+382.0,—6) V does not
represent the most sensitive state that could be obtained.

I think the cause of this greater potential sensibility is the
following :

When a recedes from / in consequence of a potential increase
of 4, which is brought about by increase of charge of 6, the negative
induced charge on 6 will diminish in consequence of this motion,
or rather the potential value of 6 will be diminished ; for a positively
charged body (a) recedes from 6. The greater the potential difference
is between a and #, the greater will be the potential diminution in
question for a definite angle; in other words the potential diminution
of 6 required for a receding of a over a definite angle will be the
less, i. e. the potential sensibility will be the greater. Besides the
said change of the induced charge at the same time increases the
angular displacement, which is another reason for greater potential
sensibility.

2. It follows from the foregoing, that greater potential sensibility
obtained in this way, must be attended by an increasing capacity ;
for when through a definite addition of charge to 4 in a state with
greater potential difference between a and + a slighter potential
increase will set in in consequence of the motion of a, this will imply
a greater capacity of 4. Capacity measurements (method Harms,
Phys. Zs. 1904) give the same result; the capacity in the state
(+ 8,0—2) V amounted namely to 5,2 e.s. units; that in the state
(+ 20,0—3) V 6,0 es. units. Both values are the mean from a great
many determinations.

What is the reason why, in spite of this increase of capacity, the
increase of potential sensibility more than counterbalances it, will
appear from the application of the following consideration of the
capacity.

Though for an electrometer the sensibility of charge is in direct
ratio to the potential sensibility, and at the same time in inverse ratio

665

to the value of the capacity, it does by no means follow from this
that the sensibility of charge will be greatest for a capacity as small as
possible, and a potential sensibility as great as possible; for the latter
quantities are not independent of each other, as appears clearly among
others in what was said under 2. therefore I cannot entirely concur
with Lasorpk’s statement, in his: ‘‘Methodes de mesure, employées
en radioactivité, page 66”, where he says: “l'appareil le plus sensible
aura une grande sensibilité aux Volts et une faible capacité”; in
this statement the above mentioned relation is namely not taken
into account.

Thus in consequence of the existing mutual dependence of capacity

and potential sensibility it will be possible — and it will be shown
here that this really applies to the discussed electrometer —_ that

it will be favourable for the sensibility of charge, to take the capacity
not as slight as possible, when namely an accompanying increasing
potential sensibility more than compensates the disadvantage of
this procedure.

That this case presents itself in the described apparatus may be
shown by first examiming of what the capacity of the apparatus, i.e.
of the needle 6-++-d really consists. This capacity consists of : capacity
of the part 6, which refers to arising or vanishing lines of force
leading to a or c, and capacity of d.

Now | would distinguish in this capacity between:

a. useful capacity, by which I mean capacity which has an influence
on the motion of a;

b. injurious capacity which lacks this influence, and which is really
a disadvantage here, because it binds charge of the ionisation
current without making it demonstrable. Of the above mentioned
capacity only that corresponding to the lines of foree between a and d
is certainly almost entirely useful capacity (see below); the rest is
injurious.

And in this lies the cause why the state with greater potential
difference between a and 6, though attended with greater capacity,
can yet mean greater sensibility of charge; for this increase of capacity
concerns here the capacity of 4 with respect to a; this is increased,
(according to 2) hence the useful capacity of 6 is increased; the
greater now the ratio of useful to injurious capacity is, the greater
the sensibility of charge.

For the rest, as regards the value of the injurious capacity in the
apparatus, the following remarks may be made:

1. The injurious capacity of d with respect to / will not be of
great influence, since the distance to / is great.

44%

666

2. So far the lines of force starting from the lower rim of a, or
from the back of a, ending on 6, were not taken into account;
they represent injurious capacity. This influence will make itself
slightly felt in the middle of the needle, but will nave little effect
there on the motion.

3. It is difficult to say anything definite about the value of the
injurious capacity of b with respect to ce.

At any rate it will also appear from what follows, how for very
sensitive states the total influence of the injurious capacity may
almost be disregarded.

In the case of the quadrant-electrometer, on the other hand, the
injurious capacity is that of large surfaces with respect to a metal
needle lying close by.

Before confirming what has been said above about this increased
sensibility of charge for greater potential differences between a and
b by the communication of some experimental results, a few par-
ticulars may be added abont the mode of motion of the needle
during the current measurement.

Mode of motion of the needle during the current measurement :

When the needle 4 is charged starting from potential 0 V_ by
means of an ionisation current, when therefore the potential
difference between a and / decreases, a will begin to move away
from 4; consequently a motion of the scale division under the
crosswire will take place through the reflection of the mirror, which,
however, will not be uniform. For the different positions occupied
by a both the potential sensibility and the value of the capacity of
6 will be different; for the smaller the angle with b, the greater is
the potential sensibility, as well as the capacity.

The causes are the following: 1. With a smaller angle the distance
between qa and / is smaller and therefore the diminution of the
induced charge for a definite change of angle greater.

2) With a smaller angle the potential difference itself is also
greater, and this again causes a greater decrease of induced charge
for a definite angle.

For both reasons greater potential sensibility, but at the same
time greater capacity is to be expected at a smaller angle, but here
too for the same reason as for conditions of charge with greater
potential difference between a and 6, the result will be a greater
sensibility of charge

In agreement with this the curves I show, how for every state of
charge the potential sensibility decreases with greater angle between
a and b,

Capacity determinations gave the further result that the capacity
amounted to 5.75 e.s. units for the state (+ 20,0—3) measured from
an angular displacement (recession), corresponding to 550 mm. seale
displacement, whereas it gave the value 6 e. s. units, when this dis-
placement only extended over 250 mm.

Measurement of the current.

With the different above mentioned states of charge ionisation
currents were measured, obtained with two different very slight
quantities of polonium, which were placed in a dish on the bottom
of f; the larger quantity is called A, the smaller 4. The velocity
with which the scale moved under the cress wire was determined,
and then the intensities of current were derived in absolute measure
from this by means of the knowledge of the capacities and potential
sensibilities holding for some of the states of charge.

The curves IL. represent the result of the measurements for the
quantity A; it appears from this, that in accordance with expecta-
tion the sensibility of charge increases for states with greater potential
difference between a and (; at the same time this confirms what

60 p a

Sensibility of charge

Displacement in cm.
ts)

o aco seconds 400
Fig. 2.

was discussed before, that namely the sensibility of charge for one
and the same state is greatest, when @ is nearest 0.

From the experiment in itself the ratio of the current intensities
of the two quantities of polonium could already be derived, and
that even for each state of charge taken by itself. It will namely be
equal to the ratio of the times required by a to pass through the
same angle for the quantity 4 and for B. This ratio, which would
have to yield the same value for every state of charge, amounted
successively to 2.5, 2.7, 2.7, mean 2.6.

According to the above it was now possible at the same time
by means of the measured capacities and the known potential sen-

668

sibilities to determine the currents for A and B in amperes, from
CX V-inerease per sec. . :
the formula : 44 == = in which C represents
SS) S< AKOee

the capacity of the needle / +d. As mean values from the values
for the 3 most insensitive states we thus obtained :

14 = 1.3 X 10-8 (quantity B)

24 Ore >< 10718 ( 5p A)

Limits of sensitiwity of the apparatus.

Besides being dependent on the state of charge of the system, the
sensibility of charge can also be modified by varying the thickness
of the suspension wire and the angle between the needles.

It was now of interest to ascertain how far the influence of
a change of the state of charge in this respect could extend, how
far in other words the apparatus might gain, resp. lose sensibility
of charge by a constantly increasing or diminishing potential difference
between a@ and 6. Experiment showed, that there are limits on either
side, at which the apparatus presents a very peculiar character ;
this will successively be examined for a smallest sensibility, and
then for a greatest sensibility.

a, Limit of smallest sensibility.

Though for the just mentioned state of charge (-+ 8, 0, + 2) V
the phenomena were similar to those for the other states of charge, yet
the limit of sensibility appeared to be close in the neighbourhood,
viz. at the state: (+ 4,0,0) V; this will most clearly appear from
the experiment in which the potential sensibility was examined by

| [ te aie
0 5 7 =T =
\ | IL Behaviour of the most insensitive state
Sg
° 6 =e = =
=
5 7
g XN
ee nN
a 5 ic at S = al
SNe
21 eae
0 36 Volls 32

669

the regular increase of the potential value of 4. It appears from
curve III how, in contradistinection with the other states, @ first
recedes from 6, and then approaches 6 again.

The explanation of this deviation from the ordinary phenomena
is very obvious; for the potential value of a being low, 6 will soon
rise above this value in potential value, and this more and more;
hence the diminution in lines of force between a and 6 first con-
tinues, till the potential value of 6 has risen to +-4V; then lines
of force arise again between a and 6, whose number increases with
the rise of the potential of 4, so that finally the needles will, instead
of receding, approach each other.

In accordance with expectation it appeared from the experiment
for the current measurement that the needle first receded from 4,
stopped, and then approached 0.

This state of charge appeared, therefore, to be unsuitable for the
current measurement, of course under for the rest entirely definite
circumstances of thickness of wire, height, and angle of the needles.

b. Limit of greatest sensibility.

In the following examples of states of charge illustrating this
case a certain difference with the foregoing ones may be observed;
for the rest this modification was taken voluntarily; 6 is here
namely in the initial state already at positive potential, while the
potential value was /owered during the measurement, in other words
in contrast with the preceding cases a approached to 4 through
increase of the lines of force between a and 6.

In the following examples the potential decrease for 4 amounts
every time to 2V, and it is always stated how much then the
deviation is for a, expressed in mm. of scale displacement.

A) state (+ 80, +60, +60,) V.| (2) state (+80, +40, + 36,) V.

GED Se Vi S2smm: b +838 V. 130 mm.
ss q 513 , 6) 55 + 36 af Oe
apo“ 71) 4 | » +24 ,, theneedle

A SEPIA aE ae | turns.
ie state) (meet) ees
(3) state (+80, + 30,+26,) V.| (4) state (+ 80, +10, +4,) V.
iy arts) Wo Oils | b +8 V. theneedle
>» 26 5, theneedle | turns.

turns.
(5) state (+ 120, + 40,+ 32) V.| (6) state (+ 120, +10, +2) V.
6 + 388 V. the needle 6 + 8 V. the needle

turns. | turns,

The phenomenon that occurred now was the following: when e.g.
in the 3 state 6 was charged to + 26 V, after having first been
brought to -+- 28 V, we did not once more observe a deviation which
amounted. to somewhat more than that for the change of the
potential value of 6 from -+ 30 V to + 28 V (since the sensibility
at smaller angle zncreases), but a passed over so great an angle that
the whole scale disappeared from the field, and a assumed almost a
position parallel to 6: the needle turned suddenly. In state 4 this
phenomenon occurred immediately at the first potential decrease of
b with 2 V, and the sume applies to the 5 and 6" states,
whereas in contradistinetion with this the first state exhibited stable
states throughout the scale for definite potential values of 0.
The experiment seemed therefore to point to the existence of an .
unstable state of equilibrium of a, which gradually shifted to an
increasing angle with 6 as the state of charge became more sensitive.
To ascertain, whether this displacement was a gradual one, the
inrning point was approximated as nearly as possible for every state
separately; this was done by diminishing ® in potential value not
by 2 Volts every time, but only by parts of 1 Volt. The result of
this was that, as had been expected, the 2"¢ and 38'¢ states were
still realisable throughout the scale, the 4", 5, 6 states on the
other hand only partially, but again in such a way that the said unstable
state of equilibrium, hence the turning point, occurred at a greater
angle, as the state of charge was more sensitive.

When after the turning a had reached its new state of equilibrium,
it was not possible to make a return to its position through a slight
potential increase of 4, which, considered in itself, would give rise
to a state of charge with a stable equilibrium ozéside the region of
turning. This too pointed to the existence of an unstable equilibrium.

The explanation of the existence of such an unstable equilibrium
at the point of turning seems to me the following :

In what precedes the change was already discussed of the
induced charge on 6, in consequence of an angular displacement
of a; we saw how this change takes place for a definite angular
displacement to a greater degree, the greater the potential difference
is between a and 4, and the smaller the angle is between the needles.

Taking this into consideration we may ask what will take place
when e.g. the state (+ 83, + 30, + 26,)V is realized, and when
the negative charge is continually supplied to 6.

In this the ratio of useful to injurious capacity will namely con-
tinually change for the before-mentioned reasons; it will become
continually greater; at a definite angle the influence of this injurious

capacity can even ‘all but vanish. This circumstance can also be
expressed thus, that then even a supply of negative charge will no
longer make the potential of 4 go down, because the approach of
a to 6 brought about by this supply just compensates the expected
potential decrease.

The angle, for whic) this consideration holds, will still be found
outside the region of turning and may be realized by means of a
storage battery.

If more and more negative charge is added at this angle to 4, e.g.
through an ionisation current, the potential value of 6 will even
continually rise in consequence of the preponderating influence of the
approach of a to 6. Finally the state becomes this, and it is then
that the turning takes place, that for a further approach of a toda
supply of charge to / is not even required any longer. For the mere
induced charge on 6 called forth by the approach will be more
than sufficient to give rise to an electrostatic couple, which can be
in equilibrium with the formed torsion couple.

That, however, in case of such a turning the parallel state is not
entirely reached, which was already pointed out, may be accounted
for in this way that the lines of force between a and 6 at decreas-
ing angle will also act on the back of a in appreciable quantity,
and this more and more as the angle becomes smaller, so that through
this circumstance the electrostatic couple, which tends to make the
angle between a and 6 smaller, is counteracted. It will follow from
this, that after the turning, the two needles will always continue to
form a (generally small) angle with each other.

It follows therefore from this explanation of the angle of turning,
as was already pointed out on p. 47, that, when the measure-
ment is made in the neighbourhood of this angle, the capacity which
must then be taken into account, will chiefly consist of useful capacity,
by which the sensitivity of the state is to be explained.

In conclusion a single example of a measurement of air-ionisation
and of Rubidium-ionisation.

In thcse measurements the needle a@ was brought to potential zero ;
the state of charge was: 0 V., — 26 V., — 32 V.

The ionisation space contained only air; volume 1 litre; the
number of seconds successively found for the passage through 10 mm.
WAS Low dewolemont Ooq Hae

Then a quantity of Rubidium salt was placed in a dish with an
area of.50 em’, on the bottom of /; it was found that successively :
9, 10, 10, 11 seconds were required for the passage of 20 mm. In
this case 7 was at + 80 V.

Physical Laboratory of the University at Groningen.

672

Chemistry. — “The metastable continuation of the mixed crystal
series of pseudo-components in connection with the phenomenon
allotropy”. Il. By Prof. A. Smits. (Communicated by Prof.
J. D. vAN DER Waals).

(Communicated in the meeting of Sept. 26, 1914).

In the first communication on this subject ') different possible
continuations of the mixed crystal series in the metastable region
have been discussed, in which chiefly the mixed crystal phases
coexisting with liquid were considered.

The metastable continuation of the coexistence of two mixed crystal
phases was only mentioned in a single case, where namely continuity
of the mixed erystal phases in the metastable region was supposed.

It is now, however, the question what can be said of this
coexistence for the case that the said continuity does not exist. We
consider, therefore, one of the figures from 7 to 12 inclusive from
the previous communication, and ask what can be predicted about
the metastable continuation of the lines p and m.

On the whole a transgression of the melting temperature without
melting setting in, or in otber words supersolidification, is considered
possible also on slow rise of temperature. The continuity discussed
by Vax per Waats between the sublimation line a 6 and the melting
point line 4c of a single sub-
stance, see fig. 1, starts from
this supposition; we shall, there-
fore, also here have to take the
possibility into account that the
melting fails to appear at the
eutectic temperature, and_ that
the coexistence continues to exist
between the two mixed crystal
phases. It is, however, the ques-
tion whether this possibility is
limited. It follows from the con-
tinuity between the sublimation
line and the melting-point line
considered by vAN DER WAALS that
such a limit has been assumed
for the coexistence between solid + vapour and solid + liquid.

1) These Proc. XVI p. 1167,

673

Above the temperature of the higher cusp e, and below the pressure
of the lower cusp d, the solid substance can no longer exist by
the side of the gas resp. liquid.

For our purpose the cusp c is the most important, for this point
expresses that there exists a limit for the coexistence solid + gas,
which implies that the orientated condition of the molecules in the
solid substance coexisting with its vapour cannot exist any longer
at a definite temperature, in consequence of the increasing molecular
motion. If this holds for the solid substance in coexistence with
vapour, there must also be a limit of existence for the solid substance
without vapour, and as the contact with the vapour will diminish
the stability of the solid state in consequence of the molecular
attraction between the molecules in the solid phase and those in the
gas phase, we may expect that the limit of existence of the solid
substance without vapour will lie at a higher temperature. This
temperature limit of existence will vary with the pressure, and thus
we shall be able to draw a line wv in the P7-figure indicating the
limit of existence of the solid substance.

For a binary system this holds of course, for both the components.
When, therefore, we pass from the triple point of the components
to the quadruple point, we get something similar. As Dr. Scurrrmr
has demonstrated ’) and as is expressed in Fig. 2, the lines for
Sat Se+ G, Sit Spg+ L merge continuously into each other

also by means of a ridge with two cusps and an unstable inter-

1) These Proc, XIII p. 158,

674

mediate portion, and here a line pg can be given for the limit of
coexistence of S4+ Sg, because either S4 or Sp has reached its
limit of coexistence there, which makes it impossible for the said
coexistence to occur any longer.

It follows therefore from this that the lines p and m extend
metastable to a definite temperature above the eutectic one.

Transition from monolropy ¢o enantiotropy.

As is known it often happens that a substance under the vapour
pressure presents the phenomenon of monotropy, whereas under
higher pressure enantiotropy takes place, as has e.g. been indicated
in the P7Z-figure 3.

The theory of allotropy again enables us to get a clear insight

into the signification of this phenomenon.
Suppose the 7. X-figure 4 to hold for a pressure above the triple

point O, and below the triple point O,, then according to the said
theory the conclusion may be drawn from the fact that at higher
temperature enantiotropy occurs, that the situation of the internal
equilibrium with respect to the pseudo system is dependent on the

pressure. For only in this case e.g. the situation of the line for the
internal equilibrium in the liquid with respect to the pseudo system
will shift with the pressure, and if this displacement is such that
the point /, moves downward with respect to the pseudo binary
T,X-figure, /, will coincide with c, S, with d and S, with e at a
given pressure, or in other words under this pressure two solid
modifications of the unary system will be in equilibrium with each
other and with their melt at a definite temperature (triple point
temperature).

At this temperature the two modifications have therefore the same
melting-point pressure, so that this temperature can also be ealled
a transition temperature under the melting-point pressure.

If we raise the pressure still more, we get a 7\r-figure as given
in Fig. 5, from which it appears that whereas the direction of the
lines for the internal equilibrium in the solid phase excluded: the
appearance of a stable point of transition at lower pressure, it must

now at higher pressure neces-
¢ sarily lead to a transition point.

We see further that the solid

phase which appears at the

stable point of solidification now
lies on that mixed erystal line
on which the solid phase of the
metastable melting equilibrium
lay before, and vice versa, so
that the form of erystallisation
of the solid phase at the stable
point of solidification will now
be equal to that in which the
metastable phase showed itself
at a pressure be/ow the transi-’
tion pressure.

On further increase of pressure

EE ea & the puints /, and s, move still

Fig. 5. more to the left, and the transi-
tion equilibrium gets deeper and deeper below the equilibrium of
melting.

The P, 7-projections of the points s, and /,, at different pressures
will form the stable melting-point line, that of the point s, and /,
the metastable one, whereas those of the points s’,, s', form the
transition line as indicated in fig. 3.

It therefore appears from the foregoing that the transition from

676

monotropy into enantiotropy can be explained in a simple way
by means of the theory of allotropy.

Now the question rises where the transition line eo, starts from.
A possibility has been given in fig. 3, from which follows that the
transition line starts in a metastable point of transition under the
vapour pressure O,. This is the view to which lead Ostwatp’s *) and
Scuaum’s*) assumptions on the existence of a metastable point of
transition under vapour pressure*). Now it is the question whether
this is the only possibility. It has been pointed out just now that
the metastable coexistence is confined between the two mixed erystal
series md and pe (see Fig. 4), and as the metastable point of
transition arises by intersection of the internal equilibrium line of
the solid phases with the above mentioned mixed crystal lines, it is
clear that it may happen that this intersection does e.g. noé exist
under the vapour pressure.

If in such a ease enantiotropy does oecur at higher pressure, the
transition line will proceed in a metastable way up to that pressure
and that temperature at which for the first time an intersection
between binary mixed crystal lines and internal equilibrium lines
takes place, and there the transition line will then suddenly terminate
in a point that indicates the
limit of existence of the
coexistence between two solid
phases which are in internal
equilibrium, as fig. 6 shows.

Now it is clear that the
main cause of the transition
from monotropy to enantio-
tropy can jind its origin
exclusively in this that the
situation of the pseudo figure
varies more greatly with the
pressure than that of the
unary figure, but in by far
the most cases, namely there
where the pseudo components

Fig. 6. are different in molecular
sizes, the situation of the pseudo figure will vary less with the

1) Z. f. phys. Chem. 22, 313 (1897).
2) Lieb. Ann. 300, 215.

*) Cf also Bakuuis Roozesoom, “Die Heterogenen Gleichgewichte” I, 187.

677

pressure than that of the internal equilibrium, and the phenomenon
discussed here will have to be attributed to this superposition.

In conclusion it may be pointed out that other particularities may
still present themselves, when the internal equilibrium line of the
liquid phase under the vapour pressure lies so much on one side
that there exists no meta-
stable melting point under
this pressure. If we now
think that this case occurs,
and that the internal equili-
brium line for the liquid
phase under the vapour
pressure lies greatly on
one side towards the right,
and that this line moves
towards the left on increase

of pressure, we get what
follows: The phenomenon Fig. 7.

of phase allotropy’) is wanting under the vapour pressure, monotropy
can however, occur at higher pressure.

The metastable melting-point line will start at the absolute zero
e.g. in the case of fig. 10 of the preceding communication *), and
run further as represented in fig. 7.

If on the other hand we have to do with the ease of fig. 12 of

Fig. 8.

1) For the occurrence of a substance in two or more similar phases the word
phase allotropy might be used, while the occurrence of a substance in different
kinds of molecules, for which I before introduced the name homogeneous allotropy,
might be designated by molecular allotropy.

2) loc. cit.

ihe preceding communication, a P7-figure is possible as fig. 8 shows.

These considerations open our eyes to the possibility that enantiotropy
occurs under higher pressure, notwithstanding the phenomenon of
monotropy is not found wader the vapour pressure,

Amsterdam, June 25, 1914. Anorg. Chem. Laboratory

of the University.

Chemistry. — “On the vapour pressure lines of the system
phosphorus.” (Ul. By Prof. A. Smits and 8. C. Boksorst.

(Communicated by Prof. J. D. van per Waats).
(Communicated in the meeting of Sept. 26, 1914).

The continued investigation of the phosphorus purposed to decide
with certainty whether the red and the violet phosphorus must be
regarded as two different modifications exhibiting the phenomenon
of enantiotropy, as seemed to follow from Jonipors’') researches and
also from our first investigations.

Confining ourselves te the communication of the result we can
state with certainty that the supposed point of transition between
red and violet phosphorus does uot exist, and that only one solid
stable modification of the phosphorus has been found, which is violet
in coarser crystalline state, but red in a more finely divided state.

The vapour tensions of different phosphorus preparations approach
to amounts which form one continuous vapour pressure line, when
the heating is long continued.

An apparent discontinuity may arise under definite circumstances
in consequence of too rapid heating. If namely, the preparation at
lower temperature contains too much of the more volatile pseudo-
component, too high vapour pressures are observed at these lower
temperatures, in consequence of the not setting in of the internal
equilibrium. In the neighbourhood of 450°, however, the setting in
of the internal equilibrium becomes appreciable, and this transformation
being attended with a diminution of the vapour pressure, the vapour
pressure line will present a course that reminds of a discontinuity.
When we worked very slowly and started from states which could
only differ little from internal equilibrium states, any discontinuity
had, however, disappeared.

At the same time this investigation furnished a fine confirmation

1) CG. R. 149, 287 (1909) and 151, 382 (1910).

679

300° 350° 400° 450° 500° 550° 600°

Vapour pressure line red phosphorus determined by means

of the glass spring indicator,

— = —_ — SS
| Vapour pres- ; Vapour pres- |
Temperature | Sarena atin | Temperature "sure in atm.
(e) (eo) |
300 0.05 480 5.0 |
325 0.1 490 6.25 |
350 0.2 500 esl |
375 0.4 510 9.4
400 0.7 520 2
410 0.9 530 PiS32
420 15 540 15.65
430 1.55 550 18.75
440 1.90 560 22.95
450 2.45 570 28.6 |
460 3.15 580 35.6
470 4.0 589.5 43.1 Triple point
45

Proceedings Royal Acad. Amsterdam. Vol. XVII.

680

of the theory of allotropy, as it necessarily led to the conclusion
that the stable red or violet modification is really complex, and
consists at least of two components, which greatly differ in volatility.

As the denomination ved phosphorus is universally known, we
will also apply this term to the stable modification, though, as was
said before, this modification is violet in coarser crystalline state.

The adjoined figure represents the vapour pressure line, as it has
been found by us after laborious study, and the table gives the
vapour pressures at different temperatures, as they can be read from the
vapour pressure line. In a following communication this investigation
will be treated more fully.

Amsterdam, Sept. 25, 1914. Anorg. Chem. Laboratory
of the University.

Chemistry. — “The application of the theory of allotropy to electro-
motive equilibria.” IL. By Prof. A. Smits and Dr. A. H. W.
Atrrn. (Communicated by Prof. J. D. van DER WaAats).

(Communicated in the meeting of Sept. 26, 1914).
Introduction.

The application of the theory of allotropy to metals necessarily
led to the assumption that every metal that exhibits the phenomenon
of phase allotropy, must contain different kinds of ions. As was
already mentioned before, these kinds of ions can 1. differ in com-
position, the electric charge per atom being the same; 2. differ in
valence with the same composition, and 3. differ in composition and
charge per atom.

On extension of the said theory to the electromotive equilibria it
was now demonstrated 1. that the unary electromotive equilibrium
finds its place in a Aw figure of a pseudo system, 2. what can be the
relation between the unary and the pseudo-binary system, and 3. what
phenomena will have to appear when in case of electrolytic solution
resp. separation of metals the internal equilibrium is noticeably
disturbed. The phenomena of anodic and cathodic polarisation appeared
by this in a new light and the passivity of metals revealed itself as
a disturbance of the internal equilibrium in the metal surface in the
direction of the noblest kind of ions’), which view seemed already
to be confirmed by a preliminary investigation *).

Thus we had arrived at the region of the passivity of metals, and
!) These Proc. XVI p. 699.

*) These Proc. XVII p. 37.

681

it became desirable to get acquainted with the immensely extensive
literature on this phenomenon.

The most important hypotheses that have been proposed as an
explanation of this phenomenon, and which have been collected by
FREDENHAGEN ') in an interesting summary, are the following:

1. The oxide theory of Farapay, who assumes that passive metals
are covered by a coat of oxide *).

2. KriGer FINKELSTEIN’s *) valence theory which slightly modified is
also adopted by Métrer‘). In this it is assumed that the passivity
consists in a change of the proportion between the components of
different valence.

3. Le Buianc’s velocity theory *), which supposes the phenomena
of passivity to be due to the slight velocity with which the formation
of metal ions would take place.

4. The velocity theory of FREDENHAGEN °), MutHmMann, and FRAUvEN-
BERGER’), who start from the supposition that the passivity is caused
by the slight reaction velocity between the anodically separated
oxygen and the passifiable metal, which causes oxygen charges or
solutions of oxygen in metal to originate.

5. The theory of Grave‘), who assumes a retarded heterogeneous
equilibrium metal-electrolyte which is under catalytic influences.

If we now consider the passivity which has arisen by an electrolytic
way, it seems to us that too little attention has been paid to the
primary character of the phenomenon.

First of all we should inquire to what it is owing that in case of
anodic polarisation of base metals the potential difference is modified
in such a way that the tension of separation for the O, is reached,
and we should also question why in case of cathodic polarisation
of base metals the potential difference changes in such a way that
the tension of separation for the H, is reached.

1) Z. f. phys. Chem. 63, 1 (1908).

®) Farapay has not expressed himself so positively as is generally thought. In
a letter to R. Taytor Farapay writes explicitly [Phil Mag X 175. Jan. 2! (1837)]:
“IT have said (Phil. Mag. IX. 61 1837) that my impression is, that the surface of
the metal is oxidized, or else, that the superficial particles of the metal are in
such a relation to the oxygen of the electrolyte as to be equivalent to an oxidation,
meaning by that not an actual oxidation but a relation...

8) Z. f. phys. Chem. 39, 104, (1902).

) Renee re » 48, 577, (1904). Z. f. Electr. Chem. 11, 755, 8238, (1905)

5) Chem. News 109, 63 (1914).

6) Z. f. phys. chem. 48, 1 (1903).

7) Sitzber. K. Bayr. Akad. 34, 201 (1904).

8) Z f. phys. Chem. 77, 513 (1911).

45*

682

These phenomena being only observed above a certain current
density, it is clear that we have to do here with a disturbance
which makes its appearance when the electric current is passed
through with too great velocity.

We have, therefore, to do here with a question of velocity, and
as an explanation of the primary character of the passivity pheno-
menon Farapay’s oxide theory is to be rejected from the beginning.

With regard to Grave's theory we may remark that it seemed
very improbable already at a cursory examination, Nernst has
namely demonstrated that in the phenomenon of solution equilibrium
of saturation always prevails in the boundary layer solid-liquid. In
connection with this we may, therefore, expect that this continues
to hold for the phenomenon of solution by an electrolytic way.
There is no reason at all to make an exception here.

With regard to the second theory it should be observed that the
valence hypothesis, on which it is founded, is implied in the con-
clusions to which the application to metals of the theory of allotropy
leads. This theory generally concludes, namely, as was already said
before, to the existence of different kinds of ions in the metal phases
and points out that one of the possibilities is this that the metal ions
with the same composition only differ in valence.

The application of the theory of allotropy to the heterogeneous
electrolytic equilibria has further shown that when the metal phase
is complex, apart from the nature of the difference between the ions,
the anodie and cathodie polarisation, and also the passivity of metals
can be explained.

Diametrically opposed to this theory are the theories 3, 4 and 5, and
it is now clear what will have to be decided. By an experimental
way we must try to get an answer to the question as to whether
the phenomenon polarisation and’ passivity resides in the boundary
surface between metal and electrolyte, as the theories 3, 4 and 5
suppose, or in the metal surface itself, as the theory of allotropy
has rendered probable.

For this purpose the investigation about the complexity is the
obvious way. When experiment has proved the complexity, we can
try to find out whether it possesses metal ions of different valence.

Experimental part.

1. To examine whether or no the phenomenon of polarisation and
that of passivity resides in the metal surface, it seemed to us the
simplest course to attack the metal surface by means of chemical
reagents, and to see if it has changed its properties in consequence

683

of this. If a metal really contains different kinds of ions they will,
as was stated before, differ in reactive power; hence an attack may
result in a change of the concentration in the metal surface, in the
sense of enobling. It is, however, to be seen beforehand that the
investigation in this direction will be successful only when the in-
ternal equilibrium in the metal surface in contact with the electro-
lyte is established slowly enough. If this equilibrium is established
with very great velocity, no disturbance will of course, take place,
even though the ion-kinds differ greatly in reactivity.

It appeared in our previous investigation about polarisation that
the metals Ag, Ca, Pb are exceedingly little polarisable, from which
we inferred that these metals quickly assume internal equilibrium.
Hence the etching of these metals promised little success. Quite in
agreement with our anticipations it appeared that the potential dif-
ference metal- */,, norm. salt solution was not to be changed
for these metals by previous etching.

To examine this the electrode of the metal that was to be investi-
gated, fastened to a platinum thread was etched with acid, and then
quickly rinsed with water. Then this electrode was immerged in
a ‘/,, norm. salt solution, and made to rotate, after which the
potential with respect to a ‘/,, N. calomel-electrode was measured
as quickly as possible.

When the above mentioned metals according to our anticipations
had yielded a negative result, the metals Co, Ni, Cr, and Fe were
examined with the following result:

Metal | Potential rise through etching
| by HCl 0,108 V
Co | 5 abSoy 0,109 ,,
| » HNO; 0,107 ,,
by HCl 0,04 V
Ni » HNO; 0,10 5,

» Br-water 0,00 ,,

by HNO; 1,00 V
Gr , Br-water 0,60 ,,

Fe by HNO3 above 1,00 V

684

It follows from this table that these metals about which it was
derived from the phenomenon of polarisation that they assume their
internal equilibrium much more slowly than Ag ete. really become
nobler when etched with acid, as was expected.

This temporary change of the potential difference in the sense
noble must find its origin in a change in the metal surface, and so
it is perfectly clear that theories 3,4, cannot be of any use here.

At the same time they throw a peculiar light on Grave’s theory.
Grave thinks that the heterogeneous equilibrium metal-electrolyte
can be easily retarded, but that the hydrogen exerts a positively
catalytic influence on the heterogeneous equilibrium. According to
him iron would become passive by extraction of the dissolved hydrogen,
which would take place on anodic polarisation. Now specially in
ion-state hydrogen is certainly a catalyst for the transition passive
— active, but it is quite unpermissible to derive from this that
hydrogen catalyses the heterogeneous equilibrium. It is of importance
to state emphatically that according to Gravr’s theory it could by
no means be expected that an enobling of the metal surface would
be brought about when it was etched with HCl or H,SO,, in which
the metal can absorb hydrogen. We have to do here with a pheno-
menon that cannot be counteracted by the positively catalytic influence
of the hydrogen on the internal transformations in the metal surface.

Further we made the following in our opinion very important
experiment with iron. An iron electrode forged to a platinum wire
was made passive one time through anodic polarisation, another
time through immersion in strong nitrie acid. Both times the potential
of these passive states of the iron electrode immerged in */,, N.FeSO,
solution, was measured with respect to */,, norm. calomel, in which
the following appeared.

The potential difference of the passive iron, both after anodic
polarisation and after etching with strong HNO, at first decreases pretty
rapidly, then remains constant for a time, and then descends again
rapidly. We now compared the temporarily constant potential differ-
ence of the quickly rotating electrode in the two cases, and then
found what follows:

Tension of the constant part of

OSEEN OIE the potential of passive iron
Passivity arisen by anodic polari- -+0,20 V with respect to 1);9 Norm.
sation Calomel electrode

Passivity arisen on attack of -+-0,205 V with respect to*!/;9 Norm,
strong HNO; Calomel electrode

685

From this experiment the important conclusion could, therefore,
be drawn that the two passive states are the same.

At the end of this series of experiments we may finally already
conclude that from the fact that where anodic enobling was observed,
also ore enobling could be demonstrated, follows that the two
phenomena must be explained from one and the same point of view,
as the theory of allotropy makes possible.

2. As the course followed bade fair to lead to success, we have
changed our mode of procedure so that we could expect still greater
effects.

Our purpose was now to attack the metals while they were im-
merged in the salt-solutions, and measure the potential with respect
to the calomel-electrodes at the same time.

Very effective in this respect is bromic water, with which in some
cases enormous effects were obtained, and a catalytic influence was
also discovered of Br-ions for Ni.

Nickel.

The first experiment was made with a screwshaped Ni-electrode,
which was kept in rapidly rotatory mction by a motor, and served
therefore at the same time as stirrer. The result was as follows.

Ni-electrode in 100 cm$ '/,;g N. Ni(NO3)9-Solution.

| Potential of the Ni-electrode with

Observations | respect to !/;) Norm.Calomel-electrode
Initial value + 0,15 V
with one drop of Br-water + 0,44 ,
pO GrOps!) iy, -) + 0,51 ,
5 7 * + 0,64 ,,
eel is 7 7 + 0,67 ,
5 8 ene 5 3 + 0,80 ,
Now a pretty abrupt descent of

the potential set in.
| After 4 minutes the potential is
constant
+ 0,42 V

At last 2 drops of pure Br. are )
added i) qr URE

686

It follows from this table in the first place that addition of bromic
water makes the potential of the nickel rise at first by about 0,65 Volt.
Then a maximum is reached, after which a considerable decrease
takes place. We further see that when after the potential did not
change any more, the bromic concentration was raised to saturation
by the addition of three drops of bromine, the potential of the Ni
changed only exceedingly little.

This very remarbable result’) led us to suspect that the disturb-
ance of the internal equilibrium caused by the action of the bromine,
is catalytically influenced by Br’-ions which had arisen when the
metal was etched. With certain Br’-ion-concentration the positive cata-
lytic action of the Br’-ions is so great that it can just compensate the
disturbing action of the bromine, and the br’-ion-concentration increasing -
continually, a considerable decrease will then have to set in. If now
the bromine concentration is increased considerably, both the disturb-
ing action and the catalytic action is greatly increased, after which
ihe condition can become pretty well stationary, and addition of
more bromine has litthke or no influence. To test this supposition
the potential of the Ni was first carried up by bromine water, and
then KBr was added with the following result :

Ni-electrode in 100 cm3 !/;9 Norm. Ni(NO3)2-solution.

| Potential of the Ni-electrode with

Observations | respectto !);9 Norm. Calomel-electrode
Initial state | + 0,07 V
With 5 drops of Br-water + 0,52 ,,
Bo OMe eke H + 0,64 ,
» 2 cm? N.KBr solution + 0,24 ,,
» 2 drops of pure Br + 0,35) ,,
After this a slight decrease takes

slowly place.

We see from this that addition of KBr made the potential of Ni
really decrease greatly, but then it was necessary in order to get
more certainty about the signification of the phenomenon to examine
in how far Ni behaved here as a Bromine electrode.

‘) The same result was oblained with a Ni-electrode glowed in vacuo, from
which follows that possibly dissolved hydrogen exerts no influence on the pheno-
menon.

687

For this purpose besides a Ni-electrode, also a_ Pt-electrode
covered with Pt-black was placed in the same Ni-nitrate-solution,
and then after addition of Br-water the potential of the Ni- and of
the Bromine-electrode was determined.

Then the following was found :

Ni and Pt-electrodes immerged in 100 cm3 N. Ni (NO3)9-solution.

7 oe

Potential of the Br-elec-

| Potential of the Ni-elec-

Of an unassailable metal which behaves as bromine electrode it
may be expected according to the formula :
V Cai,
Vinet. — Veo. = A=A, + 9,058 log’? ———=
C By!
that the addition of the first small quantity of bromine will give
rise to a considerable increase of the potential difference, while a
subsequent increase of the bromine concentration must exercise a
much smaller influence. Our bromine electrode very clearly exhibited
this behaviour ; the first 10 drops of brominewater made the potential
rise 0,85 Volt, whereas the subsequent addition of 1 em* resp. 3 em*
of bromine water no longer practically changed the potential.
Increase of the br’-ion-concentration must lower the potential differ-
ence of the bromine electrodes again, and this too was observed.
By the addition of 1 cm’® of N.KBr-solution the potential fell 0.04
Volt. That this lowering is not greater is owing to this that during
the action of Bromine on nickel bromine ions had already been
formed.
In conelusion we removed all the bromine by addition of Na-

1) This negative value must be attributed to the catalytic influence exerted by
KBr in the preceding experiment.

688

thiosulphate, and then the potential fell to — 0,04 V., which was
about the initial value. If we now compare the behaviour of the
Ni-electrode with this behaviour, we notice that the addition of the
fist quantity of bromine has a smaller influence than for the bromine-
electrode, and that the addition of more bromine has a much greater
influence here than for the bromine-electrode.

While the potential of the bromine electrode no longer changes
on further addition of Bromine up to 3 em*., it increased for the
nickel-electrode by an amount of 0,384 V., so that the total rise
amounted to 0,95 V.

And we see further that while the addition of KBr brought about
a decrease of only 0,04 V. for the bromine-electrode, it came to
four times the amount, viz. to 0,16 V. for the nickel-electrode.

All this suggests that the nickel-electrode does not behave at all
as a bromine-electrode in the experiments mentioned here, which is,
indeed, not astonishing, as the br pretty strongly attacks the Ni-electrode.

It is, therefore, clear that we have to do here with a very parti-
cular behaviour of the metal itself, and that the explanation, as was
already surmised, must be this that during the action of bromine
on nickel a disturbance of the internal equilibrium takes place in
the meta! surface, in the nobler sense, and that this disturbance is
counteracted by addition of Br-ions, from which follows that bromine
ions execute a positively catalytic action. The result is that we have
observed bere a great disturbance of the internal equilibrium in the
metal surface caused by chemical action, which proceeds continuously,
in the same direction as was found in case of anodic polarisation.
The electrolytical solution of metals is, however, very certainly the
most efficient means to disturb the internal equilibrium in the metal,
and thus in this way an anodic polarisation of 1,88 V. was observed
for Ni, which after the current had been broken off still amounted
to 0,95 V., a value which is in fairly good agreement with that
found now. The disturbance brought about by Br during the rinsing
of the electrode with water being again neutralized, the previous
etching experiments with Br had a negative result.

Chromium.

Of all the metals which we have investigated up to now, chro-
mium is nearest akin to Ni.

The following table represents the result obtained when bromine
was added to a rotating chromiumelectrode immerged in a ‘/,,
N.CrCl,-solution.

689

Cr-electrode in 100 cm3 1/;9 norm. CrCl,-solution.

Potential of the Cr-electrode with

Observations | respect to !/;9 norm. Calomelelectrode
Initial state with active chromium!) | — 0,26 V
with 3 drops of Br-water — 0,08 ,,
then slowly descends to
—- 0,24 V
with 1 cm3 of Br-water + 0,62 ,
rises in a few minutes to
-++ 0,79 V
with 2 cm3 of Br-water + 0,79 ,
with | cms of N. KBr solution + 0,78 ,

Then the preceding experiment was repeated with a solution of
Cr(NO,), with the following result :

Potential of the Cr-electrode with

Observations respect to '/;) Norm. Calomelelectrode
Initial state — 0,35 V
with 9 drops of Br-water + 0,73 ,,
» 1 cm of N. KBr-solution + 0,74 ,

In the first place we see from this that the chromium elecirode
undergoes an exceedingly strong enobling, in which the metal beco-
mes passive, as could be demonstrated. By 1 cm’. of bromine water
the potential rises more than 1 Volt. Further we see that addition
of KBr has no influence on the Cr-potential, which proves both
that chromium does not behave here as bromine electrode, and
that Br'-ions do not exert a catalytic influence on the setting in of
the metal equilibrium. The metals Co, Al gave a smaller rise of the
potential when attacked by Bromine.

We shall revert to this behaviour later on.

1) The commercial chromium is passive, and can as Hrrrorr states, be activated
by heating with strong HCl, Z. f. phys. Chem, 25, 729 (1898) and 30, 481 (1889),

690
Tron.

The metal iron yielded a remarkable result. The potential of a
rotating iron electrode immerged in 100 em*. of '/,, NFeCl’, could
be ajjected neither by addition of bromine up to saturation, nor by
addition of a solution of N.KBr.

This remarkable result must be explained in the following way.
As we. shall soon see, iron is strongly attacked by a solution of
FeCl,, and when acted on in this way iron becomes nobler. Now
Br. also attacks iron pretty strongly, and this attack would undoubt-
edly also lead to an enobling of the iron surface. Evidently, how-
ever, the disturbance called forth on attack by Br, is slighter than
that caused by FeCl,, on account of which the addition of Br could.
of course have no influence in the just mentioned experiment. What
is further most convineingly proved here is this that the iron abso-
Jutely cannot behave as bromine electrode in consequence of the attack.

This is quite in accordance with what has now been found by
us, that namely an enobling of the potential of a metal-electrode
caused by addition of bromine, must be attributed to a disturbance
of the internal metal equilibrium, at least when the metal is attacked
by bromine.

Chlorine acting more strongly on iron than bromine, it was
expected that when the former experiment was repeated with chlo-
rine instead of with bromine, a marked rise of the iron potential
would be found. As the following table shows, this was actually
the case.

Fe-electrode in 100 cm3 of N.FeCl3-solution.

a ST

Potential of the Fe-electrode with
| respectto !/;9 Norm. Calomel electrode

Observations

Fe in Norm. FeCl3-solution — 0,292 V
> 0,108 V
In a current of chlorine. — 0,184 ,

We may be sure that the iron which is strongly attacked by
chlorine, cannot have behaved here as chlorine electrode, and that
this experiment therefore proves that we have succeeded also for
iron in disturbing the internal equilibrium in the surface.

Another phenomenon which is in perfect harmony with this view,
and which had already been observed by FINKELSTEIN *), is the elec-

1) Z. f. phys. Chem. 39, 91 (1901).
phy

691

tromotive behaviour of iron with respect to solutions containing a
varying ferro- and ferri-ion content, as appears from the following
table.

ferrosalt

Fe-electrode in solutions with varying ratio RSRGISEIE:

| Potential of the Fe-electrode with

Obseqvation | respect to 1/19 of N. Calomel electrode

Fe-electrode in 1 N. Ferrosulphate | — 0,622 V
» YN. Ferro + 14N.
Ferrisalt — 0,400 ,,
in 1 N. Ferrisulphate | — 0,292 ,,

As was said in the introduction, the complexity must first be
proved, and then we may try and decide whether the ions differ
in valence.

The theory of allotropy already considered the anodic polarisation
phenomenon of iron a clear experimental proof, and now the attack
experiments have furnished in our opinion the first irrefutable proof.

And now that this stage is reached the electromotive behaviour
of iron with respect to solutions with varying ferro- and ferri-ion
content appears in a new light.

Now that we namely know that iron must contain different metal
ions, it was natural to try it
the observed phenomena may
be accounted for from the new
point of view on the assump-
tion that iron contains ions_ of

different valence. And_ really,
for so far as we can now sur-
vey the region of the observa-
tions, this attempt is entirely
successful. ‘.

If we construct a A,wx tigure
for the system Fe-electrolyte in
the way as was already indi-
eated by one of us, the con-
nection between the pseudo-bi-

nary and the unary system
drawn in fig. 1 harmonizes well

with the experimental facts.
The stable unary electromotive two-phase equilibrium is indicated

692

by the solution / and the solid phase S. This solid phase, therefore,
contains very much of the less noble pseudo component a. The
metastable unary electromotive two-phase equilibrium is indicated
by the solution ZL’ and the solid phase S’,

As was set forth before, on anodic polarisation the metal phase S
will move down along Sd, hence become nobler, whereas the metal
surface will move upward along Sa on cathodic polarisation, hence
become less noble.

The stable unary electromotive equilibrium requires an electrolyte
which contains only exceedingly few ferri-ions (?) by the side of
the ferro-ions («). When iron is immerged in a solution of ferri-
chloride, the system tends to assume unary electromotive equilibrium,
in which we may assume the metal phase to send ferro-ions into
solution, whereas ferri-ions are deposited from the solution on the
metal.

As follows from the A, v-figure, a solution containing many ferri-
ions could only be in pseudo-electromotive equilibrium with the iron
for much less negative potential of the iron. Hence there will be a
tendency to make the electrolyte richer in ferro-ions, and the metal
in ferri-ions, but until the unary equilibrium concentration has been
reached, the iron potential will possess a too small negative value,
as was also observed.

It is further to be seen that the negative value of the iron poten-
tial will have to increase in a solution of ferro-sulphate, when
during the measurement the ferri-ions are precipitated as much as
possible.

This follows, indeed, from the following table.

Initial potential of Fe in }/;g N. FeSO4-solution ') = — 0,538 V

Potential - idem . with a little NH,CNS =—0,578,,
” ” idem Uy Ue oy HPO, = — 0,569 ”
= . idem » » » NH,oxalate=—0,555,,

The removal of the ferri-ions makes the iron clearly baser.

It is here the place to point out that in the just mentioned etching
experiments with chlorine, this substance has only indirectly caused
etching. It is namely very well possible that the action of the
chlorine has consisted in this that the ferro-ion emitted by the iron
is immediately converted into the ferri-ion, in consequence of which
the electrolyte remains as far as_ possible from the concentration
of the unary electromotive equilibrium, and that this gives to
the electrolyte its maximum etching action with respect to the iron
electrode.

1) This solution contained traces of ferri salt.

693

In this case the chlorine would, therefore, indirectly bring about
an inerease of the disturbance of the internal equilibrium. What is
not improbable for iron, may also be true for nickel in the experi-
ment with bromine, when namely the nickel possesses ions of
different valence, but this cannot yet be stated with certainty.

Besides this figure accounts for the discontinuous course of the
potential, when passive iron immerged in an iron-salt solution, passes
into the active form.

Iron which has passed into the passive state by anodic polarisation
or by attack with strong HNO,, is greatly enobled superficially, and
the potential possesses even a positive value. The concentration of
the surface of passive iron, therefore, corresponds to a point on the
line eb, and that below the line A= 0.

When this passive iron is immerged in a solution of ferro-sulphate,
transformations will take place, in consequence of which the unary
electromotive equilibrium is approached, and while the potential is
falling, the metal surface moves upward along /e, till it has arrived
in e. Here a second metal phase must occur, viz. d, and as long
as the two metal phases occur side by side, the potential of the
metal remains constant. The phase e must be entirely converted to
d, and when this has taken place, the potential descends further,
till the unary electromotive equilibrium has been reached, and the
metal phase has been superficially transformed into S.

This is exactly the behaviour that has been observed by many
others and also by us. According to our measurements the three-
phase equilibrium cde must lie at + 0,20 V. with respect to */,, N.
calomel electrode. The place of the dotted line 4 =O is therefore
not correct here; it must be thought between ZS and cde.

We too found that the transition passive-active is accelerated by
H-ions, and we are therefore obliged to assume that hydrogen is an
accelerator for the internal transformations in the metal, as are also
the ions of the halogens. On treatment with strong HNO, and on
anodie polarisation the hydrogen is superficially removed, and this
greatly promotes the internal transformation, so that the strongly
metastable state which we call passive iron, is observed for some time.

Through the diffusion of the hydrogen from within towards the
surface the passive iron, no longer subjected to the action of strong
HNO, or anodic polarisation, will soon again return to the active
form.

Summarizing we come to the following conclusion.

1. Farapay’s oxide theory, which seemed already sufficiently
refuted by others, cannot give an explanation of the origin of the

694

passivity. If a metal is once passive, it can undoubtedly be covered
by an oxide coat on anodic polarisation, but the formation of this
coat is a secondary phenomenon.

Leaving apart whether on anodic polarisation oxygen charges
give rise to a certain rise of the potential, it should be borne in
mind that it is exactly the origin of these gas charges that is to be
explained. Only when the metal during the passage of the current
undergoes. a rise of the potential and the tension of generation of
the O, is reached, these gas charges can arise, and so a theory
which purposes to explain the phenomenon of passivity, will have
to account for this potential rise.

lt follows from this that the theories of FrepkENHacen, MutrHMANN,
FRAUENBERGER and others leave the essential part of the passivity
phenomenon an open question.

3. Our experiments have proved that the phenomenon of
passivity resides in the metal itself, and that though this phenomenon
is decidedly a phenomenon of retardation, this retardation is not a
retardation of the ion hydratation in the electrolyte, as Le Brane
thinks, but a retardation of the ion transformations in the metal-
surface.

4. It is perfectly true, as Grave states, that hydrogen accelerates
the setting in of the electromotive equilibrium. That the hydrogen
would accelerate the setting in of the heterogeneous equilibrium metal-
electrolyte, 1s an untenable supposition.

The hydrogen accelerates the establishment of the homogeneous
internal equilibrium, but has often appeared to be inadequate to
neutralize the disturbance of the equilibrium brought about by etching.

5. With regard to Finkeisrein’s (Kriienr’s) view it might be said
to be impled in the new conceptions to which the theory of allo-
tropy has led, but that the said observers, not understanding the
deeper signification and the drift of their assumption, were not
able to embody tneir view in a theory.

6. W. J. Miier’s views, which are only distinguished from
those of FINKELSTEIN (KriGER) by the assumption that the states of
different valence formed different phases, are theoretically incorrect,
and have therefore not led to any result either.

7. The trustworthy experimental data about passivity mentioned
in the literature, just as the new results in this department described
here, can all be easily explained by the application of the theory of
allotropy to the electromotive equilibria.

Anorg. Chem. Lab. of the University.
Amsterdam, Sept. 25, 1914.

695

Chemistry. — “On gas equilibria, and a test of Prot. van pnt
Waats Jros formula.” I. By Dr. F. E. C. Scoerrer. (Communi-

eated by Prof. J. D. vAN per Waats).
(Communicated in the meeting of Sept. 26, 1914).

1. Introduction.

It may be supposed as known that the situation of the equilibrium
of a gas reaction at a definite temperature.can be caleulated, when
at that temperature we know the energy of reaction and the variation
in entropy free from concentration for molecular conversion according
to the chemical equation of reaction. Both quantities are algebraic
sums of the energies and entropies of the reacting gases separately,
in which the terms referring to substances of different members of
the equation of reaction have opposite signs. Energy and entropy
of a gas free from concentration are pure functions of the tempe-
rature ; in the expression for the “equilibrium constant” as funetion
of the temperature the transformation energy and the change in entropy
free from concentration at one definite temperature and the tem-
perature coefficients of both occur as constants. The transformation
energy of a great number of reactions may be directly derived from
BertHeLor and THomsen’s tables; the temperature coefficients are in
simple relation with the specific heats, and for this a great number
of data are found in the literature; the transformation entropy, how-
ever, is generally not determined directly, but from the chemical
equilibria by the aid of the above expression.

If one purposes to calculate the chemical equilibria from caloric
data, one will have to apply instead of the said mode of calculation
of the transformation entropy either direct determinations, or another
mode of calculation, in which exclusively quantities of the gases
separately are used. The determination of electromotive forces of gas
cells might be counted among the direct measurements ; for the tem-
perature coefficient of the electromotive force is a measure for the
transformation entropy. But this method cannot be applied for a
great number of reactions e.g. for dissociations in molecules or atoms
of the same kind.

Hence the calculation of chemical equilibria will succeed only when
we have a method at our disposal to calculate the entropies of the
gases separately or the algebraic sum of the entropies of a gas equi-
librium from the constants of the substances.

The thermodynamic entropy of a gas is a quantity, which through
its definition is determined except for a constant, and it is therefore

Proceedings Royal Acad. Amsterdam. Vol. XVII.

696

clear that the above mentioned calculations of the entropy of the
gases separately have only sense for another definition of entropy.
If the entropy is defined as a function of the probability of the con-
dition, it is possible to find a definite value for this entropy ; but
this value will vary with different meaning of the “probability”.
Thus the expressions derived by Kerrsom'), TreTropr *), and Sackur *)
for the entropy of gases present differences which are the consequence
of different definitions of probability. These differences only oceur in
the constant part; if these differences cancelled each other in the
algebraic sum, a test by the equilibrium determinations could not
give a decision about the correctness of the entropy values. When,
however, the algebraic sum of the entropies according to SACKUR
and Trrropr are drawn up, it appears that these differences continue
to exist also in the algebraic sums, and it must therefore be possible
from experimental determinations at least if the accuracy is great
enough to get a decision which expression is correct.

While these calculations yield a value for the entropy of the
gases separately, Prof. vaAN per Waats Jr. has derived an expression
for the “equilibrium constant” of gas reactions, from which the
algebraic sum of the entropies can be easily derived; the entropy
of the gases separately is again determined here with the exception
of a constant. Besides this expression tries to take the variability of
the specifie heat with the temperature into account‘). I intend to
test this formula and the above mentioned expressions of Sackur
and Trrropr by a unmber of data from the chemical literature.

2. The expressions for the entropy of gases.

For monatomic gases Kersom, Sackur, and Trrropr give the value
for the entropy free from concentration (eventually after recaleula-
tion) successively by the following expressions:

3 3 5 3
he 5 Rlrn T + 3 Rin R - : RinN+ 5 Rinm—3Rinh + C, . (1)
. : . : s a
in which C, represents according to KeEsom R /n a+ R{ 4-+ in ale A

: 3 3
according to SACKUR 5 Rin 2a + R, and according to Trrropr

1) Keesom. These Proc. XVI, p. 227, 669, XVII, p. 20.

2) Terrope. Ann. de Phys. (4) 38. 434. 39. 255, (1912).

8) Saokur. Ann. d. Phys, (4) 86. 958, (1911); 40. 67, 87, (1913).
4) These Proc. XVI p. 1082.

697

4,257 R and 5,257 R.
The values given by Sackur and Trerropr for di-atomic gases, are:

Hy = —Rln T41—RinR——Rin N+ -Rlnm —

“ “ ray

9 7
—5Rmh+RnM+—Rm2+—Rinx+C,, . . (2)

x
o

in which C, according to Sackur amounts to R, according to

(
Trrrope to > R.
We get for a tri-atomic gas:

3
Ay=\= 8 RaT+3RnmR—4RinN + 5 kRinm —

1
—§ Rink + = Rin M,M,M,+-6Rn2+5Rna+ C,, . - (8)

in which C, amounts to 3 R according to Sackur, to 4 R according
to Trrrope.

Besides the known values NV and h, the moments of inertia of
the molecules occur therefore in these expressions. For the di-atomie
molecules J/ is the moment of inertia of the dumbbell shaped mole-
cule with respect to an axis through the centre of gravity, normal
to the bar of the dumbbell; for the tri-atomie molecules J7/,,./, and
M, are the three chief moments of inertia, which accordingly depend
on the relative position of the three atoms in the molecule.

For equilibria in which only mon- or di-atomic molecules parti-
cipate, the moments of inertia of the di-atomie particles therefore
occur, which can be approximately calculated from the different
determinations of the mean molecule radius. For a_ test of the
formulae by equilibria of tri-atomic molecules, however, a hypothesis
concerning the relative situation of the atoms is indispensable, which
is more or less arbitrary, and can make the test less convincing,

3. The equilibrium ABZ A+ B.

For the simplest gas equilibrium ABZA-+ 4, in which the
atoms A and #& ean be of the same or of different kinds, we

1) In the expressions of Trrrope |.c. the terms with 2 are omitted, which
seems justified.

46%

698

find for the algebraic sum of the entropies free from concentration
making use of the expressions of § 2:

nH, —1 = 2 (=i) monate = (=) aiat. —

MAMNB

—— Rinh —
m4+mBp

l 1 3 3
=>5 Rin Li RinR—~ RinN +— Rln

3 1
a Rin2 == Rinx—-RinM+C,,

(’, amounts to '/, R when Sackur’s values are used, to
*/, R when Terrope’s values are used.
Sackur and Terrope’s calculations are based on the following
assumptions for the specific heats:

in which C

3
Comonat: = 2 es ts Cy diat. —= ry RR.

The value of the transformation energy in its dependence on the

temperature is therefore given by:
ys}, SP Oia Soy fades

In this expression and the following the molecular values 2 of
the substances of the second member of the chemical reaction equa-
tion are. always taken positive, those of the first member negative.

Inserting these values into the expression for A., we find:

RT In Kp = — YnET=0 — */, RT + T2nH,= — RT,

in which 27/7, is represented by the above derived expressions.
We can transform this expression as follows:

nk T= 1
nike melee +—mT—inmM+InC,, . . . (4)
RT 2
in which
InC ai (jo OND +- ue Ink — E m2ax+C,; (4a)
£ 2 m4 + mB 2 2 é

C, amounting to —1 according to Sackur’s expressions, to 0 according
o TETRODE.

4. In the fifth communication on the law of partition of energy
Prof. van pyr Waats Jr. derives the following equation for the
dissociation equilibrium of a di-atomic molecule:

&,—€& — —

oi as 0 (aa i. ies Mee er ro)

MA imp a 2 on. Gata Ce
€, — &, here represents the transformation energy at the absolute
zero for one particle; n, and n, represent the number of split and
unsplit molecules per volume unity; hence we get:

699

cae SnET—0 * SnET—o K ie
Onan Nii Re a Sia

Equation (5) can, therefore be written in the following form:

1 — —
+ = In T—In MpIn(1—e ) +imC,, . (6)

SnET=0

nk, = ——
n RT

in which
is 3 MAMP $ 1 1 :
nC, = — ln ————__ -— In2Nh + —Ink — —In2x . . (6a)
f 2 ma+mp - 2 2
Equation (6) differs from equation (4) in this that in (6) the term
with » oeeurs, which takes a vibration of the two atoms in the
molecule into account; equation (6a) quite agrees with (4a), if in
the latter Trrropr’s value is substituted; Sackur’s value yields a
unity difference.

5. The equilibrium J,Z 2J.

In the chemical literature a series of acenrate observations occur
of Starck and Bopenstein'); the dissociation constant of iodium
is given by them in concentrations, i.e. gram molecules per litre.
The equations (4) and (4a), resp. (6) and (6a) yield for their disso-
ciation constant :

vh
> E; —— 1 = SS x
ie Kigy a +5 In T—In M + E (: es )| Vin C. @

in which log C, = log C, + 3 (according to Trrrope and v. p. Waazs Jr.);
log C, = log C, + 2,566 (according to Sackur).
Making use of the values: V = 6.85 107°. (Prrrin), £ = 1.2110—'6,

127
h=5.8810—-2’, m4 =mz = ———., we find:
6.85 1023
log C, = — 36.313 (according to TerropE and van DER Waats Jr)
— 36.747 (according to Sackur) . . . . . . . (Va)

In equation (7) there occur iwo (resp. three) quantities, which can
be caleulated from the observations: +n Hypo, M (and »).

As the term with » can only have slight influence on the result,
we write equation (7) as follows:

vh
SS SS
Sa ere pa ae thy TM Toa tora EE |
9.303RkRT ' 2 ee oale oa 9
— 36.313 (resp. — 36.747) . . (8)

Let us now assume that 4 remains below 20u, which seems justified

1) Zeitschr. f. Elektrochem. 16, 961 (1910).

700

in virtue of the observations of the absorption lines and their influence
on the specific heats of other gases (see among others BsmnrruM); we
then find as extremes for the term with pv:

3.104. 4.86.10—U
cero and log (1— 207 )

Starck and Bopenstein’s observations now yield the following
table for the terms of 8:

TABLE I.

Second member of 8

t(Cels)| T Kg 108) log Kg p | term);—90,,) Y2log T| ——_—__—___—_
Bc! Sa 4=0 |4=202
|
800 | 1073 | 0.129 | 0.111- 4] 0.693-1 | 1.515 | — 30.909 | — 31.216
900 | 1173 | 0.492 | 0.692—4 | 0.665—1 | 1.535 | — 31.470 | — 31.805
1000 | 1273 | 1.58 | 0.199-3] 0.630-1 | 1.552 | — 31.960 | — 32.321
| | |
1100 | 1373 | 4.36 | 0.6393) 0.615—1 | 1.569 | — 32.383 | — 32.768
1200 | 1473 | 10.2 | 0.009-2| 0.5911 | 1.584 | 32.738 | — 33.147

Van per Waats’s equation for 2—=0O and Terrropr’s entropy
expressions yield, therefore, the values of the seventh column of the
above table; Sackur’s values always yield 0,4343 less; Van DER WAALS’S
equation with 2= 204 yields the values of the eighth column.

If we now write equation 8 in the form:

=n Eir— 1)

+ T log Me IEE 2. 4) ON ree (9)

2.303R°
we find:
TABLE II.
ATC ATC, | ATC.
y 9 ‘ 9
: ao) v ( Al ee es ( AT Je ON ( a7 ja
1073 — 33166 ==336310) | — 33494
ery | = 19 | = TS8 al
1173 — 36915 371493 | — 37308
37-7 | .88.15 | Hea Saad
1273 — 40685 — 41238 | | — 41145
STS = 38.2 | | =ege55
1373 — 44462 — 45058 | | — 44990 |
— 37.6 | | — 38.0 | | —asaee
1473 eeAS 22 20a — 48862 | — 48824
mean — 37.6 | mean-38.05, | mean—38.3

| | | |

701

It will be clear that the values of ———* represent the values for

Al
log M ecaleulated from equation (9). Therefore the value of J
becomes 10-876 according to Trrropr, 10-359 according to Sackur,
10-86 according to Van per Waats for 2=0, 10-33 for 2= 204.

It is clear from the calculation that the variation of 2 from zero
to 20m does not cause a change in the order of magnitude of J/,
that therefore the fact that the frequency is unknown yet renders
the rough calculation of W possible, and that reversely the frequency
cannot be calculated but from exceedingly accurate observations.
With the measurements available at present this is not yet possible,
as appears from table 2.

If the iodine molecule is represented by two spheres, the masses
of which are thought concentrated in the centres, and if the distance
from the centres is d, the moment of inertia with respect to an axis
through the centre of gravity and normal to the molecule axis is

a
2m i) . From this follows for the limits of d:
10—276, resp. 10-883 — 2 sees a d—=170:10—* resp: 7 10=9 (10)
: ~ 6.85 1023.4

a value which as far as the order of magnitude is concerned is in

satisfactory concordance with the diameter calculations according to
other methods.

6. Sackur and Trrrope’s entropy expressions which were used in
the preceding paragraph are founded on the assumption that the
specific heats of the gases are independent of the temperature; the
test of these formulae can therefore only be a rough one.') In the
expression proposed by Van per WaAats, the variability of the specific
heats is, however, taken into account.

According to this expression the transformation energy for the
iodine dissociation is represented by :

< = aes Nvh
SnE = SnE y=) + °/, RI eee (11)
ekT —]

Hence the algebraic sum of the specific heats becomes :
hy

dSnE 1 hv\? kT
=== fh — Sh = ———

dT 2

\) A number of calculations of chemical equilibria carried out by the aid of
his formula are found in Sackur. Ann, d. Phys. (4) 40. 87 (1918),

702
The specific heat of the two iodine atoms is 3 FR, that of the
iodine molecule therefore

5 , : ‘hy \? ekT
~ HER (ae eee li. Ti, eae

The real specific heat of iodine at 300° C. is according to STRECKER
8.58 — 1.985 = 6.545. If this expression is substituted for (12), the
equation is satisfied for 2 — cir. 15. If we use this value for equa-
tion (8), we get in analogy with tables 1 and 2:

TABLE III.
Second member | TC
t(Cels) (v-term), 15, of 8 (709); 15, (e ~a"
| Aa jell d=15e4
800 } On7s led — 33406
| — 38.01
900 e051 5 BTN — 37207
| | == 1SRED5
1000 OWS |) . = Baeep — 41032
| ; | — 38.35
1100 0.705—1 — 32.678 — 44867
— 38.21
1200 0.684—1 — 33.054 — 48688
| mean — 38.20

This value yields for the atomic distance:
d= 0.82 10-8 cm.

If this value is compared with that for the mean molecule radius,
which has been determined in three different ways, it appears that
the value for the atomie distance as it is found above, is smaller
than the mean molecule radius. We must derive from this that
the atom centra in the iodine molecule lie closer together. Remark-
able is the agreement of the found d-value with that of the atom
distances, which were calculated by Manprrstoor from the width

TABLE IV.
Gas Radius of Inertia 108
(o@) 0.566
HCl 0.22
HBr 0.165
Jy 0.41

of the infra-red bands for three gases '). This agreement appears
from the foregoing table, in which the values of the three first
mentioned gases are derived from MAnprERsLoor.

I hope soon to come back to the application of the used expres-
sions to some other equilibria.

Postscript. During the correction of the proofs a treatise by
QO. Stern in the Annalen der Physik of June came under my notice,
in which an expression is derived which shows close resemblance
with that of Prof. van per Waats. Application on the iodine
equilibrium can also here lead to a small moment of inertia, which
is however considered improbable by Stern.

Amsterdam, Sept. 1914. Anorg. Chem. Laboratory
of the University.
Chemistry. — “Equilibria in the system Pb—S—O, the roasting

reaction process’. By Prof. W. Reinpers. (Communicated

by Prof. 5. Hoocrwerrr).
(Communicated in the meeting of Sept. 26, 1914).
Introduction.

1. The manufacture of galena into metallic lead is mostly carried
out in this manner that the sulphide is first partially roasted and
the mass then again strongly heated with unchanged or freshly
added lead sulphide out of contact with air. Lead is then formed
with evolution of SO,.

The reactions that take place in this process known under the
name of “Rostreactionsarbeit” are generally given in the text-books
as follows:

PbS + 20, = PbsO,

2 PbS + 30, = 2 PbO + 2 SO,
and then: PbS + PbSO, = 2Pb + 2 SO,

PbS + 2 PbO = 3 Pb + SO,

1) Manperstoor. Thesis for the Doctorate. Utrecht. 1914.

704

For a proper insight into this process and to answer the question
whether these reactions actually do take place it is necessary to
study the equilibria between the different phases that may be formed
therein.

After various older researches among which deserve to be men-
tioned those of H. C. Jenkins and E. H. Smita *), a systematic
research as to these equilibria was carried out some years ago
by R. Scnenck and W. Rasspacn *). They determined the equilibrium
pressure of the sulphur dioxide evolved when three of the four
phases PbS, PbSO,, PbO and Pb are heated together in an evacuated
tube at 550° to 900°.

The conelusions which they drew from these measurements as to
the nature of the equilibria occurring therein could, however, not -
be correct in many respects. Their idea has in fact been consider-
ably modified in various. subsequent publications thereon *). But
even the last concluding articles still contain many contradictions
so that it is not plain what equilibria they have actually determined
and which phases are stable in the presence of each other.

In the following will, therefore, be discussed (1) the different
equilibria imaginable in this system and (2) the results will be
communicated of researches which in consequence thereof have been
carried out conjointly with Dr. F. Gouprisan.

2. The equilibria between Pb and the compounds PbO, PbS,
PbSO, and SO, may be considered as those in a system of three
components, namely Pb, O, and S$. The isotherm for the equilibria
between the different phases can, then, be indicated by a triangle
with these components as apexes. (See fig. 1),

Let us now first suppose that

a. only the phases Pb, PbS, PbSO,, PbO and SO, are possible

4. the gaseous phase is pure SO, and the lead phase pure lead.

In the last supposition we therefore neglect the small amount of
PbS in the vapour and the solubility of PbS in molten lead; in the
first supposition no notice is ‘taken of the basic sulphates which
according to the later researches of Scuenck and RassBacH *) occur
as intermediate phases between PbSO, and PbO.

1) Journ. Chem. Soe. 71, 666 (1897).

2) Ber. d. d. chem. Ges. 40, 2185 (1907). Metallurgie 4, 455, (1907).

5) Ber. d. d. chem. Ges. 40, 2947 (1907); 41, 2917 (1908). R, ScHenck, Physi-
kalische Chemie der Metalle.

4) Ber. d. d, chem. Ges. 41, 2917, (1908).

705

Ss We shall see later how the
deduced equilibria are being mo-
dified when we drop these sim-
plifications.

sy 3. Let us imagine PbS heated
at constant temperature between
600° and 800° in an enclosed

space wherein a limited quan-
o lity of oxygen is forced. PbS
30 is then partly converted into

Fig. 1. PbSO,.
The two phases will be capable of existing in the presence of each

S0,

other and in an unchanged condition at a series of temperatures
and pressures,

If on lowering the pressure this falls below a certain limit, one
of the two following reactions will take place

PhS PhsOs == 2 Ppa Oo SONY ae, ty
or PbS + 3PpS0,=4Pb0 +480, .... 2)

In both cases there are formed in addition to the two existing
solid phases two new phases, namely fused Pb and SO,-gas, or solid
PbO and SO,-gas. Hence, between these four phases a monovariant
equilibrium will set in, which, at a constant temperature, is possible
only at one special pressure. This will be p, or p,.

Only in a very special case, namely with an eventual transition
point where the five phases PbS, PbSO,, PbO, Pb, and SO, might
coexist, p, and p, are equal. As a rule, however, they are not and
in consequence only one of the two monovariant equilibria can
be stable.

For if p, > p, the reaction (1), in the presence of the five phases,
will take place from the left to the right and the SO, formed act
on PbO according to equation (2) in the direction <—. Hence, the two
reactions together result in the following conversion:

2PbS-+2PbSO, —4Pb +480,
4S0, +4Pb0 =3PbSO, + PbS

This transformation takes place until one of the phases of the
first member of the equation is used up, whilst the other with Pb

706

and PbSO, is left. PbS and PbO are, therefore, not capable of
existing side by side of each other.

If, conversely p, < p, the different reactions take place in the
opposite sense and Pb and PbSO, recede from each other.

Hence, of the phase pairs Pb + PbSO, and PbS + PbO only
one can be stable, the other forms a metastable equilibrium.

Here we have a case quite similar to that occurring with reci-
procal salt pairs where also only one of the two pairs can be stable.

4. Let us now also consider the two other monovariant equilibria
which may be assumed to exist with SO,-vapour and which are
indicated by the equations

2 PbO + PbS 223.Pb 4: S0) =. ee
Pb ++ PbSO,=2 PhO'4- SO, ee

In the case p, >> p,, it follows at once from the incompatibility
of the phases PbS and PbO that the equilibrium (4) can be stable,
but not equilibrium (3).

Moreover, we then must have p, > p, for otherwise after the
reaction (1) in the direction — might follow the reaction (3) in the
direction < which reactions might jointly cause the conversion (5)
in the direction <—, which is in conflict with the premiss.

Finally we shall have p,<p,, for then the stable equilibrium may
also be again attained by the reaction (2) in the direction > followed
by (4) in the direction <—, namely:

PbS +3 PbSO,—4 PbO + 480,
480,-+8PbO = 4 Pbh+ 4 Ppso,

PbS + 4 PbO =4Pb-+ PbSO,
Hence, we get this result:
If Pb + PbSO, forms the stable phase pair, then only the mono
variant equilibria (1) and (4) are stable and p, > p, > p2 > Ps:
If PLO + PbS form the stable phase pair, all the reactions
occur in the opposite sense and only the monovariant equilibria (2)
and (3) are stable, whereas then p, > p. > pi > Ps-

5. Starting from the mixture of PbS and PbSO, (for instance a
in fig. 1) we will, on withdrawal of SO, travel either through the
monovariant equilibria (1) and (4) (region PbS, PbSO,, Pb and region
PbSO,, Pb, PbO of Fig. 1) or the equilibria (2) and (3) (region

707

PbS, PbSO,, PbO and region PbS, PbO, Pb) to finally retain the
equilibrium Pb-—+ PbS or Pb-+ PbO after eliminating the SO, as
much as possible.

Hence, the reactions (1) and (3), which are generally quoted as
taking place in the roasting reaction process cannot possibly indicate
both stable equilibria.

Of the p-T-lines which Scnenck and RossBacn determined by addi-
tion of “PbSO,, PbS and Pb and of PbS, PbO and Pb one at least
must, therefore, indicate an instable equilibrium or an equilibrium
between phases other than those which were brought together in
the reaction tube.

We will see later that both equilibria are metastable and that the
pressure lines recorded by them relate to the equilibrium between

other phases.

6. The supposition made in (2) sub @ is not correct. Between
PbSO, and PbO there still arrive three basic salts as intermediate
phases, namely PbO.PbSO, , (PbO), PbSO, and (PbO), PbSO,. The
first of these can be in equilibrium with PbdSO,.

The four monovariant equilibria mentioned in (3) now become:

Bhs a eEsOr= UPHELD SOS 9 coin. se ot
PbS -—- 7 PbSO, = 4 PbO. PbSO, + 4S0,. . . . (2)
DsPhO PESO: AaPbSi= FED 51805 7-2) Sh 6)
Pb! sPusOr== 2 ibb@:.PbSO, SO, =." 08! sa

and the alternative found must read:

either Pb + PbSO, stable and then p, >p, >p, > p, and only (1)
and (2) stable,

or PbS + PbO. PbSO, stable and then p, << p, << py <p, and only (2)
and (3) stable.

Experimental.
(conjointly with Dr. F. Goupriaan).

7. In order to investigate which of these two phase pairs was
stable and at the same time to know the SO,-pressure of the stable
equilibrium, an intimate mixture of PbS and PbSO, (6—8 grams)
was heated in a porcelain tube connected by means of a ground
joint with a manometer and an air-pump.

The lead sulphide was precipitated from a solution of lead acetate
with H,S and after washing, dried by heating in a current of nitrogen
at 200°—300°.

The lead sulphate was precipitated from a solution of lead acetate
with sulphuric acid and also dried at 300°.

708

The mixture was introduced in a porcelain boat. The remaining
space in the reaction tube was oceupied by a porcelain rod so as
to render the gas-volume as small as possible and thus to accelerate
the setting in of the equilibrium as much as possible.

The heating took place in an electric furnace. The temperature
was measured with a Pt-PtRh thermocell and a galvanometer.

8. Although the reacting substances had been previously dried at
300° there still was evolved, on heating at 500°, in vacuo, a little
moisture, which condensed in the colder part of the tubes and was
removed by a repeated evacuation and gentle heating.

Subsequently the dissociation pressure was measured at different
pressures between 500°—700".

The equilibrium set in very rapidly so that when the tempe-
rature had been raised and more gas began to evolve there
could generally not be noticed any change in pressure after 20—30
minutes. Then a further evolution of SO, was caused by a short
heating at a somewhat higher temperature and after cooling to the
original temperature the course of the absorption of the SO, was
recorded. This also took place very rapidly. The equilibrium was
thus attained from both sides and yielded figures which differed
from each other at most 2 or 38 m.m. Also the same pressure again
set in after an evacuation. The equilibrium is, therefore, independent
of the total composition, which was confirmed by a change in the
proportions of PbSO, and Pbs.

The results are contained in table I. (Fig. 2 Curve I).

TABLE I.

7 PbSO, on 1 PbS | 5 PbSO, on 1 PbS || 3 PbSO, on 1 PbS

t D t p | t p
5820 | 26 604 50 || «590 | 30
606 56 634 | 100 || 620 2
630 94.5 || 660 | 185 |) 670 | 999
655 156 688 346 |
680 280

After the tube had been evacuated a few times and a certain
quantity of the dissociation product might thus have been formed,

709

and as it had been shown that always the old equilibrium again set
in, the oven was allowed to cool and the tube was withdrawn.

The reaction product was strongly caked and of a lighter colour
than the original mixture of PbS and PbSO,. Here and there were
visible granules with a strong metallic lustre so that at first the
suspicion was raised that lead had formed as a reaction product.
On closer examination by means of a magnifying glass these granules
proved to be very beautifully formed crystals of “galena’” which
had deposited, besides in the reaction mass, also against the porcelain
boat and the extremity of the porcelain rod. The analysis showed
this to be perfectly pure PbS, whilst in the reaction product itself
not a trace of free lead could be detected.

Hence, no lead has formed so that the reaction product must be
basic lead sulphate. PbS +- PhO.PbSO, form the stable phase pair,
Pb + PbSO, the metastable one.

9. This was confirmed by the following experiment:

An intimate mixture of PbSO, and finely divided lead scrapings
in the proportion of 10 PbSO, to 1 Pb was heated in an evacuated
and sealed tube for 3 hours at 600°.

The product obtained gave with hydrochloric acid a very distinct
evolution of H,S.

A weighed quantity was now heated in a small flask with strong
hydrochloric acid and the gas expelled collected in an ammoniacal
solution of hydrogen peroxide. This solution was boiled for a while,
then acidified, and the resulting H,SO, precipitated as BaSO,.

Five grams of mixture containing originally 0.380 gram of Pb,
yielded 0,040 gram of BaSO,, equivalent to 0,041 gram of PbS.

According to the equation:

4Pb+ 5PbSO,=+4Pb0.PbSO,+ PbS . . . (5)

0,142 gram of Pb has been required for this 0.041 gram of PbS.
Although the lead has not yet entirely disappeared, a considerable
quantity of the same has been converted into PbS‘).

10. The pressures observed almost entirely agree with the values
found by Scuenck and Rasspacu for the mixture of PbS+PbSO,+-Pb
as well as for PbS + PbSO,-+ PbO. They conclude that the pressures

1) Afterwards it came to our knowledge that also Jenkins and Smrrtu (l.c. p.691)
had already made an experiment from which this is shown. They heated a mixture
of equal molecular quantities of Pb and PbSO, in a porcelain crucible at dull red
heat for half an hour; from the residual mass could be expelled with HCl
a quantity of HS corresponding with 1,41°/, of sulpiur.

(10

relate to the equilibrium between the first three phases and that the
second trio is not stable. From the preceding it follows that both
equilibria are metastable and that the pressures recorded relate to
the equilibrium PbS, PbSO,, PbO.PbSO,, SO,.

The fact that the lead present exerts so little influence on the
equilibrium pressure proves that reaction (4), which should lead to
a higher pressure p, and the reactions (1) and (3) in the direction
— which should lower it either compensate each other or, in com-
parison with the reaction (2) proceed so slowly that they do not
perceptibly alter the pressure. Probably the more finely divided
lead is soon converted and the remaining lead, united to larger
drops, offers such a small surface of attack that it can react but

very slowly.

11. When now from the PbS + FbS50, so much SO, has been
abstracted that all has passed into PbS + PbO.PbSO, the equili-
brium has become divariant. The residual phases will be capable
of existing by the order of cach other in a series of pressures < p,.

If, however, the pressure falls below a definite limit, a third
condensed phase appears. Two phases are concerned here, namely —
Pb and (PbO),.PbSO,.

As noticed in the case PbS + PbSO,, only one of the two can
be in stable equilibrium with PbS and PbO.PbSO,.

This depends on which of the phase pairs PbS + (PbO), PbSO, and
Pb + PbO. PbSO,, which can be converted into each other by
double decomposition :

PbS + 5 (PbO), PbSO, 24 Pb + 6 PbO.PbSO,. . . (6)

is stable.

12. In order to investigate this an intimate mixture of finely
divided lead scrapings and basie lead sulphate in the molecular
proportion of 38:1 was heated for three hours in an evacuated and
sealed tube at 670°-—680°.

The PbO. PbSO, had been prepared by the moist process, accord-
ing to D. Srrémuoim'), by digesting finely powdered PbSO, with a
1—2°/, NH,-solution. The analysis of the product obtained gave
84.88°/, PbO, theory for PbO.PbSO, 84,79°/,.

The heating of the mixture Pb + PbO.PbSO, yielded apparently
a but little changed product. It gave, however, a slight sulphide
reaction. Thus it seemed that the mixture selected did net form the

\) Zeitschr. f. anorg. Chem. 38, 429 (1904).

711

stable phase pair. We must, however, consider that the lead phase
need not be pure Pb, but may contain dissolved PbS and hence
there exists the possibility that the PbS found was present, not asa
free phase, but as a solution in the molten Pb.

The amount of PbS was, therefore, determined quantitatively.

From two grams of the mixture were obtained 17,4 mg. of BaSO,
corresponding with 17,8 mg. of PbS. For the formation of 17,8 mg.
of PbS according to reaction (6) are required 70 mg. of Pb. Before
the heating 2 grams of the mixture contained 1,082 grams of lead.
Hence, there remains 1,022 gram of Pb, which in 100 grams contains
17,8 ,
Pe tO —— 7 orams Of. Elo:
1022

From the observations of Frirprich and Leroux?) it follows that
the lead solution saturated with PbS at 680° contains 2,5°/, PbS.
Hence the PbS will be present in the heated mixture not as a free
phase, but as a solution in Pb, and Pb -—+ PbO.PbSO, will form
the stable phase pair.

13. This conclusion was further confirmed by the dissociation
experiments, starting from a mixture of PbS and PbO.PbSO,.

These experiments were conducted in a manner similar to that
in the case of PbS and PbSO,. The SO,-evolution started at 680°.
The equilibrium set in quite as easily as with PbS + PbSO, and
could be determined readily from both sides. Also, after removal of
larger quantities of SO,, the same equilibrium pressure was again
always obtained. In order to prevent fusion the mass was not heated
above 800°.

The results obtained are united in table II (Fig. 2, Curve II).

TABLE II.

t p
712 27.5
740 63
750 78
753 87.5
770 123
790 233

1) Metallurgie 2, 536 (1905).
47

Proceedings Royal Acad. Amsterdam. Vol. XVII.

749

These values correspond very well with the pressures found by
Scuenck and Rasspacn with a similar mixture and with a mixture
of PbS + PbO which has been heated above 800° and then cooled.

On opening the apparatus it appeared that the reaction product,
although not fused, had strongly caked: the porcelain boat was
strongly attacked and on the rod a sublimate of very beautiful
PbS-erystals had again deposited. It was not doubtful that the
reaction mass contained metallic lead; there could be found large,
soft paper-marking and malleable particles. Finally, it was proved
by extracting a portion of the reaction product first a few times
with ammonium acetate and then with lead acetate. All the PbSO,
and PbO then dissolves. The residue was treated with fuming HNO,,
which converts the PbS quantitatively into PbSO,. After expelling ~
the HNO, and filtering off the PbSO,, any Pb formed eventually as
Pb(NO,), must be present in the filtrate.

The filtrate gave a strong lead reaction. The reaction mass thus
contains metallic lead.

Hence Pb + PbO.PbSO, are the stable phase pair and the pressures
measured relate to the reaction :

2 PhO.PbSO, + 3PbS—=7Pb+580,.... @%

14. From the above it follows that with a sufficient excess of
basic lead sulphate the end of reaction (7) will be a mixture of
PbO .PbSO, and Pb. (In the latter, however, a little PbS will still
be dissolved).

This equilibrium is divariant and, on a sufficient reduction of
pressure, will pass into a monovariant equilibrium.

The third condensed phase occurring therein cannot be a second
metallie phase for the solution of PbS in Pb already present is
mixable with pure lead in every proportion.

Hence, it must be the basic sulphate (PbO), . PbSO, which follows
the PbO.PbSO, and the reaction occurring is indicated by the
following equation :

Pb -+ 4PbO.PbSO, = 3 (PbO), PbSO, + SO, -. . 296

The monovariant equilibrium of this reaction will in turn be
followed by still two other monovariant equilibria wherein occur
the reactions represented by the equations:

In these reactions primary formed lead therefore disappears on

behalf of PbO until, finally, only Pb + PbO is left.

713

15. Pressures appertaining to the first monovariant equilibrium
were obtained by starting from a mixture of Pb and PbO. PbSO,.

Not until 700° an evolution of gas was perceptible. The equilibrium
sets in with much greater difficulty than in the first two cases;
generally two or three hours were required. Probably this is due
to the fact that the metal conglomerates and thus offers but a small
contact surface with the basic salt. It is also very certain, however,
that the greater vapour tension of the PbS will have strongly promoted
the setting in of the previous equilibria of which PbS was one of
the active phases. The equilibrium could again be attained from
both sides.

The following pressures were measured (Fig. 2 Curve III) :

TABLE III.

t p
750° 36.5
771 61
789 98

The tube was subsequently evacuated at 789° and the equilibrium
pressure again determined. This proved to be unchanged. Even on

350
300
250
200

150

100 A

————

500° 600° 700" 800°

Fig. 2.
evacuating a second time the pressure reverted to its old value. The
pressures measured therefore relate toa purely monovariant equilibrium.

714

16. Without opening the apparatus the experiments were now
continued with the same mixture at 789° The tube was, therefore,
evacuated for the third time and then again a few times and each
time the equilibrium pressure was again measured. It now appeared
that the old pressure no longer set in, but that a lower pressure
was attained and the more so when more SO, had been withdrawn.
In suecession were found 93, 75, 61, 54, 41, 34, and 28 m.m.

This different behaviour can be explained in two ways.

1. The equilibrium is no longer monovariant, but divariant. Instead
of three solid phases there are only two, one of which possesses a
variable composition. This phase might be a very basic sulphate
with a variable content in PbO. The fusion diagram PbO — PbSO,
of Scuenck and Rasspacn gives, however, but little support to this ~
conception.

2. The pressures measured are not true equilibria pressures, but
indicate a stationary condition.

For if, on evacuating, the pressure falls below the equilibrium
pressure of equibrium (9) the basie sulfate (PbO), PbSO, can decom-
pose still further and give rise to the formation of (PbO), PbSO, .
Pb + PbO. PbSO, then strive, according to reaction (8) towards the
pressure p,, (PbO), PbSO, + SO, according to reaction (9), however,
in the direction — towards p,. And when finally both reactions
take place with equal velocity, we obtain an apparent equilibrium
at a pressure between p, and p, and dependent on the quantities
of the different phases.

It is even possible that PbO is also formed and that reaction (10)
thus takes place simultaneously.

17. The second assumption was the most probable one. In order
to test it more closely a mixture of Pb and (PbO), PbSO, was heated
in the pressure tube. From this mixture PbO only can be formed
as the third phase so that only one reaction, that of the monovariant
equilibrium (10), should be possible.

(PbO), . PbSO, was obtained by fusion of 1 PbSO, with more than
3 PbO. As porcelain is strongly attacked by PbO, the mixture was
heated in a magnesia boat previously heated and saturated with
lead oxide.

The result of the measurement at 780° was p= 23, after evacua-
tion at the same temperature again 22 m.m., then at 800°, 38 and
after evacuation successively 30, 22, 16 m.m. Thus no constant
equilibrium is attained.

On opening the pressure tube nearly all appeared to have been

(ailis)

fused and ran through the boat although the temperature had not
got above 800°, whereas the eutecticum of PbO and (PbO), . PbSO,,
according to Scnenck and Rasspacu is at 820°. Probably the MgO is
attacked by the PbSO,. The want of a suitable material which is
attacked neither by PbO nor by PbSO, or Pb at this high tempe-
rature renders a correct determination of dissociation pressures for
reaction (9) and (10) a matter of great difficulty.

If we accept the value of 20 mm. at 780° as the correct one for
the equilibrium (10), the p-7-line for this equilibrium would then
run as indicated by line V in tig. 2.

The p-7-line of equilibrium (9) then lies between III and V and
is indicated schematically in Fig. 2 by line IV.

18. Although from the preceding it is evident that PbS and PbO
cannot be coexistent, a few experiments were made nevertheless in
order to confirm this opinion.

Scnenck and Rasspacw in all their publications consider the equili-
brium PbS and PbO to be stable although in their dissociation expe-
riments it had already been shown that with such a mixture repro-
duceable pressures were not always obtained, for instance if the
temperature had been raised to above 800°. They also noticed the
formation of sulphate, but assume that this can only be formed at
a high temperature and then remains intact on sudden cooling to
the dissociation temperatures.

We have now heated an intimate mixture of PbO + PbS for
some hours at 600—700° in an evacuated and sealed tube.

The reaction product perceptibly contained sulphate. This was
estimated quantitatively by boiling a weighed quantity of the product
with aqueous sodium hydroxide and then passing CO,. The PbSO,
present is then converted into PbCO,. After filtering and acidifying
the filtrate the sulphate was precipitated as BaSO,. A check analysis
was also made on a portion of the mixture that has not been sub-
jected to heating, under exactly the same conditions of boiling ete.

Mixture of 4 mols. PvO to 1 mols. PbS. Temperature 670—680’
Time of heating 0) lei 3 6 hours
Gram of BaSQO, per gram of mixture 0,0498 0.0758 0,1000 04121
Additional sulphate formed on

heating at 680°
ingram of BaSO, per gram of mixture — 0.0260 0,0502 0.0623

If the mixture had been converted completely into basic sulphate

716

according to the equation 5 PbO+ PbS = PbO PbSO,-+ 4 Pb, 1 gram
of the mixture should have yielded 154 mg. of BaSO,. Hence, a
large proportion of the PbO + PbS has been converted. *)

The pressures which Scuenck and Rassspacn observed with a mix-
ture of Pb -+ PbO + PbS do, therefore, probably not relate to an
equilibrium of these three phases with SO,, but to another equilibrium.

By a comparison of their observations with our measurements it
appears that on heating at temperatures below 800° this is the
equilibrium: Pb + PbO. PbSO, + (PbO), PbSO,, and on heating above
800° and then cooling, the equilibrium: Pb + PbS + PbO. PbSO,.

Also below 800° however, this latter equilibrium sets in, which
with «a sufficient excess of PbS is the most stable, as shown from
the following experiment:

A mixture of 4+ mols. of PbO to 1 mol. of PbS was heated in
a pressure tube. The evolution of gas started at 660°. After evacua-
tion the following change in pressure was observed at 750°.

time in min. pressure

0 5

7 14
20 26
34 33
42 30
70 41
100 44
160 53
220 65
280 74
340 81
400 83
460 83

The pressure thus rises rapidly to + 38 m.m. and then increases
gradually to 83.

The first pressure falls on the p-7-line of Pb + PbO.PbSO, +
+ (PbO), PbSO,, the second on that of Pb + PbS + PbO.PbSO,.
_ Similarly was found with a fresh mixture on heating at 790° a

1) The high result of the sulphate content in the check experiment is very
striking, because both the PbO and the PbS employed were free from sulphate.
Evidently the conversion of PbS + PbO into sulphate takes already place at the
boiling heat in the aqueous solution, from which it follows that also at the
ordinary temperature PbS and PbO are nol stable in each other’s presence.

1?
first halt at + 100 m.m. and then a slow rise io 236 m.m. Both
pressures are again situated on the above cited p-7Z-lines.

CONCLUSION.

19. Summarizing it thus appears that on abstraction of SO, from
a mixture of PbS and PbSO,, the subjoined monovariant equilibria
are successively met with, which are indicated in fig. 3 by the regions

Pelee Tuy IV ‘and: V..

PbS—PbSO,—PbO.PbSO, . . . I
Pb.—PbS—PbO.PbSO, . . . . II
Pb,—PbO.PbSO,—(PbO),.PbSO, . III
Pb.—,PbO),.PbSO,—(PbQ),.PbSO, . 1V
Pba—(PbO),.PbSO,—PbO . . . V

The lead phase may contain a
little PbS in solution. As the con-
tent thereof varies in the different
equilibria, this difference is repre-
sented by the indices a, ¢ ete.
Probably, however this sulphide
content is very small.

Fig. 2 indicates the pressures
in these monovariant equilibria
and the changes thereof with the

Oo
temperature.
Fig. 3.
Therein region A is the existential region of PbS + PbSO,
s Lee eBire e 5 » » PbSO, + PbO. PbSO,
x 3 Coes 7 re »» PbO. PbSO, + Pb
- a Da, : » », (PbO), PbSO, + Pb
3 ee Piney 53 > 95 (PbO), PbSO, ++ Pb
a Hild ares = 57 DO == Pb:

Hence, at the temperatures and pressures of region /’ all the
sulphur will have been expelled from the roasting material.

20. By substituting the values found in table 1 first series in
Q
4,571 T
thus obtained in pairs, Q, was caleulated for the reaction:

PbS + 7 PbSO, = 4 PbO. PbSO, + 450, + 4Q,

the equation log p= — + C and combining the equations

718

and as mean value was found — 38390 cals. Applying the same
principle to the p-Z-values of table 2 we found as the mean value
for Q, in the reaction:
3 PbS + 2 PbO.PbSO, = 7 Pb + 5S0, + 5 Q, -— 54324 cal.
In order to check these, figures we eliminate the unknown heat
of formation of the basis sulphate from these equations:
PbS + 7 PbSO, = 4 PbO . PbSO, + 450, — 4 X 38390 cal.
6 PbS+ 4 PbO. PbSO, = 14 Pb+ 1080, —10 X 543824 cal.
7 PbS + 7 PbSO, = 14 Pb +1480, —696800cal.
PbS + PbSO, = 2 Pb + 250, — 99548 eal.
From the molecular heats ')
PbSO, = 216210 cal.
PbS= 18420 ,,
SO, = 71080 %;

the calculation for the above reaction at 20° gives — 92470 eal.
The agreement is tolerable.

Delft. Inorg. and phys. chem. Laboratory
Technical University.

1) LANDOLT. Bornstein, Phys. Chem. Tabelle 1912, 870 and 853.

(November 27, 1914).

KONINKLUKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.

PROCEEDINGS OF THE MEETING
of Saturday November 28, 1914.
Vou. XVII.

ye
So

President: Prof. H. A. Lorentz.
Secretary: Prof. P. Zeman.

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Zaterdag 28 November 1914, Dl. XXIII).

SL OENE EEE eN a Se

G. J. Exvias: “On the structure of the absorption lines Dy and D,”. (Communicated by
Prof. H. Lorentz), p. 720. ,

G. J. Exvias: “On the lowering of the freezing point in consequence of an elastic deformation.}
(Communicated by Prof. H. A. Lorentz), p. 732. :

G. J. Exias: “The effect of magnetisation of the electrodes on the electromotive force.”
(Communicated by Prof. H. A, Lorentz), p. 745. 1

H. Kameruinen Onnes and G. Ilorsr: “Further experiments with liquid helium. M. Prelimi-
nary determination of the specific heat and of the thermal conductivity of mercury at
temperatures obtainable with liquid helium, besides some measurements of thermoelectric
forces and resistances for the purpose of these investigations”. p. 760.

F, A. H. Scurememaxers: “Equilibria in ternary systems” XVII, p. 767. |

F, A. H. Scarememakers and Miss W. C. pe Baar: “On the quaternary system : KC]l—
CuCl,—BaCl,—H,0”, p. 781.

T.. S. Ornstems: “On the theory of the string galvanometer of EryrHoven”. (Communicated

* by Prof. H. A. Lorentz), p. 784.

L. S. Ornstern and F. Zernike: “Accidental deviations of density and opalescénce at the
critical point of a single substance”. (Communicated by Prof. H. A. Lorentz), p. 793.

A. A. Hismays VAN ven Beren and J. J. pk 1a Fontare Scururrer: ‘The identification
of traces of bilirubin in albuminons fluids” (Communicated by Prof. H. J. Hampurcrer);
p. 807. (With one plate).

M. W. Bewerinck : “Gummosis in the fruit of the Almond and the Peachalmond asa process
of normal life”, p. 810.

Ernst Conen and W. D. Hetperman: “The allotropy of Lead” I. p. 822. (With one plate).

J. C. Kivyver: On an integral formala of Strerrses”, p. 829.

F. E. C. Scurerer: “On unmixing in a binary system for which the three-phase pressure
is greater than the sum of the vapour tension; of the two components”. (Communicated
by Prof, J. D. van per WAAts), p. 834.

Mrs. T. Enrenrest-Aranasssewa: “Contribution to the theory of corresponding states”,
(Communicated by Prof. H. A. Lorentz), p. 840.

A. FB. Hotreman: “The nitration of the mixed dihalogen benzenes”, p. 846.

J. Borsexen and W. D. Conrn: “The reduction of aromatic ketones. III. Contribution to
the knowledge of the photochemical phenomena” (Communicated by Prof. A. F. Hoiirs-
MAN), p. 849.

YP, Enrenrest and H. Kamertincu Onyes: “Simplified deduction of the formula from the theory!
of combinations which PLANcK usvs as the basis of his radiation-theory, p. 870.

48
Proceedings Royal Acad. Amsterdam, Vol. XVII. ;

720

Physics. — “On the structure of the absorption lines D, and D,”.
By Dr. G. J. En1as. (Communicated by Prof. H. A. Lorentz).

(Communicated in the meeting of April 24, 1914).

Some time ago Prof. H. A. Lorentz drew my attention to the
results of an investigation by Miss G. v. Usiscu'). From phenomena
observed by the writer during the investigation of the polarisation
state of light emitted by a sodium flame in a magnetic field after
it had passed through a tube filled with absorbing sodium vapour,
she infers that the wave length for which the absorption of the
vapour is a maximum, depends on its temperature, and in such a
way too that on rise of temperature a displacement towards the
red takes place. The amount of this at 270° would be about 0.17 A.U.
with respect to the emission line. If seemed worth while to ascertain
this result by direct observation. During the summer months of last
year Dr. W. J. pk Haas and myself occupied ourselves with this question.

At first we intended to use an échelon-spectroscope for these researches,
observe by the aid of this the spectrum of a monochromatic source
of light, and then superpose the absorption lines of sodium vapour
on this. This vapour was in an iron tube, closed on both ends by
plates of selected plate glass, and provided with water cooling; in
the middle the tube, which contained there a vessel of metallic
sodium, could be heated. Such tubes were used by R. W. Woop
for the investigation of fluorescence of sodium vapour. First a blow-
flame served as monochromatic source of light, which was blown
by means of air in which a very finely divided solution (mist) of
soda was suspended. Afterwards the flame of a Méker-burner was
preferred, burning in an atmosphere in which a mist of soda was
also suspended. This was reached by placing the flame inside an iron
exit tube, at the bottom of which a reservoir was attached, which
was in communication with the air, and into which the soda-mist
was blown by means of an aspirator. This method appeared very
efficient to obtain a sodium flame of constant intensity, which is
moreover easy to regulate. :

The lines obtained by means of this source of light, were too
broad for the investigation with the échelon-spectroscope when the
intensity of the light was sufficient for the observation, the self-
reversal moreover being very troublesome then. If on the other
hand, the light intensity was diminished till the lines were narrow
enough, the intensity was again too slight for the observation.

1) G. y. Usiscu. Inaug. Diss. Strassburg. 1911. Aun. d. Phys, 35. p. 790; 1911,

724

We have therefore then tried to see the phenomenon directly by
means of the spectrometer, which served for provisional dispersion
in the experiments with the échelon spectroscope. We were of
opinion that, the dissolving power of the prism system amounting
to 60.000, it must be possible to observe in this way a displacement
of the above given amount. Nothing was to be detected of this,
however. It is true that the at first narrow absorption line (which
_ has originated by self-reversal in the sodium flame) widened considerably
on the heating of the Woop tube up to about half the distance of
the two D-lines, but a displacement could not be perceived.

On account of Dr. pe Haas’ return to Berlin we had to stop our
joint observations at this point, and I continued the research alone.

First I tried to obtain comparatively narrow emission lines, which
should be intensive enough to superpose the absorption lines on
them in the investigation with the echelon spectroscope by eleetric
discharges in a heated evacuated Woop tube with sodium. This,
however, appeared impossible, the width remained considerable, and
the self-reversal troublesome.

Then I took another course, and used an arclamp as source of
light. To obtain monochromatic light I used the above mentioned
spectrometer as monochromator, diminishing the widths of the slits
so that the issuing light comprised a range of only about 0,5 A.U.,
for some observations 0,4 A.U. In this case the adjacent spectra
will overlap only for a small part, as the distance between two
successive orders amounts to 0,39 A.U. The dissolving power of
.the échelon spectroscope, which consists of 80 plates of 14,45 m.m.,
amounts to 450.000 *) for D-light.

The absorption lines of the are of light, which are caused by
the sodium vapour present in it, appear, observed in this way, to
be double. Both for D, and for D, there are two maxima of absorp-
tion, which are somewhat sharper for D, than for D,, and the
distance of which is smaller for ), than for D, under for the rest
the same circumstances. These distances are, however, variable. The
lamp burning normally, the distance generally amounted to 0.053
A.U. for D,, to 0.078 A.U. for D, for a point lying in the middle
of the are, when Sitrmens’ S A-carbons were used. It sometimes
occurred, however, for a certain pair of carbons that the distance
was much smaller, down to half the value; sometimes too that it
was much larger, up to almost double the said amount. When new

1) The results of the observations made about the components of the mereury
lines by the aid of Uns échelon spectroscope, were in agreement with those of
most of the other observers.

48*

722

earbons are set burning, the distance is also much larger than the
normal one, When the are hisses, the reverse takes place: the lines
erow fainter, and the distance grows smaller, in case of very decided
hissing they can even become entirely invisible. Also in different
places of the are the distance is different, for the negative carbon
the distance is much larger — about twice as large as a rule —
than for the positive carbon.

Between the two absorption maxima lies also a region of absorption,
which on the whole is of only little greater intensity than the
maxima of absorption. Now and then it makes the impression that
there are still more feeble maxima of absorption in this region; I
have, however, not been able to ascertain this with perfect certainty.

I could artificially modify the aspect of the absorption lines very
considerably by blowing a little soda mist into the are by means
of a tube placed parallel to the positive carbon, which lies horizontal ;
in order not to disturb the equilibrium of the are the blown in air
current had to be only very weak, while the quantity of sodium
could be modified by varying the concentration of the sodium
solution. It then appeared that always when soda was blown into
the are the distance of the components of the two D-lines increased,
these becoming vaguer at the same time. The greater the quantity
was of the soda that was blown in, the further the components
were split up, and the less sharp they became. This splitting up
could even reach an amount of about 0,3 A. U., in which case they
were, however, very vague. The splitting was always perfectly
symmetrical with respect to the original double absorption line. The
maxima of absorption were — for so far as perceptible — of equal
intensity, the sharpness of the two components also seeming pretty
well equal. | have not undertaken further quantitative measurements
about this, since if would have been impossible to determine the
quantity of sodium in the are, even when the velocity of supply
was known; at most this quantity could be very roughly estimated ;
nor was the phenomenon perfectly constant. Similar phenomena,
still less constant, however, were observed when carbons were used
which were soaked in a diluted solution of soda.

When the Woop tube is placed in the way of the rays of light
so that it follows the spectrometer, which cuts a small portion out
of the spectrum, so e.g. between object glass and eye-glass of the
reading glass, the absorption lines of the sodium vapour appear also
to be double, in which the distance of the components increases as
the temperature rises. At the same time, however, distinct phenomena
of anomalous dispersion are perceptible, as soon as the heating of

723

the tube takes place in a somewhat unsymmetrical way. For this
reason, and at the same time on account of the large differences of
temperature which must necessarily exist in the Woop tube, at
which there can be no question of saturate vapour, I did not under-
take quantitative measurements.

Finally in order to be able to carry out measurements which
should be liable to interpretation, | have generated the sodium vapour
in a vertical glass tube, which was first provided with some pieces
of. sodium, then evacuated down to about O.OOL m.m. of mercury,
and sealed to. This tube was uniformly heated all over its length
by an electrical way, so that the temperature may be assumed to
be the same at all places, and accordingly the sodium vapour to be
saturate. In the enclosure there were made two apertures, through
which the light fell in horizontal direction. As the glass gradually
clouded somewhat at these places, | later on applied side tubes which
were also electrically heated, while a wider glass tube was also
used. The bore of the tube, with which | carried out my final
measurements, amounted to 28 mm. For a reason to be stated later,
this tube was placed between object glass and eyeglass of the reading
glass. Of course the image suffered by this, but nevertheless it was
possible to measure the distances of the components.

The pbenomena which I observed in this way were qualitatively
in perfect harmony with what I had seen by means of Woop’s tube.
and during the blowing in of the soda mist into the are. On vise of
temperature the distance of the components increases, while they
become less sharp at the same time. Up to almost 300° the distance
can be very well measured, the vesults of these measurements have
been represented in the curves D, and PD,. At higher temperature
the width is too large to be investigated by means of the échelon
spectroscope, the phenomenon becoming very vague then, so that
the absorption maxima are clearly perceptible on slight magnitication
only, the light intensity is only little greater then between the absorption
maxima than in the maxima themselves. The greatest width measu-
red amounts to about 0,21 A.U., as is visible from the figure.
The resolution is always greater for D, than for D,; the curves
indicating the course in the two cases run perfectly parallel. On
the whole the components of D, are somewhat sharper than those
of D,; of D, the component lying to the side of the red is the
stronger and sharper, of D,, that which lies to the side of the violet.
I think I have been able to observe with pretty great certainty that
the two components of D, are each double, so that the absorption
region would be bounded here by two absorption maxima on either

724

0.05

°
200° 250

side, which can be distinguished from each other with difficulty. I
have not been able to observe anything similar for D,, there the -
absorption maxima seemed single to me. At 274° I found about
0.035 A.U. for the distance of the two absorption maxima, of which
each component of D, consists, at 290° about 0,045 A.U. The dis: -
tances of the components of YD, indicated in the figure refer to the
extreme components. The region lying between the absorption maxima ~
situated on either side is on the whole of uniform intensity, whieh, .
chiefly at tbe higher temperatures, is but very little greater than ,
that of the absorption maxima. Whether there are still more faint
maxima in this region, I have not been able to observe with certainty,
though | now and then got the impression that such was, indeed,
the case,

725

In the figure IT have also indicated the mean amount of the width
of the region of the are absorption by means of short dotted lines.
Further the curve indicated by p denotes the vapour tension of the
sodium vapour for the temperature in question. The scale of the
ordinates on the right hand side of the figure refers to this curve.
For the determination of this curve I made use of KRONER’S ') research
on the vapour tension of alkalimetals ; for this it was necessary to
extrapolate the values found by Kroner, for which purpose I used
Graitz’s”) formula, which is formed from Dupré-Herrz’s *) formula
based on that of CLapnyron by assuming the validity of Van pmr
Waats’s law for the vapour instead of that of Borne-Gay Lussac.
Grairz’s formula

ap n

p-e T — kT—™e GE

containing four constants, | had to assume four points of the vapour
tension curve. | took three points for them, which had been directly
determined for sodium by Kronur, viz. 7= 693, p=2.00 ; T= 733,
p = 420; T= 773, p= 8.64 (temperatures in absolute scale, pres-
sures in m.m. of mercury). I derived the fourth point, availing myself
of Ramsay and Youne’s rule, from Kronur’s determinations for pot-
assium and found for it 7’= 589, p=0.11. I found from this for
the constants using Brice’s logarithms, «@ = 28.877, log k = 164.88,
m = 48.748, n = 18148. By the aid of these constants I calculated
the values of p given in the figure.

One might be inclined to ascribe the observed phenomena to ano-
malous dispersion ; the observed dark lines would then be no absorp-
tion lines proper, but “dispersion lines”. If this were actually the
ease, tie light of the considered wave length would only have
changed its direction, without having undergone absorption. As to
the absorption lines in the light are, taking the comparatively small
value of the anomalous dispersion at the densities in question into
consideration, the point of intersection of the rays of light coming
from the are with the plane of the spectrometer slit could never be
far distant from the crater image. When this image is moved over
the plane of the slit we should therefore have to see light lines in
some positions instead of dark ones. As I have never observed
anything like this, not when I placed the are lamp in other positions

1) A. Kroner. Ann. der Phys. 40. p. 438. 1913.
2) Grirz. Zeitschr. f. Math. u. Phys. 49 p. 289. 1903.
8) Herrz Wied. Ann. 17. p. 177. 1882.
Dupré. Théorie mécanique de la chaleur. p. 69. Paris 1862.

726

either, so that the direction of the issuing beam of light with respect
io the light are was a quite different one, I think I may conclude
that the are lines are not to be attributed to anomalous dispersion.

Nor can for analogous reasons this be the ease with the lines
which were observed after the light’ had passed through sodium
vapour in a uniformly heated glass tube. Here too light lines would
have to be observed at some distance from the dark ones, of which
there was however, no question.

On the other hand — as I already remarked just now — when
the unsymmetrically heated Woop tube was used, I saw a sharp
light line by the side of the dark region, which latter became
blacker then at the same time; in fact besides the absorbed light,
also the anomalously dispersed light has vanished from this region.

Everything considered I am therefore of opinion that anomalous
dispersion has had no influence on my final results.

I will mention here another phenomenon, which at first made its
influence felt in a peculiar way. In my first experiments I had
placed the glass tubes in which the sodium vapour was generated,
before the entrance slit of the spectrometer, so that the whole beam
of white light passed through it. The measurements which I then
made of the distances of the components for different tubes, which
were distinguished by the thickness of the radiated layer of vapour,
were not in harmony; at the same temperature the distance of the
components was found larger as the radiated layer was thicker.
This peculiar phenomenon must undoubtedly be a consequence of
the presence of fluorescence light, which the sodium emits under
the influence of the incident white light. According to Woop’s
researches!) it is just the two D-lines which are very prominent
in the fluorescence light. This light will be the stronger as the
traversed layer is thicker. In this way it is explicable that the
absorption spectrum can be subjected to a modification which will
become greater with increasing thickness of layer.

When, however, the distance of the absorption maxima increases
in consequence of the superposition of the fluorescence light over
the absorption spectrum, which is greatly the case at higher tempe-
ratures (see the curves (D,)' and (D,)'), it is easy to see that the
maximum, resp. the maxima, of the fluorescence light must be
situated between the absorption maxima so that the curve representing
the intensity of the fluorescence light, exhibits a rise at the place
of the absorption maxima, when we move to a point lying halfway

1) R. W. Woop. Phys. Opt. p. 444; 1905,

727

between the two absorption maxima, If the absorption maxima
coincided with maxima of fluorescence, the former wouid either not
shift their places, or they would split up. Hence we arrive at the
conclusion that at temperatures above about 260° the maxima of
absorption do not coincide with maxima of fluorescence, but that
the latter maxima, resp. maximum, lie between the maxima of
absorption,

I have indicated two curves in the figure for which the influence
of the fluorescence light is visible, the curves (),)' and (D,)'. They
represent the distance of the components of D, and D, fora radiated
thickness of layer of 40 m.m., in which the tube of sodium vapour
was placed before the entrance slit of the spectrometer: the distance
from the tube to the sht was about 10 em., the opening of the
incident beam being about L : 10. Under these circumstances it was
also possible to observe the fluorescence light by means of a spectroscope.

If the tube with sodium vapour was placed between object glass
and eye glass of the reading glass, the fluorescence can only be
brought about by the light that belongs to the narrow spectral range,
issuing from the spectrometer, instead of through the undivided
white light. It is easy to see that the part of the fluorescence
light, which in this case is already very faint, the part that
finally reaches the retina, will have to be exceedingly small
in comparison with the observed light; the influence of the
fluorescence light will, therefore, have to be imperceptible then. I
have actually convinced myself that when the tube with vapour is
placed between object glass and eye glass of the reading glass the
distance of the absorption maxima is independent of the thickness
of layer traversed by the rays. For this purpose I compared a tube
of 50 m.m. bore with the tube of 28 m.m. used for the measurements ;
in these two cases the distance of the components was the same at
the same temperature.

I think myself justified in drawing the conclusion from all that
has been observed that the distance of the absorption maxima of
the sodium limes is closely connected with the density of the vapour,
and that in this way that the splitting up increases with increasing
density. That what has been observed is chiefly an effect of density,
aud not in the first place a temperature effect, is supported by the
fact that the influence of the soda mist blown into the are is for
the greater part the same as that of absorbing sodium vapour of
much lower temperature. The temperature at which the absorption
in the are takes place, will namely undoubtedly be much higher
than that of the vapour in the glass tube. On the other hand the

phenomenon in the are is dependent in a high degree on the quantity
of soda, the temperature varying very little as long as the equilibrium
in the light are is not disturbed.

In my opinion besides the density also the temperature can have
influence, though the latter will be slight. If the are lines were
exclusively dependent on the density of the vapour in the are, the
horizontal dotted lines in the figure would have to cut the curves
for D, and D, in points for which the abscissae are equal. As this
seems to be almost the case, the influence of the temperature cannot
be very large.

Also with regard to the degree of the absorption —- so the value
of the absorption index —, there can very well be difference between

higher and lower temperatures; I have, however, not examined this.
And at last, the absorption lines of low temperature are somewhat
sharper than those in the light are.

Returning to what Miss v. Usiscu derived from her experiments,
viz. a displacement of the absorption maxima of sodium vapour on
change of temperature, we may question whether this result can be
brought into connection with the observations described just now.

In the experiments under consideration the main point was the
absorption to which the components of the two magnetically split
sodium lines (briefly called ZeEMAN-components) were subjected in
the Woop tube filled with sodium vapour.

The measurements were made of the relative intensities of the
differently polarized beams of light both normal to the lines of force
of the magnetic field (transversal), and in the direction of the lines
of force (longitudinal) (in the transversal observations the beams
polarized parallel to and normal to the lines of force, in the longi-
tudinal observations both the circularly polarized ones.) These beams
of light were emitted by a sodium flame which was placed between
the poles of a magnet: the undispersed sodium light was subjected
to absorption in a Woop tube. This tube was every time heated to
a definite temperature, and the temperature being kept constant,
the magnetic field was varied till the difference of the intensities
of the differently polarized beams of light was a maximum; this
measurement took place by rotation of a glass plate, which served
as a compensator. For every temperature of the Woop tube the field
was determined, in which the difference of the intensities became a
maximum. Miss v. Usisch makes the supposition that this difference
will be a maximum when one ZeeMAN-component coincides with the
maximum of absorption, and the other is not absorbed at all. By the
aid of this the writer deduces that at 270° the displacement of the

729
°
sodium lines would amount to 0.47 A.U.; im this ease the differe2&e
of the intensities was therefore a maximum at a distance of the

ZEEMAN-components or on an average 0.34 AU.

Now on closer consideration it is clear that the correct interpreta-
tion of Miss v. Usiscn’s observations would be very intricate,
and many more data would have to be available for it. In the
first place we should have to know the correct distances and
intensities of the Zenman-components, before they undergo absorption
in the Woop tube; further the accurate course of the curve that
denotes the connection between the intensity of the lhght transmitted
in this tube with the wave length, should be known. The absorption
maxima of sodium vapour not being sharply defined lines, much
will depend on the intensity and sharpness of these maxima; this
is the more obvious when it is borne in mind that the real maxi-
mum difference of intensity observed by Miss v. Usiscn, constitutes
only a few percentages of the whole amount. With so small a
difference we should be sooner inclined to assume a difference
in absorption to that amount than as the author does, suppose
that one ZeEMAN-component is not weakened at all, the other
only a few percentages in the case of a thickness of layer which
is at any rate pretty considerable. It is easy to imagine cases in
which the absorption maxima are of equal intensity, but difference
of intensity of the ZeeMAN-components is a maximum, when they lie
outside the absorption maxima.

Everything considered the amount given by the author can only
represent the distance of the absorption maxima as far as the order
of magnitude is concerned; accordingly I do not think that the
result of my observations (distance of the absorption maxima of
about 0.15 A.U. at 270°) is in contradiction with that of Miss v.
Uniscu.

Besides it is possible that the temperature has not been given
perfectly accurately. In this respect a Woop tube presents more
sources of errors than the uniformly heated tube which I used.
Moreover the difference need. not be very great, taking the very
rapid inerease of the resolution in the neighbourhood of 300° into
consideration.

When seeking an explanation of the observed phenomena now that
it has appeared that in the first place there is here question of a
density effect, we are naturally led to look for a connection with
the widening of spectrum lines in general, and with the explanation
which Stark has given for it, which comes to this that this widening

730

would be the consequence of electrical resolutions of the spectrum
lines. It is easy to understand that the greater the density of an
(emitting or absorbing) gas, the more frequently it will oecur that
the vibrating electron systems are in the neighbourhood of electric-
ally charged systems, and will therefore perform their vibrations
under the influence of the electric field of these charged systems ;
hence the spectrum lines brought about by these vibrations will be
the more perceptible by the side of those which arise from systems
whieh do not vibrate in an electrical field. In this way we shall be
able to obtain a great number of lines, which all being superposed,
can make the impression of a broad band. It is very well
possible that definite groups of these vibrations can be predominant
which will give rise to the appearance of maxima of absorption
(resp. emission). If we wanted to give further particulars about this,
it would be necessary to enter into an examination of the mechanism
of the phenomena *).

As to the order of magnitude of the above described phenomena,
it is indeed interesting to compare it with the order of magnitude
of the electrical resolutions as Stark has observed them. When we
assume that a vibrating system is placed in an electrical field origi-
nating from an electrical elementary charge at such a distance as
the mean distance of the atoms in saturate sodium vapour of about
280° amounts to, the resolution of the D-lines, when taken as an
electrical resolution, would at this temperature agree as far as
ihe order of magnitude is concerned — with the resolutions whieh
Srark found in this part of the spectrum, always on the supposition
of a linear course of the electrical resolution with the intensity of
the field.

Above 260° the observed resolution increases pretty accurately

with the power ?/, of the density, the increase being slower at the
lower temperatures ; therefore what was observed just now about
the order of magnitude of the resolution at 280° cannot possibly
be of general validity, as this would require an increase not with
the power */,, but with the power */, of the density.

I also observed the D-lines in the solar spectrum, which also
exhibited two components each. On the whole the phenomenon was
in accordance with what is observed for saturate sodium vapour of
about 270°. The distance of the components was about 0.15 Nae

1) Even without thinking of electrical resolutions, | pronounced the opinion
already before that the “own period” of a vibrating system might vary as
it was under the influence of neighbouring systems, and that widenings of spectrum
lines might be the consequence of this. Cf, G. J. Extras, Diss. Utrechit; p. 146 et seq.

731

I did not however carry out accurate measurements about this. They
further seemed to me slightly less sharp than those whieh were
observed for sodium vapour of low temperature, though this difference
Was not very conspicuous. If the resolution were really only little
dependent on the temperature and possible other factors, we might
draw the conclusion from this that the density of the sodium vapour
in the chromosphere of the sun is as great as that of saturate sodium
vapour of about 270°.

I further made some observations on the emission lines of sodium
vapour. For this purpose I used a glass discharge tube which con-
tained some sodium, and which was heated to 200° or 200°.

It then appeared that. the emission lines, both D, and D,, were
double, and that the distance of the two light lines increased with
increasing temperature. It is not impossible that self-reversal plays
a part in this; it was, however, peculiar in this that chiefly for D,,
the two light lines on either side of the dark core differed in intensity,
which would not have to be the case for self-reversal.

With regard to the emission lines D, and D, Micnetson ') has
pronounced the opinion that they would each consist of four com-
ponents, {wo intenser ones, and two very faint ones, the distance
of the intenser ones amounting to about 0.15 A.U. Fapry and Pxror’)
are, however, of opinion, that reversal phenomena would play the
principal part in this.

In conclusion I will still state that already a long time ago I
observed for the emission lines of copper when this is in the light
are, resolutions of entirely the same order of magnitude as those
which I have now described for the absorption lines D, and D, of
the sodium, also with the aid of the échelon spectroscope. I then
observed with a pretty high degree of certainty that these resolutions
were greater as the density of the copper in the are increased. I
could not carry out measurements about this, however, as the amount
of the resolution was very variable, and besides I had no means to
determine the density of the copper in the are.

Haarlem, February-April 1914. Physical Laboratory
of ‘“Tryier’s Stichting.”

1) A. A. MicHELson and E. W. Moriey. Amer. J. (3) 34. p. 427; 1887. Phil.
Mag. (5) 24 p. 463. 1887.

A. A. Micnetson. Rep. Brit. Ass. 1892 p. 170. Phil. Mag. (5) 34 p. 280. 1802.

2) Gu. Fasry and A. Piror. CG. R. 180 p. 653. 1900.

Physics. -— ‘On the lowering of the freezing point in consequence
of an elastic deformation.” By Dr. G. J. Extas. (Communicated

by Prof. H. A. Lorenz).

(Communicated in the meeting of May 30, 1914).

A number of years ago E. Riecky ') derived from thermodynamic
considerations that a solid body subjected te forces which bring
about an extension or Compression, will in general exhibit a lowering
of the freezing point, also at those places of the surface where no
deformative forces are directly active.

This case may be extended to that of an arbitrarily deformed body.

J. Let the free energy per unity of mass be w, and the density @,
then the total free energy of a certain system will amount to

v= [ewe eer mol cme 0 (Il)

in whieh the integration must be extended over all the material
elements 9.dt. Further we make no suppositions at all on the state
of the system.

Let us suppose the system to undergo an infinitely small deform-
ation at constant temperature. We can always assume this deform-
ation to consist of the infinitely small dilatations «,, y,, 2:, and the
distortions y-, 2,2), for whieh the well-known relations hold:

0g uy 17205
oa) i ars
One mnOS 0s § &: Ox ena 2)
i oa aaa Pea eee a Taee ek IS,

when §,,§ denote the infinitely small displacements of the points
of the system.
In consequence of this deformation the free energy of the material

element odr will increase by the amount

Ow Ow 0 ow Ow Ow
o dt & &y, + ue Yy + wid Ze+ oe yz + - zs fe + eM vy) > (63)

Oar,

On the other hand work has been done by the external forces.
When the components of the joint volume forees which act on the

1) E. Riecke, Wied, Ann. 54 p. 731. 1895,

733

material element odrt are @ Ndr, 9 Vdr, and er, and the components
of the joint external tensions which act on the surface elements do
of the surface that bounds the system: p.do, p,de, and p.do, the
total work of the external forces, the displacements being §, 9, ¢ will
amount to

JA = | o (X§ + Ya + 26) dr + | (px S + Pyy + pz) do (4)
Now when the temperature is constant
Ovi — 0 Ame gua 5 o o ee (6)

holds generally as condition of equilibrium.
Hence we derive from (3), (4), and (5):

~ /fdw ; Ow Ow Ow Ou Op >
ty -- Y= = Oe als es WE | Se ed nS Ly
fe sae Rae Oly Ty 0z- 1 Oy J 022 du, r)

. 7 » (6)
= fe (X§ + Yo + 26) dr +f (pis + Pyy + p2S) do \

—

Making use of the relations (2) we get from this after partial
integration :

aT We b dw 2 Ow f
il E — cos (Nie) + a cos (Ny) + - cos (Nz) | +
7) vy vz
0 Ou 0
+ 4 be cos (Na) + a cos (Ny) + = cos (Nz) | +
+6 an s (Nz) = cos (Ny) + cos (Nz) |. o do —
ey 0z-
| Ow ) ’ )
\o a Tea eo ee ee
S iipen: ~ 02x, » Ox, > 0x2) } ° Our (7)
- (|e) ep ee Te, a
ie Oa Oy Oz Boe E Ou
0 ) 1D) dus 5)
0 * 0 a | \o o ot dlo ay
zt - OYy ts ME | Lg A 3 Oz, J = 2 Ozy
Oa Oz ee | Ow a Oy a
r ost
ae rae dt =foxs + Yy +Z8)dr +f + pyy + pz$) do |

The quantities §, 1, and ¢ for the different points of the system
being quite independent of each other, we obtain from (7) the relations;

734

yr — ae ‘0s (Nix) - a) 2 _ Ny pi) 10s (Nz | al
Px 0 Ves a ( ‘ ) + ary s (i y) + yaa Ss (: 2) == ()
Oxp Ow Ow
Dy — 0 yoy cos (Na) 4- 2d cos (Ny) + ae cos (| =I) (8)
: 1Oy» Oy Oyz
Oy 0 p ow f
». -- 0 \—— cos (Ne) - — cos (Ny) -- — cos (Nz)) =0 %
pee |ge em (Ne) + Gr em (NE Gee ON | 0
Ow a) ow
uM. Nilaeeat
: ) (c =) ¢ (¢ in 0 (¢ =| ae
Sees nee ei
‘ Ow Ow Oxp
68) (2) | a
OY x U Se WEA ae \ . 0 5 )
ae On : Oy + Zz are
dy dy dup
e Y (3) ; : (e3) ‘ (e5) ee
ib Sar | iy Oe ae

If we now introduce the internal tensions Vz, Yy, Ze Y=, Zr, My;
usual in the theory of elasticity, then hold for the components of
these tensions on an element of the surface:

tye ole ee
¥ v= Y,eos (Nx) -+ Yycos(Ny) + Y= eos(Nz) i .. (10)
ZN = Z, cos (Nx) + 4, cos(Ny) + Zz (cos (Nz)
Further in ease of equilibrium :
pz + Xv=0 pik Yn ==0 2+ Zn =0.
From (8), (10), and (411) Follower

ow Ow Ow
Le = —_ a Wf, — Sie Z: = —
Pees y Q dy, 2 Oz, |
F a ‘eae
Me — Ly = —@ ui Lx = XxX: — ae Xy = Vx ae oo |
A Oy: 2x ay |

The relations (12) introduced into (9) now yield the equations

ya Ok, Oy 0%:

Ow Oy Oz

ig Oy Oi.
—— = -f es

Ow Oy Oz
ae 0Z, d0Z, , 024,

y (13)

REL re Pale:

the known conditions of equilibrium for a deformed system,

735

2. If we now consider a material element which ean be arbi-
trarily deformed, we can subject its state to an infinitely small
variation. With respect to the deformation this. variation. will be
determined by six mutually independent quantities, three dilatations,
which determine the change of volume, and three, which determine
the change of form. Hence speaking thermodynamieally, the Variation
of state of this element (which need not necessarily be infinitely
small, provided it is to be considered as homogeneously deformed)
is determined besides by the temperature, by six mutually independ-
ent quantities. It now follows from (3) and (12) that for a virtual

isothermal variation of siaie the following equation will hold for
the unity of mass
1 E r r Yr : z oa
dy = — 33 (Xcae + Vy Yyt Beez + Veyst+ Zpza+Xyty) .. (14)
U -

If we now start from the unity of volume, and eall the free
enerey of it yr, the following form holds for it
dy! = — (Anez Vy Yy eee Vaya t Duta + Xyity).-, < ~ (15)
(In this it should be borne in mind. that after the variation the
volume will in general be no longer equal to unity).
Now :
ow
ue)
holds generally for the free energy on change of temperature, when
in the expression for the external work with an infinitely small
variation no -term with JZ’ occurs as factor.
Hence:

STMT e Aiton ie Yaya ete. coe (GU)

ae
diy - (Xawx-+ Yyyy+ 2222+ Veyz4+ 2x2 + Xyxy) — dT. (17)

holds. for virtual variations of state, in which also the temperature
can undergo a change.
When we start, from unity..of volame, we have

dp! = — (Kyte Vy yyjt 4222 is Yeyz+Zyz¢ Xyhy) —7dT. (18)

where 7 represents. the entropy of the unity. of volume.

3. Let us now consider a system consisting of two phases, a
liquid and a solid state. We assume the system to be at rest. Let it
further as a whole be subjected to the hydrostatic pressure p, while
arbitrary deformative forces can be active on the surface’ of the
solid phase, with the exception of that part that is in contact with
the liquid phase; we exclude volume forces. Consequently the same

Proceedings Royal Acad. Amsterdam, Vol. XVIL.

736

hydrostatic pressure will prevail everywhere in the liquid. We direct
our attention to a part of the system that contains a portion of the
boundary plane between the solid and the liquid phase. We assume
the surface that bounds the considered part of the system, for so
far as it falls inside the solid phase, to be invariable of position,
whereas we can subject it to variations of form for so far as it
falls inside the liquid phase. On this latter part acts then everywhere
the vertically directed hydrostatic pressure p. We take the part of
the solid phase that falls inside the considered part of the system,
as homogeneously deformed.

Let the considered part of the system contain m, unities of mass
of the solid phase, m, unities of mass of the liquid phase. The
direction of the normal to the boundary plane, which points from
the solid towards the liquid phase, may be called J.

For the part of the system in question are the free energy, the
mass, and the volume resp. :

y=m, p, + m, fp, |
M=m, + m, \ erreprerme ime ge (1149)

V = my», + mv,

when v, and v, represent resp. the volume of the unity of mass
of the solid and the liquid phase.

We now subject this part of the system to a virtual change. For
this purpose we make a small quantity of one phase pass into the
other at constant temperature. This will be attended with a change
of the total volume of the considered part of the system. In virtue
of the suppositions made above this change of volume can only take
place through the change of position of that part of the surface
bounding the considered part of the system, which lies in the liquid
phase. For the rest the state of the liquid phase will not change.
In order to keep also the solid phase in the same state, to leave
the quantities determining the deformation unchanged, it will be
necessary, to make the tensions of the part of the boundary surface
of the considered part of the system lying inside the solid phase
undergo intinitesimal variations. Since this part of the boundary
surface remains unchanged, no work will be required for this. The
only quantity of external work that we have to take into account,
will be that which is attended with the change of the part of the
boundary surface lying inside the liquid phase.

When dm, and dm, represent the changes of the quantities of the
two phases, then on account of (19), we shall have:

737

dw = yw, dm, -+ w, dm,
0= dm, + dm, ee ees (0)
SV =v,dm, + v,dm,

th connection with the above considerations the work done by
external forces amounts to:

dA = — pdbV = — p(v,dm, + v,dm,) . . . . (21)

If we now apply the condition of equilibrium (5), we obtain,
making use of (20) and (21),

Sat Peewee | Daten Pe els ve veh Jone ee (((2id)
This equation represents the condition of equilibrium for the two
phases in the case considered here.

4. Let us now imagine that the system consisting of the two
phases undergoes a real, infinitesimal change. The condition of
equilibrium (22) will then retain its validity. It is clear that it will
give us then a connection between the differentials of the variables.

As variables determining the state, we choose for the solid phase the
dilatations and distortions wz, v/y, Zz, yz, 2x, vy, besides the tempera-
ture 7, for the liquid phase the volume v and the temperature 7. We
ascribe the value zero to the variables xy, 7, 22, yz, 2x, and 2, in the state
from which we start (which, however, need not be without tension).
In order to be able to distinguish the difference between an eventually
ultimately reached final condition (which need not differ infinitely
little from the initial condition in mathematical sense) and the initial
condition from an actually infinitely small change of condition, we
shall ee the latter by dz,, dyy, dzz, dyz, dzz, day instead of by
®xy Yys 22) Yxx Fx» Ly, Which we shall use for the final condition that is
eventually to be reached. This does not alter the fact that the latter’
quantities are always treated as if they were infinitely small.

Proceeding in this way we obtain by differentiation from (22):

dw, dy, dup, cm Oy,
dT dity yt — dzz d bs poelle
or any pele sag. Urayee eg
(23)
Ow, Ow, i
4+ ain ty + pdv, + 0,dp = T OT te es dv, + pdv, + v,dp

a
. ia : eH &
In this ; dx, denotes the increase of the free energy y,, when
or
the initial state undergoes a dilatation diz ete., just at this was the
ease in (3) and the following formulae.
Now according to the theory of elasticity we have:

49%*

738

1
(y= ——— (Wa saeiy se Wa) os os 8 ¢ (24)
Syl
while further the well known relations:
Ow, Ow, be
aT tia eae ne

hold for the liquid phase.
On introduction of (12), (24), and (25) we get from (23).

a ae SEN ats |
(2],—4,) dT = ip( a >) ar [(Xa—p) dv ++ |

0. 1 Q, (26)
Se (Yy —p) dyy IF (2. —p) dzz + Y.dy: =e Zz x aI X dey]
We can now put:
r Ll
Uh = ’ (27)

T
-In this we ean call the “heat of melting” 7, by which that quantity
of heat is to be understood which must be added to convert the
unity of mass from the solid to the liquid phase, without the con-
dition of the two phases changing for the rest. We then get:
abe iy ibe ck Ths
aT = —|-— —— |} dp + —— [(.— >) dz, --(%—p) aay
TIO (28)
+ (4:—p) dzz + VYzdy. + 4,dzz + X,da,|
When the only deformative force is the hydrostatic pressure, we
get the known formula of Tuomson and Crausius, since then the
following equations generally hold:
Xx — p=0 iy —p=0 Z.—p=0 |

N2 Sy

29
Y.=0 Z,—=0 x Oe ee)
Tefal 1
dT = — (= ~ da ere (3X0)
7 \Os 01
If on the other hand dp = 0, we get:
dT = —— [(X.—p) dre + (Yy—p) dy + (Zp) dee + |
Pre Or (31)
+ Y.dy. + Z,dz, + X,dxy| |

Since the form between square brackets, provided with the negative
sign, represents the work performed in the deformative forces, with
the exception of the pressure p, a deformation will bring about a
lowering of the freezing point, when this work is positive.

5. We shall now assume that the initial state (for which we put
Vay Yyy Zz Yzs 22, ty. EQual to zero) is to be considered as without

739

tension. In this case (81) will also be applicable; we may then,
however, replace 7 and e, by 7, and o9,,, in which 7, denotes the
heat of melting, and o0,, the density of the solid phase in the tension-

less state; then we have

Tt
dT = —— [(Xs—p) dts + (Yy—p) dyy + (Z—p) de. +|

PP 10

ro
+ Y.dyz + Zdzz + X,day]

If we disregard quantities of the second order, which we are
allowed to do when we consider the dilatations and distortions
as infinitely small, we can integrate (32), placing 7, r,, and @,,
outside the integral sign. We then get for the lowering of the freezing
point in the state determined by @z, Wy. Zz, Yes Za Vy,

T
PQ r0

Uz «ae
f (eo ie ae eae

AL =
0

(33)

Y.dyz =F Z,dzz + X,da|

The heat of melting in the state determined by 2,, yy, 2:. Ys, Zr, dy
will differ- from that in the tensionless state by an amount that is
of the same order as the dilatations and distortions themselves. For
an infinitely small change follows for the change of the free energy
from (14):

1
dy = — — (Xzdxx + Yydyy + Z.dzz + Y.dyz + Zydzz + X,day)
o 7 :

Hence the difference in free energy between the deformative and
the tensionless state amounts to:

HAS exo IES Do

all
sh = =! — [Xzdxy 4+ Yydyy + Zdzz + V.dyz + Zrdzz + X,da,].
0 ye,
0

For the difference in entropy between these states follows then
from (16)

Te ceo Pick
0 28
Ay = at [Xzdaz + Vydy, + Z.dzz + Yzdy: + Zrdzez + X,de,].
(sae

From (27) follows then for the difference in heat of melting:

ditty Cis Eno
6) fll
Ar = — T— {= [Xida,z-++ VY dy,4 Zdzz+ Y.dyz+ Zyde,+ Xydx,| (34)
or Q k :
0

740

This will also apply to the case that the initial state is not
tensionless; only (384) does not represent then the difference in

melting heat between the state v,...yz... and the tensionless state,
but the difference between the state a,...y:z... and the initial state,

which is not tensionless in this case.

6. Let us now suppose that forees act on the surface of the
solid phase which are exerted by solid bodies which rest on the
solid phase, and in consequence of the presence of which the sur-
face of the phase is not in contact with the liquid phase. We can
then imagine that a small part of the solid phase that is in contact
with the solid bodies which exert forces, is converted to the liquid
state, without the solid bodies changing their places. For this case
we can again draw up the condition of equilibrium.

We take the boundary plane of the solid phase as X Y-plane, and
suppose that the Z-axis is the normal to this plane which is directed
from the solid to the liquid phase. For the total free energy, the
mass, and the volume the following relations hold in this case:

Y—m, yp, +m, wp,
M=m, +m, Mier. tc. « (23);
V=m,v, + m, »,

Let now an infinitely small quantity of the solid phase be con-
verted to the liquid phase, then:
JE = mdw, + w,dm, + mdi, + ,dm, . . . (36)
During the conversion the volumes v, and v, will have to change,
as the total volume remains constant, as we supposed. The considered
change being a virtual change, we may assume that as far as the
solid phase is concerned, this change is brought about by variation
of z- alone. Then we get:

Ow,

OU —— 20220 3 os 9 5)
Further :

ge Ou, ; ae

Cae carrag Nes SCCM IEON IO 5 1 ici « ((ic\)

By introduction of (87) and (88) into (86) we get:

he Op, dw,

OF =m, au diz 3M; Fatt dv, + dm, + w,dm, . . (39)

Just as before (see above under 3) the tensions at the surface that
bounds tne considered part of the system will have to vary now
too. We supposed, however, that this surface does not change its

741

position, so that no work will be done by external forces. The
condition of equilibrium is now:

Oui Qe eters tae e.g | (A)

We must use here the double sign seeing that there is only a
conversion possible in one direction. The sign = will hold for the
boundary equilibrium, i.e. the equilibrium at which a transition from
the solid to the liquid phase will just be possible. Now the equations
(35) give further ve

dm, + dm, = 0

: 41
m, dv, + v,dm, + m,dv, + v,dm, = 0 ( y
in addition we have
1
OSS = Uae on 0 ro (IBF
Qe; An :

If we limit ourselves to the boundary equilibrium we get from

(12), (85). (89), (40), (41) and (42) making use of the equation
Z, — p= 0*. i faliQet os? Soi
Wit Pepe tpl, «= = |S 5 lee)

Hence we get the same relation as condition of equilibrium between
solid and liquid phase as we had for the case that the two phases
were in contact. Therefore the conclusions about the lowering of
the freezing point will also be the same. Of course as pressure on
the solid phase must then be taken into account the hydrostatic
pressure, to which must be added that which is exerted by the
solid bodies which are on the solid phase.

7. We shall now consider more closely the amount of the lowering
of the freezing point, in which we shall make use of the expres-
sion (32). To caleulate this amount it is necessary to know the
relation between the quantities x... y:...andthe tensions X,... Y....
In the most general case, the quantities 2... y:... being considered
as infinitely small quantities, we shall be allowed to assume a
linear relation of the form:

Xx S Oy, @e + Oy gYy F Oy ,%z FO Yo Ah Gyytz + yy ity

: me ae a : : (45)
Ve yy + Oy yy + Gy,22 + Oy Ye FOyee Qo hy
in which
Pia Ge fe Ss ee (AG)
will generally hold, because the tensions X,... ¥.... according to

(8) may be considered as the partial differential quotients of the free

742

energy per unity of volume taken with the negative sign. Further
the coeflicients «@ must be considered as functions of the temperature.
To this most general case, in which the number of coetficients amounts
io 21, answers a crystal of the lowest symmetry. This leads, of course,
to very intricate calculations. ‘

We prefer, therefore, to consider the simplest case, viz. an isotropous
body. For this holds, if we use the prevalent notation ’).

— ale lee is BX (vx a Yy + z 2) (47)
Seas ae ity, :
from which equations can be derived ;
sear six z gr YA
ot Se eke ae Sa C2 + y »||
Y,=— —YV,
K
In this the relation :
136;
a es
“7420 ae

exists between the coefticients AK and @ on one side and the elasticity
coefficient / on the other side. -

Let us now consider a circular cylinder, the axis of which coin-
cides with the Z-axis. Let one end be rigidly fastened, while forees
resp. couples act on the other. Let the length in the direction of
the Z-axis be /, and the radius of the cylinder &. The conditions
of this problem may be satisfied by putting oo

Xp == xy == () Y,—=09 merely seni, 11,1 (240)!

If P,, Py, P; ave the components of the force, Qe, Q,, Q, the com-
ponents of the couple acting on the end plane, then for the other
tensions hold the expressions :

3s sy * PP. 86) (R2—2x)—y? - P, 1446
5 Px (8 +89) ( eee ay EM

aR* | 2k 1436 Ri1430°
age 2Q..%@ b, 1446 P, (8+ 84) ( (R?—y* ice =i
“" @R! 2R1+30 oa peat 538
Further :

_ 3) Cf. among others G, Kircurorr, Vorlesungen tiber Mechanik,

143
ip 0 ape ea ez -
126
E1260
See Ie re (52)
21430
E1+26
Fico eile Ys

We shall now discuss some special cases.
1. Compression resp. extension.
In this only P:=£0 is put, from which follows :
La Pe Ne SS)
aR?
(in this the liquid pressure p is neglected).
Then the lowering of the freezing point is

it
AT =— [ete
7,0

oso

Making use of (52) and carrying out the integration, we get :
tee

si OF
7.0, 2h

AT = —

which formula is in perfect concordance with Rinckw’s. *)

We apply this to ice, which we shall treat as an isotropous
substance.

RieckE assumes 0,7 ke. for the drawing-solidity of ice per mm’, and
calculates with this O°.017 for AT. As for most substances the
_pressing-solidity is considerably greater than the drawing-solidity, this
diminution can probably be made larger in the case of compression,
so that it can be measured comparatively easily and with suitable
apparatus even the just mentioned lowering of the freezing point
would also be liable to be measured.

2. Sagging.

In this case we only assume that P,==0. When we consider a
point for which «= Rk, y = 0, then it follows from the formulae that :

Py 1420

i) =) Ve é
ah? 1+-30

The lowering of the freezing point of the considered point is:

1) E. Rirexeg, loc. cit. p. 7386 form. (20),

744
Making use of (52) we get after integration :

T +30 Y#
TRo, 15208 Sa

In order to obtain a limiting value for Y., we make use of the
results of an investigation by Hess’) on. the sagging of ice
erystals. He charged a crystal 2.9 em long, 1.0 em broad, and 1,2 em
thick at its end with a weight of 5000 grams, without rupture taking
place. Let us assume by approximation that an ice cylinder of a
diameter of 1 em could bear the same load. We can then derive a
limiting value of VY. from (54).

If we introduce this into (52), we find finally, assuming that 0 = 3,
which is about correct for a great many substances, — 1.19 x 10-4 —
degree for AZ, which quantity is probably not lable to measure-
ment. That this quantity is so small, is the consequence of the sinall
value of the maximum tangential tensions which ice can bear.

We considered the point on the circumference for which «= R,
y=0. If on the other hand we take the point for which w= 0,
y= Rk, we get the formulae

Yin =
ak?

Py Mos Wa =O,

If as before, we again assume that an ice cylinder of a diameter
of 1 em. can bear a load of 5000 grams at its end, we find for Z,
a value which appears to be greater than the value assumed ‘by
Riecke. If we calculate the lowering of the freezing point by means ,
of this, we find 4 7’—= — 0°.081, an amount that can be easily measured.

We see at the same time that the lowering of the freezing point
has different values at different points of the surface; a state of
equilibrium is therefore impossible. The rod of ice will diminish on
the upper surface and on the lower surface, and that much more
quickly than on the sides, which will also diminish a little. Further
this diminution will increase towards the end where the rod is loaded.

3. Torsion.

In this case only Q-—|—0. From the formulae (51) follows then
for the point 2=0, y= &

2Q.

Viet) x, = — 3
aR

Taking the small amount of the tangential tensions which ice can

1) H. Hess Ann. d. Phys. 8 p. 405, 1902,

745

bear into consideration, the lowering of the freezing point will again
become very small in this case. Since the tangential tension all along
the cylinder surface has the same value, equilibrium with the sur-
rounding liquid will now be possible.

Haarlem, May 1914 Physical Laboratory of
“Tryier’s Stichting’.

Physics. — “The effect of magnetisation of the electrodes on the
electromotive force.’ By Dr, G. J. Er1as. (Communicated by
Prof. H. A. Lorentz).

(Communicated in the meeting of June 27, 1914).

1. The question in how far magnetisation of the electrodes is of
influence on the electromotive force in a circuit in which there are
electrolytes, has already often been examined, without it being
possible to derive a definite answer to this question from the results
of these researches. Thus Gross') found no definite direction of the
current in concentrated solutions of ferro salts, while in concentrated
solutions of ferri salts the magnetized electrode (both electrodes
consisted of iron) became the anode. ANDREWS”) arrived at the same
result working with strong acids as electrolytes. NicHois and FRANKLIN *)
obtained results which were in concordance with those of Gross
and ANbDREWs, in case a pole of a magnetized iron rod came in
contact with the electrolyte, which consisted of a solution of chromic
acid. In this case the electromotive force greatly increased with the
magnetisation, and reached the value of about 68 millivolts in a
field of 20000 Gauss. If on the other hand the neutral region of
the magnetized rod was in contact with the electrolyte, the sense of
the electromotive force was opposite. Row1nanp and Bru‘) found
that the magnetized electrode became cathode when acids that
attacked the iron, were used as electrolytes. Squirr*), who took
nitric acid as electrolyte, came to the same result. The maximum
electromotive force amounted to 36 millivolts, in a field of 10000

1) Tu. Gross. Sitz. Ber. d. kais. Ak. d. Wiss. 92. Dec. 1885.

2) ANDREWS. Proc. Roy. Soc. 42 p. 459, 1887; 44 p. 152, 1888.

8) E. L. Nicpots and W. 8. Franxur, Am. Journ. of Science 31 p. 272. 1886;
34 p. 419, 1887; 35 p. 290, 1888.

4) H. A. Rownanp and L. Bextu. Am, Journ. of Science. 86 p. 39, 1888.

5) G. O. Squmer. Am. Journ. of Science. 45 p. 443, 1893,

746

Gauss; on further strengthening of the field this amount did not
change. Also Hurmucrsct *) found the electromotive force in the same
-sense, when diluted acetic acid or oxalic acid was used as electro-
lyte. In a field of 7300 Gauss the electromotive force amounted to
14 millivolts. Finally Bucanrer*) has occupied himself with this
question. His result is in so far entirely negative that he finds no
electromotive force which would reach the value of 10~-° Volts for
neutral solutions of ferro salts in the case of magnetisation of the
electrode in a field of 1200 Gauss. He further pronounces the opinion
that the electromotive forces found by Rownanp are caused by
mechanical disturbances of the equilibrium (‘‘Erschiitterungen’’), which
would be the consequence of the origin of the magnetic field. Then
Bucuerrr compares Hurmucescu’s results with what has been theoreti-
cally derived by Dunem*), and coneludes that no concordance exists
between them. Dune arrives at the formula:

/ERY 7 i
ad .% (1)

in which / represents the magnetisation of the electrode, 2 the electro-
chemical equivalent of the iron, x the susceptibility, and d@ the
density, the electromotive force / being taken positive, when the
magnetized electrode is cathode. When we eliminate H;, /, and # by
the aid of the relations:

B= H;+ 421 33 he Jal Th03 5156

we get instead of (1)
R ioe Al i S| (2
t= Gada hi co,

It has appeared to me that in consequence of an inaccurate expres-
sion for the energy of a magnetic field, this value of / is about fe
times too small, so that we may write by approximation because
has a large value:

f IB oh:
P=.

which expression, however, only holds when the electrolyte is a
neutral iron solution.
When the experiment is arranged in such a way that 5 may be
put equal to the external intensity of the field H7, we see from (3)
1) Hurmucescu. Eclair. Electr. Nr. 6 and 7, 1895.
2) A. H. Bucnerer. Wied. Ann. 58 p. 564, 1896 ; 59 p. 735, 1896 ; 61 p. 807, 1897.
5) P. Duuem. Ann. de la Fac. des Sciences de Toulouse, 1888—89. Wied. Ann,
Beibl. 13 p. 101, 1889.

; 747

that the electromotive force would have to increase with the square
of the intensity of the field. On introduction of the values for iron

7 == 29 So INS Gees d=7.9
we get for
H = 10000 Gauss ESOS = 2 Wot

In Bucnerer’s experiment the intensity of the field was 1200, if
the induction 4 bad had the same value, the electromotive force would
have been 2.4 x 10—* Volts. As this amount is much less than the
smallest value whieh Bocnerer could measure (10~° Volts), its negative
result cannet be considered in conflict with the theoretical resuit.

The results of the other investigators, who worked with acids as
electrolytes, ave not at all in agreement with formula (3), in fact
they could hardly be so, as (8) rests on the supposition of a neutral
iron solution.

As the case that the electroiyte is a dilute solution of the metal
of electrodes, which is assumed to be equal for the two electrodes,
is the only one that is liable to exact thermodynamic treatment, |
have calculated the value of the potential difference for this case in
what follows. Further I have communicated the results of experiments
made on this subject.

2. Let us now consider‘) an arbitrary system in which also
electric currents and magnetic fields can be present. As variables in
this system we choose the temperature 7, further a number of
geometrical quantities «,,«@,..., and finally the magnetic induction %;
when the last quantity is known everywhere, then, besides the
magnetic field. the electrical current is also determined everywhere.
The external forces exerted by the system, are the components of
force A,, A,... corresponding to the geometrical quantities, besides
the external electromotive forces &,. In order to be justified in leaving
JouLr’s heat out of consideration we shall assume that the conductors,
for so far as a current passes through them, possess no resistance.
We shall further assume that the system loses no energy by electro-
motive radiation and we exclude currents of displacement.

If the .system undergoes an infinitely small virtual variation, we
first inquire into the work performed by the system on its surround-
ings. If .the variations of the geometrical quantifies are d«
the corresponding work can be expressed by

ny Olersa op

1) The train of reasoning on which the general method of treatment followed
here is based, was suggested to me by Prof. Dr. H. A. Lorenvz, for which | will
express here my heartfelt thanks.

748

a A da, Apdo Dom tiete G Oe

Further the external electromotive forces will perform work per
unity of time equal to

dW,
=—{(€.§), dr.

For this we may write:
dW,
— fe + €,, @) dr +{G €) dr,

in which € denotes the electrical force. Now in the conductors
¢ — o(€ +- &,).
From the supposition that in the conductors 6 will be infinitely

large, follows that here € + €, must be = 0, whereas outside the

disappears. When we make use of the expression :
$ =ccurl f°)

we get after partial integration

The second term disappears on account of the supposition that
no energy leaves the system through radiation. We finally get then
by the aid of the relation:

Pagers ee

dW. 0d
= — Jagp——= lo @
at, wah re a Ot ) a

If the variation of 8 in the time dt is JB, we get:

BW, = — {(9, 4%). dr, wt. ae

The total work performed by the system now amounts to the
sum of (4) and (5),

1) Here Lorentz's system of unities is used.
y

749

SW = Ada, + A,da,4+ .. —[o 1 GR5))in Che oF oo (3)

If we now introduce the free energy of the system, the following
well known relation holds for it
w= E—-T.H
when E represents the internal energy, H the entropy. For au
infinitely small variaton we get from this:
JW = dE—T . dSH—H. dT.
Further
T.dH= dQ=dE + dW,

in which dQ is the quantity of heat added to the system. Making
use of (6) we get from this:

dW — Ada, —A,da,.... + [ (9,08) de— a

Let in a certain initial state, in which the variables a,,a,..
have the values «,,, @,,--
energy ¥,. In the magnetic state, in which & will have a certain
value everywhere, and the temperature and another quantity, e.g.
the external pressure have remained constant, the geometrical
variables will assume other values, which we shall denote by a,, @, ..
We can now make this transition take place in two steps. We first
give the geometrical variables the values «,,a,, 8 remaining = 0;
hence the free energy will increase by an amount A, W%

Further, while a,,@,... remains unchanged, we can bring the
magnetic induction B from zero to the final value; then the free
energy will inerease by Ay. In this way the final state is reached,
in which the free energy will be: ;

v= UW+ A w+ Aut . . . . ’ . (8)
Then according to (7) the following equation will hold:

by t= f [19 AB) de 5 3 SG oe ee (M)]

3. Let us now return to the above discussed case, in which two
electrodes of the same metal are placed in the dilute solution of a
salt of this metal. The concentration of the solution can be different
at different places. We think the circuit closed by means of a wire
connecting the two electrodes. Let one electrode be in a magnetic
field, in consequence of which it is magnetized. We think the
magnetic field excited by an electromagnet, the leads of which
possess no resistance,

750:

In the second eireuit in which the electrolyte is found, we think
inserted an electromotive force -— /, which is in equilibrium with
the electromotive force /’ existing eventually in consequence of the
presence of the magnetic field; we shall assume that sense of circuit
which is directed inside the electrolyte towards the magnetised
electrode, to be positive. We shall assume also the resistance of this
second circuit to be zero.

We shall subject this whole system to an infinitesimal variation.
Let this variation consist’ in the passage of an infinitely small
quantity of electricity e through the second circuit, and that in that
sense that is directed inside the electrolyte towards the magnetized
electrode. We shall moreover ‘assume that in this variation the
magnetic induction remains unchanged. in all the points of the’
system. We shall further assume that the surface that bounds the
second circuit, does not change its position.

In the first place we shall consider the work of the external
forces. These forces consist of: 1. the electromotive forces in the
first cireuit (that of the electromagnet); 2. the electromotive force
— FF in the second circuit; 3. the external pressure p. As we have
supposed % to remain constant in all the points of the system, the

[dwt

Which represents the flux of B through the first cireuit will not
change either. It follows from this that no electromotive force is.
active in this circuit, so that the work of this force is zero, The,
electromotive foree —# in the second cirenit will perform. work.
equal to —.e, when a quantity of electricity e passes. The whole
volume of the second circuit being supposed constant, the work of
the external pressure will amount to zero.

value of

In all the work performed by the system is therefore
OW = Ee. ss

Let us then consider the change of the free energy of the system.
For this purpose we shall examine what are the consequences of
the passage of the quantity of electricity e through the electrolyte
in the direction of the non-magnetized electrode towards the mag-
netized one. We shall eall the former the anode, the latter the
cathode. 7

If w and v represent the absolute values of the velocities of cation.

751

and anion in the solution, then n= is the quantity which
v
Hirrorr has called “Ueberfiihrungszahl” of the cation.

Of a current i the part n.t is carried by the cation, the part
(1—n).i by the anion. So the number of gram equivalents of the
cation in the unity of volume will increase per unity of time by :

L is
. ee ec) = aay

as div.i—0 is; represents the charge of a univalent gram ion.
In the same way the number of gram equivalents of the anion will
increase by the same amount per unity of time, so that the solution
will remain neutral. If / is the valency of the molecule, and m the
molecular weight, the mass of the salt will increase per unity of
time by an amount:

GO 5,

= (i, 7).

If the quantity of electricity e, passes through the unity of surface,
and if i, represents the unity vector in the direction t, the increment is:

m.eé

dy = —— (I,, yn) - Sh cies, ives bas) Migs (GL)
k.g

In the volume elements which lie on the surface, the increment
of the mass of salt will be per unity of surface :

Re eo gee tk ke AN

when NV is the direction of the normal directed inward. The total
quantity of salt inside the solution will now increase by an amount:

fo + fara] fo Cooma + fet. nda] =o
S ease) 8

7
When we apply Gauss’s theorem and make use of the equation
divi = 0. The quantity of salt, therefore, does not change.

The only change consists in this that the concentration in the
different volume elements is modified, and that a quantity of elec-
tricity e dissolved at the anode, has deposited at the cathode.

We shall examine what change the total free energy of the
system has undergone in consequence of what has taken place in
the electrolyte. Above we found the expression (8) for the free
energy, (9) holding for the “magnetic”? part of it. We further chose
the variation so that the magnetic induction did not undergo any
change. In the first place we must now take into account that at

Proceedings Royal Acad Amsterdam. Vol. XVII.

(52

the anode a certain volume of iron has been replaced by the solution,
whereas at the eathode the solution has been replaced by iron. The
Gy . .
volume of iron —.—.— will correspond to the quantity of elee-
( Fy 3
tricity e, when a denotes the atomic weight, 4, the valeney of the
atom, « the density of the iron. If we assume that at the anode
no magnetic field is present, the substitution of iron solution for
iron will not bring about any modification in the magnetic part of
the free energy. At the cathode, however, this substitution will give
rise to a change in the expression (9), which, when «, represents
the permeability of the iron solution, uw that of the iron, amounts to:

b b
! a.e ES 183
Jd (AyweY)= a he ee ea Bi ae cee . . (13)
0

when B means the absolute value of 3 and B this value at the
- eathode. When we speak of “at the cathode” or “at the anode”,
we mean by this that we must take the value of the considered
quantity at a plane that is at a very small distance from the
cathode resp. anode, this to evade the difficulties which the phe-
nomena taking place in the boundary layer might cause; we
shall examine this question more closely further on. On account of
the smallness of the considered volume we may assume that the
value of £B is the same everywhere inside the volume. If we put
u, = 1+ 4x,, in which «,, the susceptibility per unity of volume,
is to be considered as a small quantity, we get about :

x a.é B _ B
d(AyW)=— |= (1 dare, — [58 aes
0

when x

represents the susceptibility at the cathode. If we assume

1
u to be very great for iron, so that — is to be neglected with respect
Uu
to unity, and if we replace B by H, the absolute value of the inten-
sity of the tield in air at the cathode, we get:

6 (4uY)=—s7— — (1—Az'x,) (2 1 eee
Instead of (13), using the relation :

1
B(1——)=4e4,
u

in which / is the absolute value of the magnetisation we may
further write :

753

Age ath ee =
J, (Au ¥)= - ———.]fCU—T,)dB. . . . . (16)

Dak neon

0
We must further take the changes of concentration in the different
elements of the electrolyte into account. If we introduce the concen-
tration ¢ as the number of grammolecules of the dissolved substance
per unity of mass of the solution, this is modified by the passage of
the quantity of electricity e. If the density of the electrolyte is @,
then the variation of density, when the volume remains unchanged,

will amount to:

QOS U0 6 6 56 0 neyo A(hM))

in which dy is given by (11) and (12). By means of this we find
easily for the change of concentration :

1—me
Jc = 0p Set i ee ee oe 8, (LS)
mm. 0)
Now for dilute solutions very nearly :
YR Ole Cee Wien ail gts reassess (LO)

holds, in which x is the so-called absolute specific susceptibility per
unity of volume; which is considered as independent of @*). We
get from this by the aid of (17) and (18):

Ota ODr.
This then gives, as x, must be considered as small :
B
| f) dB = — 2a By dv.

0
When we multiply this expression by the volume element dr, theti
introduce the value of dy from (11) and (12), and integrate witli
respect to the whole volume of the solution, we get:

f 2ay.m ‘ PITTA TIN {ise
J, (AuW) = — - TA (Be liu gn) = | [ae och iy t do.
V Ss
If we assume n to be constant, which is permissible, on account
of the relative smallness of this term, if we suppose further that
at the anode B=O, at the cathode in air B=—H, we get:

2TmM.y.en —

J, (Au ¥)= Taree! Alo Hee oe (20)

1) Relation (19) holds of course only as long as the specific magnetic properties
are independent of the concentration.

50"

~I
ox
rss

as for the cathode holds :

— forty dome.

4. We must further consider the change of the “non-magnetic”
part of the free energy; as we saw above the values must be
assigned to the variables which they will have in the magnetic field.

The only change which is involved in this, is the change of con-
centration of the solution. If the free energy of the unity of mass
of this is w, then that of the volume of solution @ of density @ is

d¥Y, =0.o0.e,
when ¥*, is the free energy of the solution. When we make use of
(17) and (18), and further of the relation :

ow
=== — oe eee (te
ae P (21)
which follows from (7), the variation of this will amount to:
: 7 Ow 1—me
dd, = dv ly + P + =| BD 5 (2:2)
Q 0c m

For the free energy of the unity of mass of the solution we shall

use the well-known equation :
w=w, tact per+... .+ RVelogc,. . . . (28)
in which yw, means the free energy for c= 0.

In this we must give to the variables c and v the values which
they possess in the magnetic field in the state of equilibrium.

On the other hand we can, however, also imagine that different
concentrations can permanently exist in the different volume elements
of the solution, in such a way that no change can be brought about
in this by the magnetic field. Thus we shall obtain the potential
difference between the electrodes on arbitrary distribution of the
concentration. The supposition made is a fiction; the more so as
we have assumed also the resistance equal to zero; in general the
velocity of diffusion will namely increase as the resistance decreases,
with which permanent concentration differences are in contradiction.
This supposition, however, must always be made for such problems,
in order to be able to apply the laws of the reversible processes ;
hence we also make them here.

With the aid of (22) we get from (21)

E p RI a
dd ¥, = dv | w, +— + — (1 + loge) — RTc + — | .w.
0 m m

When we use here the expressions (11) and (12), and integrate

755

over the whole volume of the solution, we get:

m : RI
Cie = fe . (i, ’ vn) : EB — =. == (1 ai log oj hie ar =| . at
m m

kg .

m jo. aya Fa a
+ = | é.in,.2.| wp, +— + —(1 + loge) — RTc-+ —1|.do.
hg 0 m m
& a
When we take n again as constant, we get:
mM. e@ 1 1 Iiedhe
a — =.—1%, —wW,, t$pl— — — | + —log—— RT (c,— of
k Eas OE, Qs, ue C5 =

when we denote the quantities referring to the anode by the index

1, those referring to the cathode by the index 2.
We may further write:

bos = Won + (2)

or, because

OW,
jiiwase

1 1
Woo =U. + P{ ———}-
Q, 02

There remains finally

1 :
US ret Rt | To? =e —0)| | joy cue (24)

e
‘§ m Cy
From the well known theorem for the free energy :
dv 4+ 6¢w—0
we get with the aid of (10), (16), (20), and (24):

B \
pee. PO ot) |
ji — (1—T,) dB — - oaks
d kg
0

Ww a. 1 C
-— . RT .| —log — — (¢,—e,)
kg E Os |

in which 4 is the electrochemical equivalent of iron.

Hence the potential difference consists of two parts, viz. oue part
(the first two terms), which depends on ‘the magnetic field, and a
second part, which depends on the concentrations at the electrodes.
The second term of the first part will increase proportional to the
second power of the external intensity of the field, the first term,
too, in case of small intensities of the field, where we may replace
(16) by (15); at great intensities of the field, however, / will reach

756

the value of saturation, so that this term — which far exceeds the
other “magnetie’? term — will increase only about linearly with
the external intensity of the field. The sense of the electromotive
force determined by the first term is directed inside the solution
from the non-magnetized towards the magnetized electrode. The
second part of the expression becomes equal to zero for c, =e, ;
with neglect of the contraction which the solution undergoes on
concentration, this expression agrees with the potential difference -
calculated by Hertmno1tz'), between two electrodes which are in
solutions of different concentrations.

If we assume c,—c,, and neglect the terms which depend on
the suseeptibility of the solution, the following form holds for not
foo great intensities of the field (in which « is still to be considered
as very great) i

phe (26)
2d
If we use electromagnetic unities, this becomes:
SF aah
7 Smad’

which agrees with (38).

In order to simplify our considerations we have disregarded the
transition layers between iron and electrolyte; in them phenomena
will namely take place which cannot be examined in detail. It now
remains to prove that in the caleulation of the free energy the in-
fluence of these transition layers may be neglected. For this purpose
it is necessary to assume that the thickness of the transition layers
is of the order of magnitude 7, when / represents so small a quantity
that we may assume that inside the thickness / the liquid is in
equilibrium with the electrode. We shall further assume the limits
of these transition layers on one side inside the iron, on the other
side inside the solution. Let the quantity of electricity e, which we
have passed through the solution, be of the order of magnitude §; the
same thing will be the case with the thickness of the iron layer,
which has dissolved at the anode, deposited at the cathode. This
iron layer may be infinitely thin with respect to the thickness of the
transition layer, and entirely fall within it-

We have already taken into account the change of the “magnetic
part” of the freé energy, which is the consequence of the displacement
of the iron and the dissolved substance. Now we have still to take
into account the change of the state of the transition layers, which

1) H. Hetmunoirz. Wied. Ann. 3 p. 201, 1878,

Miel
TOM

is the consequence of the conveyance of iron and dissolved substance.
The quantity of dissolved substance supplied resp. extracted in the
transition layers is of the order £, just as the quantity of electricity
e. As the volume of the transition layers is of the order of magnitude

/, the change of state inside these layer will be of the order 7

Now there was equilibrium in the transition layers before the
variation; hence a variation of the free energy per unity of mass

2
of the order of magnitude (=) will correspond to a change of state

§ ; ae
of the order 5 (the external work is zero). The variation of the

total free energy of the transition layers will therefore be of the

Yeo

s am
order qe Thence we see that this variation may be neglected with

respect to the other variations of the free energy, which are of the order §.

5. We shall now still examine what will be the equilibrium
concentration in the magnetic field, i. e. that concentration which
will finally exist after the diffusion has been active between the
different volume elements. For this purpose we consider an infini-
tesimal variation of the total free energy YW of the system. We
choose this so that all the parts of the system, with the exception
of the solution, remain unvaried ; moreover we leave the magnetic
induction 3 unvaried. We can, therefore, restrict ourselves to the
variation of ¥Y, the free energy of the solution in the magnetic
state. For this free energy holds the expression according to (8)

and (9):
Ue = || le w+ | 13) 25 |r,

when we use the expression (23) for w.
As the susceptibility may be considered as small, we may put
Ore ail €

a Jew 4G O—daay) [ae co 5 of 6 (8H)

We shall now let the variation consist in a change of the con-
centration, accompanied with a change of the specifie volume ; in
this we leave the volume of every volume element unvaried, so
that the external work is equal to zero. We get the relation between
concentration variation and volume variation by eliminating dg from
(17) and (18), by which we get:

6c = 10 fo a ee eed

Now we get from (27), keeping in view that 6 remains unchanged:
Je, = fle .dy+w . do —20 B* dx, | dr.
Making use of (19), (21), and (28) we get from this, when we
apply the thesis of the free energy :

OI; 1—mc 0
[ [e+ e+ Pane y|.0e.dr =o
Sie de

@ m

Further exists the relation :

fe seh SUE

the total mass, from which follows :

[a Ton 0:

— 0
s ue w+ Tactics ~ —2nxB* .y¥ = const. . .’ ee)
c

The formula

follows from i two relations as condition of equilibrium for the
solution in the magnetic field. For this we may put, just as above
in the expressions (22)
P RI a a “
hy + — + —— (1 + logo) — RT¢ + — — 2B. = const,

m m

from whieh follows, because at the anode B =0, at the cathode B=A,
just as above for (24):

RT ;

— log? — RT (c,—c,) = 2ay. 7). . « + G0)

Mm Cy

5), we get for the potential differ-
ence in the state of equilibrium, at which also the solution is in
equilibrium

When we introduce this into (2

B
Ae
= (I=1) dB.) 2 ne
€

6. In order to test the obtained result by observation, IT madea
number of experiments, in the first place with iron. The iron
used for this was electrolytic iron, which Prof. Franz Fiscumr at

1) With ee of the contraction which the solution undergoes, this result is
in accordance with the result derived by Vorar (Gétt, Nachr. Math. phys. KI,
1910 p. 545),

759

Charlottenburg kindly procured me. The magnetized electrode con-
sisted of a circular plate, which was of the same size as the pole
plane of the electromagnet, and was rigidly fastened to it, a glass
plate serving as isolation. The other electrode was outside the field.
The concentration of the used solution of ferrosulphate was generally
5°/,. The results obtained with this may be summarized as follows.
On excitation of the magnetic field I always obtained a current in
the sense as the theory requires. The extent of the obtained effect
differed, however, greatly from the theoretical value ; the measured
potential differences were, namely, between the strengths of the
field O and about 20.000 Gauss 10 or 20 times as great as the for-
mula would require. At first the course was about proportional to
the second power of the strength of the field, the effect reaching a
value of 6.38 « 10-4 Volts at about 16000 Gauss, which did not
change on further strengthening of the field. If the used solutions
were neutral, the effect remained pretty well constant after excita-
tion of the field. On the other hand for acid solutions (which con-
tained only very little free acid) a diminution and a reversal of the
effect soon took place, till a value was reached, about ten times as
great as the first effect after the excitation of the field. It is remark-
able that Rowrnanp and Beni also always found such a reversal,
whereas Squimr found that above a certain strength of field the effect
no longer increased, which is in agreement with what I observed.
Another phenomenon that I regularly observed was the increase of
the resistance of the solution as it was longer in the tube. At last this
resistance can reach a value of some hundreds of thousands of ohms.

Besides I made experiments with nickel. The electrodes were of
so-called “Rein nickel” from the firm Kanrsaum; as electrolyte
generally a 5°/, solution of nickel sulphate was used. No effect,
however, was observed with certainty, so long as the solution was
neutral. Probably there was an effect in the sense required by the
theory, but about five times smaller than for iron, which would
therefore harmonize better with the theory. It was, however, impos-
sible to obtain certainty in this respect, as the resistance of the
solution soon became exceedingly great, even up to more than
10° 2; moreover the zero position was very variable, much more
so than was the case for iron, It is peculiar that the large resistance
only consisted for very small electromotive forces; if on the other
hand the latter was a few volts, the resistance became only a few
thousands of ohms. For solutions of nickel sulphate greatly acidified
with sulphurie acid no other effect was found than in neutral
solutions ; there was no question of a reversal here,

760

Physics. — “Further experiments with liquid helium M. Prelimi-
nary determination of the specific heat and of the thermal
conductivity of mercury at temperatures obtainable with liquid
helium, besides some measurements of thermoelectric forces
and resistances for the purpose of these investigations’. By
H. KamernincH Onnes and G. Houst. Communication N°. 142¢
from the Physical Laboratory at Leiden.

(Communicated in the meeting of June 27, 1914).

§ 1. /ntroduction. Measurements of the specific heat and of the
thermal conductivity of mercury were considered to be of special
importance with a view to the discontinuity, found at 4°.19 K. in
the galvanic resistance of this metal. The preliminary results have been
already mentioned in Comm. N°. 133, for the measurements were
carried out as early as June 1912. We wished to repeat the experi-
ments, which we considered only as a first reconnoitring in this
region, because our opinion was, that, by some improvements in the
experiments, the accuracy of the results could be considerably
increased. Special circumstances frustrated this, and now, as there
seems to be no prospect of a repetition for the present, we com-

municate the details of our investigation.

§ 2. Thermoelectric forces. The first difficulty in these deter-
minations was the choice of a suitable thermometer. The measure-
ments already performed about the resistance of platinum, gold and
mercury did not give much hope, that there would be among the
metals a suitable material for resistance thermometers. We have
therefore investigated a series of thermoelements. The gold-silver
couple, a suitable thermometer at hydrogen temperatures *), showed
down to the higher helium temperatures a fairly large thermoelectric
power, at the lower helium temperatures, however, the thermoelectric
power diminishes rapidly, so that this couple did not satisfy the
requirements. Moreover, this couple was not at all free from disturbing
electromotive forces, which appeared at places of great fall of tem-
perature in the cryostat. Nearly all other elements were subject to the
same fault. But apart from this, none of the combinations was suitable.
Notwithstanding, we communicate the results of our determinations,
because they show clearly that according to the theoretical investi-
gations of Nernst and Kersom*), the thermoelectric power of all

1) Compare H. Kameruingu Onnes and J. Cray, Comm, N°. 1070.

2) W. Nernst, Theor. Chem. 7e Aufl. 1913 p. 753. Berl. Sitz. Ber. 11 Dez.
1913 p. 972.

W. H. Kessom, Leiden. Gomm. Suppl. N°. 30) (Proceedings May 1913),

761

couples investigated approaches to zero at heliumtemperatures. The
different wires were measured against copper. After a preliminary
research, which included also the determination of the thermo-

0,
107

+1309 2°

= 499!

~400

~ $00

— 600

{00

Fig. 1.
electric forces of nickel and of six gold-silver alloys, the following
combinations were selected as most promising for investigations in
liquid helium.

Thermoelectric forces against copper.
: |
i Ag Au | Au, | Pt Pb Fe | Const. | VIA}
|
SS SaaS SS SS a paige = ie, — ——— = = 7

81° K.| —28 S78) | S257) —298 | —457 | --1293 | —5320 | — 432
{en ate ae He

20° —28 | —282 | —326 —68 | —553 | +1319 | —6280 | —819

| 4°26 —21 | —375 | —328 —58 —559 | +1309 | —6630 | —990
| | ‘¢ eg wulbas

3°20 aed — 383 — —59 | — +1309 | —6630 | — 1002
— : 7 4 Li se aE = |

| 2096 == Sone eS = = _ =) Si 1004

“1 Aw with 0,476 weight °/) Ag.

Figure 1 shows thew thermoelectric forces against copper, at the
absolute temperature 7’, given in the first column of the table. The
temperature of the second juncture was 16° C.

§ 3. Change of the resistance of alloys with temperature. As it
appeared impossible to find a suitable thermo-couple, our attention
was drawn to the change of resistance of constantin, which had
already been measured at hydrogen temperatures by KamprLINGH
Onnes and Cray. This alloy shows bere a considerable decrease
of resistance at decreasing temperature; it was, therefore, probable
that constantin could be suitably used as a resistance thermometer at
helium temperatures. Experiments have shown that this was in fact
the case. Later measurements (see comm. N°’. 142a § 4) proved that
also. manganin, whose resistance begins to diminish at decreasing
temperature and which has at oxygen temperatures a considerable
smaller resistance than at ordinary temperatures, is fit for tempera-
ture measurements in liquid helium.

§ 4. Specific heat of mercury. a. Experimental arrangements.

The method, used in the determination of the specifie heat,
agrees most with the one used by Nernst in his investigations
about the specific heat. A little block of solid mercury hung freely in
a high vacuum and was heated electrically. The increase of temperature
was determined by means of a constantin resistance thermometer.
To obtain the little block of mercury the liquid metal (comp. fig. 2
with magnified fig. of details) was poured into the vessel C through
a capillary, provided with a funnel, which could be introduced
through m. First C was in the same way supplied by means of a
funnel with a small quantity of pure pentane, which, at the intro-
duction of the mercury, remains as a thin layer between the glass
and the mercury. A little hollow steel cylinder (thickness of the

wall '/,, m.m.), which contained the heating wire — a constantin
wire, insulated with silk and covered with a thin layer of celluloid
to avoid all electrical contact with the mercury — was immersed

in the mercury. Round this cylinder a second constantin wire was
wrapped, which was to be used as a thermometer. The little cy-
linder was, by means of silk wires (stiffened by celluloid) fixed to
a little glass rod, which could be moved up and down through
the tube 4, and which was centred by constrictions in this tube.
This glass rod was connected to a silk wire, which could be
screwed up and down by turning the handle A. Now the mereury
was frozen by cooling down to the temperature of liquid air, The

Fig. 2.

possible, that the results are accurate to about 10 HRs
The thermat capacity of the hollow steel cylinder with the thermo-
meter and the heating wires was determined afterwards by a separate

763

Sen

Fig. 3.

thin layer of pentane, which is
spread over the glass, acts as a
viscous lubricant at this temperature
and prevents the sticking of the
mercury to the wall in freezing.
After having been frozen, the little
block ofsolid mercury was screwed
up by means of the handle K
and the temperature was increased
to about — 50° C. Thereupon a
high vacuum was established by
means of a GAEDE mercury pump
and the pentane was distilled off
into a tube, immersed in liquid air.
During the experiments the heat
insulation of the block appeared
to be so good, that the tem-
perature remained many degrees
above that of liquid helium, al-
though it was let down against
the glass wall. Therefore a little
gas had to be admitted in order
to eool the block. This manipula-
tion sueceeded perfectly, but the
gas could not be removed quickly
enough in the short time available
for the experiments. The loss of
heat of the mercury was thus
very considerable (decrease of the
temperature difference to half of
the original value in about JOO
seconds) and therefore the cor-
rection, to be applied to the in-
crease of temperature while heat-
ing, remains the greatest source of
uncertainty. Nevertheless it seems

experiment, Fig. 3 shows the apparatus used for this purpose.
b. Results. Measurement at the boiling point of helium. The quantity
of heat supplied to the mercury amounted to 1,10 cal., the increase of

"64

temperature, corrected for the loss of heat during the period of heating,
was 2,22 degrees K. whilst the quantity of heat, necessary to heat the
little steel cylinder with the thermometers 2,22 degrees, amounted to
O.11 cal. (result of a separate experiment). Control experiments showed
that the heating wire (used as a thermometer). and the thermometer
wire outside the steel cylinder had the same temperature. The mass
of the mercury was 314 erammes, so that 0,00142 cal./degree K. was
obtained for the mean specific heat between 4°,26 K. and 6°,48 K.

The relation of GRUNEISEN ') = = c, would”) have given ¢,=0.0087,
for 4°.27 K.

Measurement at 3°.5 K. Afterwards the experiment was repeated
at the temperature of liquid helium, boiling under a pressure of 6 em.
of mereury ; 0.000534 cal./degree K. was found for the mean specific
heat between 2°93 K. and 3°97 K.

Assuming this mean value of the specifie heat, we shall calculate
now the value of this quantity for a definite temperature according
to Desue’s formula, which holds for our very low temperatures

c= C.T?,
so that the mean specific heat between two temperatures 7’, and
[aS
ee Uh 0)
GSI)

We obtain from the two experiments C= 0.0000088 and 0.0000127
respectively.

The agreement is not satisfactory; although, taking into account
that the absolute temperature occurs in the formula in the 4" power,
and that therefore small deviations in 7’ involve very large ones
in (, we may safely conclude from our experiments, that, ith

respect to the specific heat, nothing peculiar happens at the point of
discontinuity, and that we may content ourselves with a preliminary
mean value C= 0.0000110, when we assume for the moment that
the specific heat does not show any discontinuity at all.

We have then

== Cit — 1010 0.000 0e*
or for a gramme-molecule
c= 0.00220 T?.
For the characteristic constant 6, introduced by Drsue we find
1) KE. Griersen, Verh. d. Deutschen Phys. Ges. 1913 p. 186.

*) Compare KamertincH Onnes and Hotsr, Leiden Comm. N°, 142a@ Proceed.
June 1914.

with c, = 5.96 and
13 3

C= 0:00220 7 2 = 77-988 —— ce = 464 —
ge “

C= 60:

As a matter of fact, the specific heat has been determined here
at constant pressure and not at constant volume. In the foregoing
calculation, the difference of the specific heats ¢, and ¢,, given by

Gy 6, — Aca
has been neglected. Indeed, A is about 7,2.10—° and c, and T ave
both small.

Using Desur’s formula, we can compare our results with
those of Potuitzer'’ at somewhat higher temperatures. For this
purpose we calculate a value of 6 agreeing as well as possible

c
with Poniirzer’s figures of —, we find then 110. In fig. 4 c, is
c

“
plotted as a function of 7’ according to Drie; the values, deter-
mined experimentally, are indicated by circles.

The accordance at helium temperatures is bad, as could be_
expected in consequence of the difference between the value of @

used in the calculation, and the one deduced from our experiments.

Se cast eae
a7 A all |

Qs d

IAS |

fe)
o LO =
fe] RV ae Cv SQ JOO dso

Fig. 4.

1) See F. Poxtirzer. Zeitschr. f. Elektrochem. 1911. p. 5.

766

Meanwhile we remark, that in Po.iitzer’s experiments too a distinet
deviation from Drsiwn’s curve is to be noticed, in the sense of a
decrease of @ (about 115—162) with decreasing temperature, which
would be, according to our experiments, very considerable down to
helium temperatures ; further that, according to LinprMann’s formula
and by comparison with lead (88), 661 is to be expected for
mercury.

§ 5. The thermal conductivity.

The thermal conductivity was determined by means of the appa-
ratus, represented in figure 5. A U-shaped tube, with double
walls, and closed at ene end, was provided .

NG with mereury. The closed branch contained
Shaan a constantin wire S, insulated by means
of celluloid, which made contact with the

a mercury at the free end. This wire’ was

5 used as a heating wire. The current return-

ein ed through the mereury itself by means

of a wire, in contact with the mercury at

M8 the open end of the tube. The fall of tem-

perature was measured with 38 constantin thermometers 7’, 7,
and 7’, consisting of wire of '/,, mm. thickness, wrapped around
a small glass tube. The experimental arrangement is further ex-

plained by the diagrammatic figure. All wires were connected to
each other by two wires, insulated by thin layers of celluloid and
further running free through the liquid helium.

In consequence of a wrong manipulation during the preparation,
the tube had lost a little mercury, so that only the two lower
thermometer wires could be used. The heat developed in the heating
wire and the difference in temperature thus produced were measured
at two different temperatures, the one above and the other one
below the point of discontinuity in the electrical resistance. The
section of the cylinder of solid mercury amounted to 0.47 em’,
the distance of the thermometers to 5,0 em.

At the boiling point of helium the supplied energy was 0,633
watt/sec., the difference in temperature produced 0.58; at 3°7 K 0,0365
watt sec. and 0,23.

From this we find for the mean thermal conductivity between
4°.5 K and 5°,1 K. £=0.27 cal/em. sec. and between 3°.7 K and
3.9 K: £=040 cal/em. sec.

The thing, which immediately strikes us, is that there is here no

767
distinet discontinuity as was found at 4°.19 K in the electrical con-
ductivity, although the thermal conductivity becomes much larger,
when the temperature decreases. As there do not exist direet deter-
minations for solid mercury, we only can make a rough estimation
with the aid of Wirpemann and Franz's law.

At the melting point, the electrical conductivity of liquid mercury
amounts to 1.10. 10° em. 2~'and of solid mercury to about five times
as much, thus to 5.50. 10* em—! 2~!. From this we find by comparison
e.g. with lead about 0.075 for the thermal conductivity. The values
here obtained in liquid helium are 3.5 and 5.5 times as large.

Chemistry. “Hqwilibrie in ternary systems’. XVII. By Prof.
SCHREINEMAKERS.

(Communicated in the meeting of Oct. 31, 1914).

Now we will consider the case, mentioned sub 3 (XVI), viz:
the solid substance is a binary compound of a_volatile- and a
non-volatile component. A similar case occurs for instance in
the system Na,SO, + water + alcohol, when the solid phase is
Na,SO,. 10H,O,; or in the system FeCl, + HCI + H,O, when the
solid phase is one of the hydrates of ferric chloride, for instance
Fe,Cl, .12 H,0.

For fixing the ideas we shall assume that of the three compo-
nents A, B, and C (fig. 1) only A and C' are volatile, so that all
‘fapours consist either of A or of C or of A+ C.

In fig. 1 CAde represents a heterogeneous region L—G; ed is
the liquid eurve, CA the corresponding straight vapour-line. The
liquid d, therefore, can be in equilibrium with the vapour A, the
liquid e with the vapour C' and each liquid of curve ed with a
definite Vapour of AC.

Previously (XVI) we have seen that this heterogeneous region
L—G can arise in different ways on decrease of pressure, viz. either
in one of the angiepoints A and ( or in a point of AC; also two
heterogeneous regions may occur, the one in A and the other in C,
which come together on further decrease of pressure somewhere in
a point of AC.

In fig. 1 we may imagine that the region L—G has arisen in these
different ways; curve ed may of course also turn its convex side
towards AC. Besides this heterogeneous region 1—G' we also find,
in fig. 1 the saturationcurve under constant pressure of the binary
: dk

Proceedings Royal Acad. Amsterdam, Vol. XVII.

768

substance /’, represented by pg [we leave the curve rs, drawn in
the figure out of consideration for the present].

Fig. 1.

In the same way as we have acted in the general case | fig. 11 (1) |
or in the peeuliar case (XI), we may deduce also now the different
diagrams.

T< Ty. At first we take a temperature 7’ lower than the
minimummeltingpoint 7’ of the binary compound /. Now we tind
a diagram just as fig. 2 for the saturationcurve under its own vapour-
pressure of / and the corresponding straight vapour-line. In_ this
figure, in which the component-triangle is only partly drawn, Agn
is the saturationcurve under its own vapourpressure; we find the
corresponding straight vapour line Cy, on side CA.

When we assume, as is supposed at the deduction of fig. 2, that
neither a point of maximum-pressure, nor a point of minimum-
pressure occurs, the pressure increases from m towards h; conse-
quently it is lowest in n and highest in 4, without being, however,
a minimum in 2 or a maximum in hk. It follows from the deduction
that the sides solid-gas and_ solid-liquid of the threephasetriangles
must be situated with respect to one another and to the side CB
just as is drawn in fig. 2.

It is apparent from the figure that the binary liquids 1 and 7 ean
be in equilibrium with the unary vapour C' and that the ternary
liquids a, c and #4 ean be in equilibrium with the binary vapours

a,, c, and #,. It is apparent that somewhere between the liquids c

1
and 4 a liquid g must be situated, the corresponding vapour g, of
which represents the extreme point of the straight vapour line Cg,.

When a liquid follows curve /n, first from / towards g¢ and after-
wards from g towards n, the corresponding vapour g, follows conse-

769

quently first Cy, from C towards g, and afterwards again this
same line, but in opposite direction, consequently from g, towards C.

Fig. 2.

Kach vapour of this straight vapour line Cy, can, therefore, be in
equilibrium with two different liquids, the one of branch hy and the
other of branch gn.

We may express this also in the following way: when we have
an ‘equilibrium /’-+- Z + G, then there exists under another pressure,
also an equilibrium + 7,+.G,, in which Z and ZL, have a
different composition; G and G,, however, have the same composition.

It is apparent from the deduction of fig. 2 that in curve jn also a
point of maximumpressure can occur. This case is drawn in fig. 3;
in represents again the saturationcurve under its own vapourpressure
and Cy, represents the corresponding straight vapourline; M7 is the
point of maximumpressure, J/, the corresponding vapour. The points
M,, M, and F must of course be situated on a straight line.

While under the pressure Pj; there occurs only one equilibrium,
viz. f+ Lip+ Gau,, under each pressure, somewhat lower than
P\, there exist two equilibria, for instance + L, + Gi, and
F+ L,+ G.,.; we can imagine these to be represented by the
threephasetriangles Maa, and /cc,, when we imagine both triangles
in the vicinity of the line #//,. It follows from the deduction
of the diagram that both these triangles turn their sides solid-gas
towards one another, consequently also towards the line /J/M,.

Suppose, we want the curves ed and pg to move in fig. 1 with
respect to one another in such a way that a point of minimum-
pressure occurs on the satnrationcurve under its own vapourpressure,

51*

770

then we see that this is impossible. Yet we can imagine a saturation-
eurve with a point of maximum- and a point of minimumpressure.

When we trace curve /n starting from n, we arrive first in the
pot of maximura- afterwards in the point of minimumpressure.
We will refer to this later.

Tp < T. Now we take a temperature 7’a little above the minimum
meltingpoint 7p of the solid substance /#. Then we must distinguish
two cases, according as the solid substance expands or contracts on
melting. We take the first case only.

Then we find a diagram like fig. 4 (XI); herein, however, the
same as in figs. 2 and 3, we must imagine that the vapourcurve
han, is replaced by a straight vapourline Cg, on side CA. We
will refer later to the possibility of the occurrence of a point of
maximum- and a point of minimumpressure.

We can, however, also get curves of a form as curve /nand the
curves situated inside this in fig. 6 (XI); these curves show as well
a point of maximum- as a point of minimumpressure,

When we draw the saturationcurves under their own vapour-
pressure for different temperatures, we can distinguish two prineipal
types; we can imagine those to be represented by figs. 5 (AI) and
6 (XD. At temperatures below 7'p these curves are circumphased,
above Z'p they are exphased. In tig. 5 (XI) they disappear in a point
H on side BC, in tig. 6 (XI) in a point A within the triangle. The
corresponding straight vapourlines disappear in fig. 5 (XI) at 7 in
the point C; in figure 6 (XI) they disappear at 7 in a point R,,
the intersecting point of the line /’R with the side CA.

771

Now we will consider some points more in detail. In order to
get the conditions of equilibrium for the system #’+- 4 + G, when
Fis a binary compound of 6 and C and when the vapour consists
only of A and C. we must equate «=O and y,=0. The conditions
(1) (II) pass then into:

Z OZ

Ew
Mite he Cig ge ae az az, |
: 0%, | 02 _, Ow ae, | )
ae” og, tb Sanur =

Now we put:
b= Was ikititird pnol A SG Je iii lon 5 2 (P)
Hence the conditions (1) pass into:

OU 0U
«—+(y — 8)—+ RTe—U+S5=0... . (8)
Ow 7 Oy
aU. oo
#,—— —6— + RTx, —U,+5=>0... . (4)
Ow, Oy
0U aU, ?
— + RT logx =——+ RT loge, . . . . . (5)
Ow Ox ;

1
When we keep the temperature constant, we may deduce from

(5):
[er + (y — B)s + RT) dz + [as + (y—A)t]dy=AdP . (6)

(3)

E — ps + “ rr | dx + [#,s — Bt]dy =(A+ C)dP. . (7)

RL RT OV OV
r + —— | da + sdy — (» + —— | dz, =({| —— — ]dP . (8)
2 2X, Ox, Ow

Here we must equate of course in A and C a=O and y, = 0.
In order to let the pressure be a maximum or a minimum, dP
must be = 0. From (6) and (7) it follows that then must be satisfied :

ip [o) a= Gann) ==, ato ogo co oe A)

This means that the point of maximum- or of minimumpressure
M (x,y) and the corresponding vapourpoint J/, (v,y,) are situated
with / on a straight line (fig. 3).

In order to examine the change of pressure along a satuyration-
curve under its own vapourpressure in its ends / and n (figs. 2 and 3)
we equate in (6) and (7) e=0 and a, =U. Then we find:

OV
[(y—B) s + RT] de + (y—p) tdy = | v- v + (B—y) F | dP (10)
OY

ae “ OV
— ps + — RT | dx — ptdy =| V, —v + 8 a CLE es (Lal)
: y

772

The ratio v,:2 has a definite value herein, as it follows from (5).
When we eliminate dy from (10) and (11), then we find:

[2+ a | era =[3V + (y—B) V, — yx] dP. . (12)

The quantities in the coefficient of dP relate all to the binary
equilibrium # + £-+ G. When we eall AV, the change of volume,
when between the three phases of this binary equilibrium a reaction
takes place, at which the unity of quantity of vapour arises, then is:

(y—B) AV, = BV + (y—8) VV, — yo «.. « «= (18)

Consequently we may write for (12):

pe SA ela 14
Ni — aura Ame mere es. 5, (124)

Now we introduce again, as in (XI) the perspective concentrations

of the substance A in liquid and gas; it is evident that the per-
spective concentration S, is equal to the real concentration «, of A
in the vapour; we find for the perspective concentration of A in
the liquid:
fa a
p—y

so that we can write for (14): .

dP ie S\ RL
é = —/{ 1 — — |—— .w sz 2 (th)
aa ) c—0 x x, Ay :

When the vapour contains the three components, then. as we have
seen previously (14) (XI) is true; when we replace herein S, by 2,,
this passes into (16).

It follows from (16) that the sign of the change of pressure in
the ends / and n of a saturationcurve under its own vapourpressure,
depends on the sign of AV,. Now AV, is almost always positive
for the binary equilibrium PLELG and it is only negative between
the points / and H'|fig. 5 (XI) and fig. 6 (X1)]. Consequently AV,
is positive in the points 4 and m of figs. 2 and 3, also in the point
h of fig. 5 (XI) and 6(X1I); AV, is negative in the point n of the
two last figures. Further it follows that the sign of the change of
pressure is not determined by the ratio «,:a (the partition of the
third substance between gas and liquid) but by the ratio S: a, (the
perspective partition of the third substance between gas and liquid).

Let us take now a liquid of the saturationcurve under its
own vapourpressure in the vicinity of the point / of fig. 2, for this
we imagine triangle Maa, in the vicinity of the side LC. From the
position of Fa and Fa, with respect to one another, follows

773

S>z2x,. As AV, is positive in fh, it follows from (16) that the
pressure must decrease on addition of a third substance. We see
that this is in accordance with the direction of the arrow in the
vicinity of h.

In the vicinity of point / of fig. 3 is a, > S as follows from the
position of triangle Kaa,. As AV, is positive, it follows from (16)
that the pressure must increase on addition of a third substance.
This is in accordance with the direction of the arrow in the vicinity
of fh.

In the vicinity of point n of the figs. 2 and 3 S is negative (we
imagine for instance in fig. 2 triangle /6/, in the vicinity of side
BC); as AV, is positive, it follows from (16) that in both figures
the pressure must increase, starting from n.

Consequently we find: in a terminatingpoint of a saturationcurve
under its Own vapourpressure, situated between Cand H, the pressure
decreases on addition of a third substance, when the threephase-
triangle turns its side solid-gas towards LC (fig. 2) and the pressure
increases when the threephasetriangle turns its side solid-liquid
towards BC.

As, therefore, at temperatures lower than 7'p (figs. 2 and 8) the
pressure always increases, starting from 7, and increases or decreases
starting from /, we find the following. When we trace curve nh,
the pressure increases continually starting from » towards / (fig. 2),
or we come starting from 7 first in a point of maximumpressure,
after which the pressure decreases as far as in / (fig. 3) or we come,
starting from 7 first in a point of maximum- and afterwards in a
point of minimumpressure, after which the pressure increases up to /.

As in point / of fig. 5 (XD the pressure decreases starting from
h, consequent it is assumed here, that the threephasetriangle furns
its ‘side solid-gas towards BC. (Cf. fig. 2 and fig.4 (XI); in this
Jast figure we imagine however curve /,n, on side CA). In the point
h of fig. 6 (XI) is assumed that the threephasetriangle turns its side
solid-liquid towards BC.

Let us consider now the terminatingpoint 7 of the saturationcurve
in fig. 5 (XI) and fig. 6 (XI). As n is situated between F and H,
AV, is negative, when the threephasetriangle turns its side solid-
gas towards BC, then is S>.2, and it follows from (16) that the
pressure increases on addition of a third substance. We then have
the case of fig. 5 (XI). When, however, the threephasetriangle turns
its side solid-liquid towards LC, then S<.w, and it follows from
(16) that the pressure decreases on addition of a third substance,
We then have the case represented in fig. 6 (XI).

774

When we consider the saturationcurve going through the point
F in fig. 5 (XI) and fig. 6 (XI), then for this point y=, conse-
quently, according to (15) S=o. From (13) follows also AV,= @.
Therefore we take (12); from this follows for y= 8

dP th 17)
de tar eee Ge ee (

As fig. 5 (XI) and fig. 6 (XT) are drawn for V > v, the pressure
must increase starting from / along the saturationcurve going
through F.

As the pressure increases starting from /’ along the saturation-
curves under their own vapourpressure of fig. 6 (XI) and decreases
starting from a point , situated in the vicinity of H, somewhere
between /’ and n must consequently be situated a point, starting
from which the pressure neither increases nor decreases. This point
is, therefore, the point of maximum- or of minimumpressure of a
saturationcurve, and is not situated within the componenttriangle,
but accidentally it falls on side LC. It follows from the figure that
this point is a point of minimumpressure; we shall call this the
point m.

The limiteurve (viz. the geometrical position of the points of
maximum- and minimumpressure) goes consequently through the
points m and R&R; it represents from m to & points of minimum-
pressure; starting from / further within the triangle, it represents
points of maximumpressure. This latter branch can end anywhere
between /7 and C' on side BC.

The terminatingpoint of a limiteurve on side SC’ can be situated
between “and C, but cannot be situated between /’and B. A similar
terminatingpoint is viz. a point of maximum- ora point of minimum-
pressure of the saturationcurve, going through this point. Consequently
in this poimt along this saturationcurve dP=0O,; from (16) it follows
that then must be satisfied :

S=2,. or, Pe - (y—S) ac, 0, eee eremea (l)

Herein w and «, are infinitely small; their limit-ratio is determined
by (5). As 2 and a, are both positive, it follows from (18): y < ~.
The terminatingpoint of a limiteurve must, therefore, be situated
between /’ and C' (fig. 6) and it cannot be: situated between / and
B. In accordance with this we found above that one of the ends
of the limiteurve is situated in fig. 6 (XI) between n and PF,

Now we must still consider the case mentioned sub 4«(XIV), viz.
that the solid substance is one of the components. A similar case

775

occurs for instance in the systems: 7+ water + aleohol, wherein
Z represents an anhydrie single, salt, which is not-volatile.

For fixing the ideas we assume that B is the component, which is
not-volatile (fig. 1), so that A and C'represent the volatile components.

Now we imagine in. fig. 1 curve pq to be omitted, so that the
curves ed and rs rest only, ed is the liquideurve of the region L —G,
rs is the saturationcurve under a constant pressure of the substance B.

We can, in order to obtain the different diagrams, act in the same
way as we did before in the general case, or as in communication
XI. For this we consider the movement of the curves ed and rs
with respect to one another on decrease of pressure.

As we assume that A is not volatile, these considerations are
not true, therefore, for points situated in the vicinity of B. Equilibria
situated in the immediate vicinity of B have viz. also always the
substance 4 in their vapour, so that the considerations of com-
munication XIII apply to these.

When we decrease the pressure, the liquideurve ed (fig. 1) shifts
further into the triangle towards the point 4, so that under a definite
pressure the curves ed and rs meet one another. Now we distinguish
three cases.

1. We assume that the curves ed and 7s meet one another first
in a point on one of the sides of the triangle; when this takes place
on side BC, then consequently the points e and 7 coincide in fig. 1,
while the two curves have no other point in common further. On
further decrease of P, this intersecting point shifts within the triangle
and it disappears at last on the side A, when in fig. 1 the points
s and d coincide. Curve ed is situated then inside the sector Brs
and curve 7s inside the region CedA. .

From this follows that the saturationcurve of B under its own
vapourpressure can be represented by curve habn in fig. 4, in which
the arrows indicate the direction, in which the vapourpressure increases.
The corresponding vapourcurve is the side CA; the liquid / viz. is
in equilibrium with the vapour C, liquid n with the vapour A and
with each liquid (a and 6) of in a definite vapour (a, and 6,) of CA
is in equilibrium. It follows from the deduction that the threepbase-
triangles (Bua,, bbb,) turn their sides solid-gas towards the point /
and their sides solid-liquid towards the point 7.

This fig. 4 is a peculiar case of fig. 2 (XIII); when we suppose
viz. that the substance 6 does not occur in the vapour, curve h,a@,b,7,
of fig. 2 (XIII) must coincide with the side CA of the triangle and
fig. 4 arises,

2. Now we assume again that the curves ed and rs (fig. 1) meet
one another first in a point of the side BC; this point of inter-
section shifts then on further decrease of P into the triangle. Under
a definite pressure we want a second point of intersection to be
formed by the coincidence of d and s (fig. 1). The two points of

B
\
C44 doe
Fig. 5.

intersection approach one another on further decrease of pressure,
in order to coincide at last in a point m. It is evident that m is a
point of minimumpressure of the saturationcurve under its own
vapourpressure; if is represented in fig. 5 by curve wambv, the
corresponding vapourcurve is the side Cd. It is evident that the
vapour m,, which can be in equilibrium with the liquid m, is
situated on the line Am.

3. We can assume also that the curves ed and rs (fig. 1) meet
on decrease of pressure first in a point J/, which is situated within
the triangle. On further decrease of pressure then two points of

Tae

intersection arise; the one disappears on BC by the coincidence of
e and 7, the other on LA by the coincidence of d and s (fig. 1).
It is evident that J/ is then the point of maximum-pressure of the
saturationcurve of 6 under its own vapourpressure, the corresponding
vapourpoint J/, is situated of course on the line JZ.

One can understand the occurring diagram with the aid of fig. 5 ;
herein we have to give an opposite direction to the arrows and we
have to replace the points of minimumpressure m and m, by the
points of maximumpressure Jf and J/,; further the triangles Baa,
and bbb, are to be drawn, in such a way that they turn their
sides solid—gas towards the line BILM,.

We shall consider some points in another way now. In order to
find the conditions of equilibrium for the equilibrium 6 -+ LZ + G,
when the vapour consists of A and C only, we equate in the

relations (1)—(8) @=1; in the general values of A and C (II)
we put c= 0, B=1 and y, = 0. The condition for the occurrence
of a pot of maximum- or of minimumpressure (d= 0) becomes then :
= (=) a 2 co 6) oso, 5 (LO)
»lhis relation also follows from (9), when we put B=41. This
means: the pot of maximum. or of minimumpressure of the saturation-
curve of £6 under its own vapourpressure and the corresponding
vapourpoint are situated with point B on a straight line (fig. 5).
In order to determine the change of pressure along a saturation-
curve under its Own vapourpressure in its ends on the sides bC and
BA (figs. 4 and 5) we put in (16) B=1. We then find

dP ie ISIN\. tase ee
sia ae sh Ae es E00)
dz ]y—0 au Goad (AWS

In this S and AV, are determined by (13) and (15), when we
put herein 3=1. Consequently S is always positive. When we
apply (20) to the figures (4) and (5), then we see that the change
of pressure is in accordance with the position of the sides solid-gas
and solid-liquid of the threephasetriangles.

Now we have treated the case that either the binary compound
J (figs. 2 and 3) or the component / (figs. 4 and 5) occurs as solid
phase. When /’ and #4 occur both as solid phases, then the two
saturationcurves under their own vapourpressure can either intersect
one another or not. We only consider the case, drawn in fig. 6, that
the two curves intersect one another in a point; the vapour, being
in equilibrium with the liquid s, is represented by s, (s, or s,).

A similar case may occur for instance in the system Na,SO, +
water + alcohol, then curve cs is the saturationcurve under its own

778

vapourpressure of Na,SO,.10H,O (/’), sa the saturationcurve of the
anhydriec Na,SO, (3). Then there exists a series of solutions, saturated
under their own vapourpressure with Na,SO,.10H,O (curve cs)
and one series saturated with Na,SO, (curve sa); the equilibrium
Na,SO, . 10 H,O + Na,SO, + L;-++ G, occurs only under a definite
pressure P,. The solution ZL, has then a detinite Composition s and
the vapour, which consists only of water and alcohol has a definite
composition s,.

In the binary system Na,SO, + water, the equilibrium Na,SO, . 10
H,O + Na,SO, -+ vapour exists only under one definite pressure; we
shall eall this pressure P,. In the ternary system Na,SO, + water +
aleohol the equilibrium Na,SO, . 10 H,O+Na,SO,+-L.-++G, exists also _
only under a definite vapourpressure P.. This pressure P. is influenced

Fig. 6.
by the watervapour and the alcohol-vapour together; now we may

show that the partialpressure of the watervapour herein is also equal
tio P, and that the pressure of the alcohol vapour is consequently
P,— P,.

In order to show this, we consider the general case that in the
system A+ B+ C (figs. 1—6) the substances A and C are volatile
and that a compound /° of 6 and C occurs.

The binary equilibrium 5 -+ /-+ G,, wherein the vapour consists
of C only, occurs under a single pressure P, only.

The ternary equilibrium 6-+ /’+ G, wherein consequently the
vapour consists of A and C, can occur at a whole series of vapour-
pressures.

When we represent the § of 45 and / by § and &,, then the
condition of equilibrium is true:

Z,
5 —e=0—A) (4 — nie): Serer.)

vars)

Hence follows:
j OAT on nh Oe
v, — bv — (1 — p){ V, — 2, e dP+ (1—§8)a,r,de#,=0. (22)
eB

When we assume that the gas-laws hold for the vapour G, then:
Ok eee RT
— SU 20) 3 SSS
Oar, a,(1—2,)
From (22) now follows:

(23)

l=6
[(d —8) V, =», + Bo] dP= —

tH)

donee ee (24)
1
The coefficient of ¢@P represents the change of volume when 1 Mol.
F is decomposed into 3 Mol 6-+ (1 — g) quantities of G; this is
very nearly (1— 8) V’,. As at the same time PV, = RT, we can
write for (24);
(Al = op) CUP Sse 5 5 9 Go 6 o 4 ira)
From this follows:
i 0 oR
ear MEPS we eet an (26)
When we call the partial pressures of A and C in the vapour )4
and Pc, then Pg=2,P and Pe=(1—a2,)P; from (26) now
follows :

Pea ands PG == Py) a2)

ater 0
l—2,

This means that in the ternary equilibrium 5+ /-+-G the partial
pressure Po of the substance C is equal to the vapourpressure of
the binary equilibrium 6+ #' + G,.

When we bear in mind now that in a system the pressure and
the composition of the vapour do not change, when we add to this
system stili a liquid, which is in equilibrium with all phases of this
system, then follows:

In the ternary equilibria B+ F+G and 6+ F+ L,+ G, the
partialpressure of the substance C in the vapour is equal to the
vapourpressure of the binary equilibrium 4+ + G,.

The first equilibrium (viz. 5+ /’+ G) exists at a whole series
of pressures; both the others oecur under a definite pressure only.

The binary equilibrium Na,SO .10H,O + Na,SO, + watervapour
has at 25° a vapourpressure of 18.1 m.m. when we add alcohol,
then, when the gas laws hold in the vapour, in the equilibriam
Na,SO,.10H,O + Na,SO, + G and Na,SO,.10H,O + Na,SO, + L+G

the partialpressure of the watervapour will also be equal to 18.1 m.m.

Now we will put the question, whether we can also deduce some-

780

thing abont the change of pressure starting from s along the curves
sa and sc (fig. 6). In communication V we have deduced the following
rule. When the equilibrium solid + Z ean be converted with increase
of volume into solid + L’ + G’ (in which ZL’ differs extremely little
from £) then of a threephasetriangle solid—liquid—gas the side
solid—liquid turns on increase of pressure towards the vapourpoint
and it turns away from the vapourpoint on decrease of pressure.

When we assume now that s (fig. 6) is not situated in the vicinity
of B or F (the equilibrium 5-+ L and + LF converts itself into
B+ L’+ G6’ and &+ L’+G" with increase of volume) we can
apply the above-mentioned rule. We distinguish now according as
the vapour is represented by s,,s, or s,, three cases.

1. The vapour is represented by s,.

First we consider the threephasetriangle /’ss,. When the side Fs
turns towards c, then consequently it turns towards its vapourpoint
s,; the vapourpressure increases, therefore, starting from s along ‘sc
towards ec,

Let us consider now the threephasetriangle Lss,. When the side
Ls turns towards a, if turns, therefore, away from its vapourpoint
s,; consequently the vapourpressure decreases starting from s along
sa towards a. :

Consequently we find that the vapourpressure starting from s
increases along sc and that it decreases along sa. It is evident that
this is only true for points in the vicinity of s; the occurrence at
a greater distance of s of a point of maximumpressure on sc and a
point of minimumpressure on sa, is viz. not excluded.

2. The vapour is represented by s,.

It follows from a consideration of the threephasetriangles /ss,
and ss, that the vapourpressure starting from s increases as well
along sc as along sa.

3. The vapour is represented by s,.

It follows from a consideration of threephasetriangles #’ss, and
Bss, that the vapourpressure starting from s decreases along sce and
increases along sa.

We can obtain the previous results also in the following way.
Between the four phases of the equilibrium 6+ #’+ L, + vapour
or s,) a phasereaction occurs on change of volume. We choose
this reaction in such a direction that vapour is formed, we call the

(Si, Sq
change of volume AV.

The point s (fig. 6) is a point of the quadruplecurve B-+ #+
+L+G; AV is positive for each point of this curve. When,
however, a point of maximumtemperature /7 occurs on this curve,

781

then AV is negative between this point /7 and the terminatingpoint
of the curve on side BC. It is apparent from the position of the
curves sc and sa (fig. 6) that point s is chosen on that part of the
quadruplecurve, where AJ is positive. We distinguish now again
the same three cases as above.

1st. The vapour is represented by s,.

It is apparent from the position of the points 7’, B,s and s, with
respect to one another that the fourphase-reaction :

Nee GV. S0)

F+ L4G (Curve sc) B+ L+ G (Curve sa)

FH+B+L FI+B+G
takes place; it proceeds from left to right with inerease of volume
Hence it follows that the equilibria written at the right of tbe
vertical line occur under lower pressures, the equilibria at the left
occur under higher pressures. In accordance with the above we find,
therefore, that starting from s (fig. 6) the pressure increases along
se (equilibrium + 1+ G) and decreases along sa (equilibrium
B+L+ GQ).

2°¢ and 3". Also in these cases we find agreement with the
previous considerations.

When a point of maximumtemperature H occurs on the quadruple-
curve b+ F+ 2+ G, then two points of intersection s occur at
temperatures a little below 77. When we consider now a point
of intersection s between // and the terminatingpoint of the qua-
druplecurve on side AC, then ATV’ is negative. This involves that

above in 1st—3'4 increase of P is replaced by decrease of P and
reversally. We find also the same when we consider the threephase-
triangles solid-liquid-vapour. To be continued.)
Chemistry. — “On the quaternary system: KCI—CuCt,— Ba Cl,—H, 0.”
sy Prof. Scurememakers and Miss W. ©. pr Baar.
(Communicated in the meeting of October 31, 1914).

In a previous communication’) we have already discussed the
equilibria occurring in this system at 40° and at 60°; the results of
the analysis on which these considerations are based, we have hitherto
not yet communicated. Now we will communicate the results of the
analysis; all the points, curves ete. quoted in this communication
apply to the two figures of the previous communication (1. c¢.). We
want to draw the attention to the fact that fig. 1 represents the
equilibria at 40° and tig. 2 the equilibria at 60°.

1) These Communications (1912) 326.

782
vACE eae

Composition of the solutions in percentages by weight at 40° (fig. 1. I.c.).

Point KCl BaClo | CuCl, H,O | Solid phases

a 0 0 44.67 | 55.33 Cu Cly.2H,0
b 0 3.72 | 42.72 | 53.56 | BaCl.2H,O-+CuCl.2H,0
c 0 28.98 0 11.02 |) Ba Cl. Hp O
d | 23.98 | 9.15 0 66.87 BaCl).2H,0+KCI
e | 28.63 Deg Og, [eres KCI
f | 21.53 0 | 22.85 | 55.62 Keeper
gz | 9.79 0 | 43.83 | 46.38 CuCl, 2H; 0- Des
b 0 3.72 | 42.72 | 53.56 | BaCl,.2H,O +CuCl,.2H,0
es 5.52 | 3.39 | 42.35 | 48.74 :
“pn | 9.88 | 2.99 | 42.07 | 45.06 | BaClh.2H,O4- CuCl. 2H0°-D gs
di VW/23508s)) V94s lao 66.87 Ba Cl,. 2H» O + KCl
2 | 21.46 | 8.90 | 8.44 | 61.20 ?
>| 20.61 | 7.63 | 14.31 | 57.45 | ;
i | 20.61 | -5:40 | 20.47 | 53.52 | BaCh.2Hs0--KCI--Dioo
f | 21.53 0 22.85 | 55.62 Ke eD ee
a 21.31 | 2.59 | 22.06 | 54.04 f
eel 20K | 5.40 | 20.47 | 53.52 BaCly.2H:0 + KCl + Dy.20.
pel Sods h 43.83 | 46.38 CuCl, .2H:0 + Dy.o»
aa 9.94 | 1.46 | 43.22 | 45.38 :
oh 9.88 | 2.99 | 42.07 | 45.06 | CuCl. 2H,O + BaCl.2H,0+ Dhow
i | 20.61 | 5.40 | 20.47 | 53.52 BaCly. 2H,0 + KCI+ Dig.
2 | 16.44 | 4.72 | 27.22 | 51.62 Ba Cly 2H,0 + Dy.o.0-
G” | q1.44 [93.65 | aales | 0.55 :

h 9.88 | 2.99 | 42.07 | 45.06 | CuCl,.2H,O + BaCly. 2H.0 + Dj.»

TABE ES IE

4 ¢3

- Composition of the solutions in percentages by weight at 60° (fig. 2 1.c.).

Point) KCI | BaCl, CuCl, H.,0 Solid phases
a OS... if eo 41.42 | 52.58 CuCly . 2H,0
b 0 6.87 | 43.57 | 49.56 CuCl, . 2H,O ++ BaCly . 2H,0
pe aaa Bi 0 68.3 BaCly . 2H,0
@ | 23.09, | 14.83: | 0 62.08 BaCly . 2H,0 + KCl
aa 32 0 0 68.8 KCI
| |
if 26.12 0 26.57 | 47.31 Kele= Dis
@ | 17:13 | 43.45 | 39.42 Dioce Dia
k | 13.67 0 46.40 | 39.93 CuCl, .2H,O0 + Dy.
S |
b o | 6.87 | 43.57 | 49.56 CuCl, . 2H.0 + BaCl, .2H,O
v |
ES | 6.32 | 5.99 | 43.68 | 44.01 :
O \
l 12.45 4.93 44,09 | 38.53 | CuCl.2H,O-+BaCl.2H.O+D,,
d | 23.09 | 14.83 0 62.08 | BaCl,.2H,O+ KCl ~*
Bos
ES | 23.15 | 10.01 | 12.01 | 54.83 |
O
i | 23.78 | 5.97 | 24.61 | 45.64 BaCl, .2H,O + KCl + Dj.2.0
FA e26u 1b ee 6 26.57 | 47.31 KEleD os
2
Ew | 24.53 3.32 | 25.46 | 46.69 E
a |
i | 23.78 | 5.97 | 24.61 | 45.64 KCI + BaCly . 2H,0 + Dj.0.
medidas |) 0 43.45 | 30.42 Dios Dix
vu
ES, | 16.50 | 2.51 | 42.20 | 38.79 :
O
h | 15.75 | 4.75 | 40.84 | 38.66 BaCly.2H,0 + Dyno + Din
bee See) ree EE ee
k | 18.67 0 46.40 | 39.93 Cue wZHO sa Dig
vu
Em | 13.04 | 2.52 | 45.24 | 39.20 i
O
1 | 12.45 | 4.93 | 44.09 | 38.53 | CuCl,.2H,O+ BaCly.2H,O+ D,,
i | 23.78 | 5.97 | 24.61 | 45.64 KCI + BaCly. 2H,O + Dy.o.
[-P)
ES | 19.53 | 5.40 | 32.37 | 42.70 | BaCl, . 2H,O + D 1.0.5
O |
h | 15.75 | 4.75 | 40.84 | 38.66 BaCl, .2H,O + D, 90+ Diy
h Msierey |) eis 40.84 38.66 BaGly. 2H30 -— Dj.o.0-F Dj.
{Ac 760i) 483 s\) APES) [88526 BaCly.2H,O + D:.,
1 | 12.45 | 4.93 | 44.09 | 38.53 | CuCl. 2H,O+ BaCl,.2H.O+D,4

Vroceedings Royal Acad. Amsterdam, Vol, XVII.

784

Physics. — “On the theory of the string galvanometer of KINtTHOVEN.”
By Dr. L.S. Ornstein, (Communicated by Prof. H. A. Lorentz.)

(Communicated in the meeting of September 26, 1914).

§ 1. Mr. A. C. Crenore has developed some considerations in
the Phil. Mag. of Aug. 1914°), on the motion of the string galvano-
meter, which cause me to make some remarks on this subject.

For a string, immersed in a magnetic field 7, and carrying a
current of the strength -/, the differential equation for the elongation
in the motion of the string is

O*y a Oy ah | JER] (1)
— +x%x— = a — + — a6
Or? ot Ox” 0

in which x is the constant damping factor, a? = —, 7, is the tension

g
and 0 is the density. The direction of the stretched string has been
chosen as the a-axis. For «=O and «=/ the string is fixed, so
y =. In deducing the equation the ponderomotive force is supposed
to be continually parellel to the elongation y, which is only approxi-
mately true, since the force is at every moment perpendicular to
the elements of the string (perpendicular to / and //); but if y
may be taken small, then the equation (1) is valid. The approxi-
mation causes a parabola to be found for the state of equilibrium
with constant H and ./, instead of the are of a cirele, as it ought
to be; however, the parabola is identical with a circle to the degree
of approximation used.

Dr. Crrnork now observes, that the equation (1) may be treated
after the method of normal codrdinates by putting

DD OZ OREN Seo os of IS),

Besides the equation 1, he deduces a set of equations, the “circuit
equations’, which give a second relation between gy; and J (from
(1) there originates in the well-known way an equation for every
coordinate y,). The obtained solutions will be independent, when
the cireuit equation is true, and again their sum is a solution of the
problem. However, from the deduction of the circuit equation it cannot
well be seen whether this is the ease, since not entirely exact
energetic considerations underlie this deduction. Now supposing the
string to be linked in a cireuit with resistance /, and self-induction
L, the circuit-equation may be easily found by applying MaxweEt.t’s

1) Theory of the String Galvanometer of EinrHoven. Phil. Mag. Vol. 28, 1914, p. 207.

785
induction-equation. For in consequence of the motion of the string

in the magnetic field the number of lines of force passing through
the circuit changes to an amount proportional to

Expressed in the units used by Dr. Crenore, the induction-equation
now takes the form:
l

dJ “Oy }
ij EI eal Aah eee 8 oo
dt Ot

0
where /# is an external electromotive force acting on the circuit.

§ 2. The problem of finding the vibrations governed by the
equations (1), (3) and the condition y=O for c=O and «=/,
can be easily solved. First, let E be O, and so the question of free
(damped) vibrations may be put. Suppose that

y = —p er J = Feat
where y is a function of 2and / is a constant. Then the equations
change into

— wf + iwxg — a

Oe eee
0a? fe)

l
0= R14 Liwl + ‘He | gd.

0
Hence
l
Oy iw
@? — iwe*) 4 a = pda.
( NP or dx? o(R+ Liw) ¢
0
: 4 . : ; FH’iw
Putting w* — 7x in the first member n* and Ae =p we
have
3 l
2
Ge
n° p+ a? =s pdx.
ie f p
0
This equation may be satisfied by
n nt :
p=Acs—x+ Bsn—2 + C
a a

provided that

or
bo
Eo

TS6

“a nl a nl :
n? C=p Asin— + — Bl 1—cos—]+ Cl). . (4)
n a dv a
whereas, because of the boundary conditions, we must have
A+. C=
nl _ nl f
A cos— + Bsin— + C=0.
ai a
This gives for the frequency the transcendental equation
nl?
1 — cos -
a nlooa a
np | — = en — = = l
n a n _ nl
sin —
a
or
een _ nl a nl
n* sin — == || Ls — — 1 —cos :
a a 7 a
From this it appears immediately that we must have
_ nl E
Ti PC AE ta! oS (5)
2a
or
¥ nl nl 20) een ;
Ww” COS = p l COS = sin . . . . . (6)
2a 2a n 2a
(5) can be satisfied by
nl
Sica (7)
2a

or, hence

. 2k ra \*
pA all :

As is immediately to be seen, these are the damped vibrations of
even order, which the string can perform in the absence of the
enrrent. It is evident that the presence of current and field have
no influence on the vibrations of even order. [f the resistance is
infinitely great, the constant p in the equation (6) is zero. In this
case the equations can be satisfied by m= 0, or w =0, i.e. the
string is at rest; and further by

nl
cos — = 0.
2a
Hence
nl oy 1 4g 8
Qa — (2 tL + ) 2 . . . . . . . . ( )

787

ae (a)
w* — iwx = | — es)

The frequencies arrived at are those of odd order, altered by
current and field. For large values of R an approximate value of

: : : Ge eas 4)
n can easily be expressed in the form ny + je From (6) follows

N; =n; + Has aes i

ag Oe Ohne ane
s being an odd number, 7 being taken zero, while for w and n, their
values for A=o must be put. Taking x= 0, i.e. neglecting the
air-damping in comparison with the electrical damping, we find
sa 4H*il

Cys 22 Le 9
3 l Ro s°x* (9)
In the solution, therefore, there is a damping factor of the form
4H]
—= t
e Res*x?

The influence of the damping is the less, the greater the value of
s is. This is directly evident, for if s is great, the string vibrates in
a great number of parts with opposite motion. The electromotive
force generated by those parts therefore is annulled.

In case # is small, the roots of the equation (6) are those of the
transcendental equation

nl 2a nl
lcos—= — = sin = (()
2a n 2a
or
2a nl

i) eal Lin, Se ee pa Sa CMa (10) *)

; nl . Xe ee
The quantity >— approaches to odd multiples of —. For small values

of A an approximate form n,--a@R can be easily indicated. Taking
again L—0O and x =—0, we find

2a Ko .

PEP *

where 7, is an arbitrary root of (10). In case the resistance is small,

Oe Se

all vibrations suffer the same damping.
For @ we find

_ nl _ n(l—a) _ ne
sin — — sin — — sin —
2 a a
—— — ie
P _ nl
sin —
a

1) Compare for instance Riemann-Weser, Partielle-Differential Gleichungen, II,
p. 129.

hence for

inl _ n(l—e) _ ne
sin — — sin — sin — .
oy de a a
1 Se Reo on (filthy)
7 _ nl
sin —
a

The real and imaginary part of this expression satisfy the equations
and the boundary conditions. A sum of solutions for different values

. oc : : dy ’ ‘
of @ satisfies the equation. If y and “ate given for {= 0, we can
: dt

with the aid of the given functions find the solution. The found
proper functions are not orthogonal, but by an appropriate linear
substitution orthogonal functions can be obtained. If y is known, I
can be calculated from (3).

§ 3. It is useful to work out the problem. Using the assumption
(2) of Crenork, we obtain for gs, the following set of equations
(taking & and / zero):

= AHS
Pot ns’ Ps = SM Sal) oe (5)
0)
and
21H _ Qs
RB se
Uv s
where
SITA
n= e
3 l

Here s is an odd number; for even values the second member
of (12) is zero, and the even vibrations are therefore unchanged.
Now putting
Ps = ay ett ‘ Ji wlagioln
and
AHI 1

2 2?
8XO Ns? —W

we find
21 Hiw st Lh,
a 8

RE A

The frequency-equation therefore is

81 Tio _ ] é
- = SS Me 5 on so (Ga)

On, ~~ (n;?—o’) a

R+

This trequency-equation has the same roots as equation (6), which
if x and / have been taken O, takes the form

wl ie ( wl 2a , =)
@ cos — = cos — — — sin — }.

2a Ro 2a lw 2a
The identity of these frequency-equations can be easily shown.
Sl H? . ; :
Put i=h, then (6a) takes the form
i} a al Siete Ns W
1s hy = Se Ee — 0
nS a? 8? (ns? —w’)
x?
The sum of inverse squares of odd numbers is 3 Further,
Oo
: Ey dat i : ,
————; therefore the first member amounts to
c
k ase a 1
1——+ 8— & == (0),
i) Pa n—w*
For tg z we have
22
eo
es a 2
tg er? a a te ey
ay
where s is again an odd number, therefore we obtain
k 2a ol
1——-+ —kig—=0 ..... .« (14)
oOo wil 2a
The equation (6) takes the form
wl k 2a ol
@ cos 1— — + ——ktg —— eee en-au (ko)
2 a leo? 2a
The equations (14) and (15) have the same roots, for the vectors
wl ‘ =
wo and cos = do not contribute roots to (15).
atl
Having found the roots of (14), we can determine y. Each root

STL

yields a Fourter series. In the case that (=o), sin must be

combined with one frequency only. For our case we have

a A, iw,t , sTx
y = >, >, ——— -e sin
$ 2 2
s (ns?—w+’)
1 Sa A, 1 xt
= sin =R e co o oe re UG)
‘ ; ;
s l ns —W,

The Fourier series which is the vector of A Dae must be equal
to the function whieh in § 2 appears as the vector of the same
exponential. This can be shown by direct development. It is apparent
that by a given frequency all the original normal coordinates are

790

et into motion. For very great and very small values of R, the
constants A in the expression (16) can easily be determined.
~. We can also use (9) and (11). Let us write (41) in the form

y = emt
: nl
cos
2a
and let us introduce the value of 2 from (9), we then find
4HT?]
nt — —— t >
8 Nagas Ng TR nse
—T Ros* a 1 — cos — i— sin —
a as a
2H tse
where d, = ————. Separating the real and imaginary parts, we find
Rus aC: : :
4 FT?
Sp aaa,
7 Re Regs tae

dé, Nett Nk
— | 1 — cos — } cos ny t + sin sin nst | As
i a a
J, M8 , 5 Pe
ap | = 1 — cos — ] sinnst — sin COS Net
R a a

J. gv st
( — cos ms ‘) As —sin ae B.|
v a a :
dy Nyt J. Nk 4 f*]
ee) | = SS HS Ag —{ 1 — cos B, = Bene
@) oa sre Be a = ( a a ) z Ras*ng 7

l l

ae % swe “y Sma
Putting fr sin dx =a, and _ dz = bs we have
e e 4

0 0

and

ree l
(eae SS = SE
R 2
l eam 2n5 SUB 4H] B
ae As ——~ «at Os Ds San
: 2 R i Ros*ns
2 ; ngl ;
For R=o we get b= — Fei Ss Therefore B.—— = bs
2
and A, = —a,. Putting
Ns
A 2 Ee ts
a Os ==
Ns R
)
Bs
(= — fit =
iy if R

t9L

we have

() = ial = capes i Bs
Ri Ns 2k
ls 8H*b,
0) SS SS SS SS i OS
R IR Res*ns

These series are convergent, if the conditions for the ordinary
Fourtmr.series are fulfilled. We can therefore calculate a, and P, with
the help of the given formulae.

§ 4. In the case # is a given function of the time, our equation
can also easily be solved.
a. First if / is constant, we have
07y Oy O°, AJ

A Ge ae ai 7
l
B=RJ+ | y de.
0

The current / and y ean be divided into two parts, the one
depending on ¢, the other not; we indicate those parts by the indices
1 and 2. For the first part we have

~<a —
ave Q
(T= TPE
therefore
ay, EH
a? ——_ —_——
0a? Re

from which y, can be determined if we take into account that y,
vanishes for «=O and «#—/. The determining of the second part
leads to the problem treated in § 3. The solution can be used in
order to fulfill given initial conditions. If an initial-value of J is
given, then y must fulfill at 40 a condition following from (3).
b. Further, we ean consider the case = EK cos pt.
Putting 1 = 0, we ean try the solution
y = cos (pt + B)
J =I cos (pt + 8)
where g is a function of v. The first equation gives

—pp—a

O°” os Ay

This eqnation can be solved by

792

P ae, o
G~ =A cos z a + Bsin Fa a+ C

or according to the above

pl
HI mat
) a )
Q=- con e— - Be «+d oo (Cl)
Pp a oy yall a
sin —
a

Introducing this result into the second equation, we obtain

Jef Ui
Ecos pt =: RI cos (pt + 8) + —— sin (pt + B)
OP

Se: - +7 }.(18)
p a p , pe
sin—
a
Now take
IN?
=
TET a pl a
sin +lj=tgea
opk p a . pl -
sin—
r

then we find

< P 2
1—cos —1
Jak a ip a a 3
Ecos pt=/14/ R? + —_( —-sin—1 — +1 } cos (pt+-B-a)

Kis P 2 pP sin ue 1
a

From this we find for the retardation of phase, 8 =e; and for
the amplitude of /
[=—
A
where 7 represents the square root in the second member. The
current / being found in this way, y can be determined from (17).
When Z does not vanish, we can suppose y and / to depend on
er; and finally taking the real part, and following the above method
we find the values of y and J.
If we express y by (2), the solution can also easily be found. We
then have

Substituting this into the second equation of § 3 (where zero has
been replaced by £ cos pt) we find

793

PRES eer ead Oy ae 5p A MRE a teeny ges eae
psi? L s? (ns? —p?)
from which J/ can be found. The sum in the second member can
be put in a way analogous to that of § 3, into a form identical
with (18). Our result does not agree with that of CreHorE (compare
p. 214). In our solution the retardation of phase is the same for all
vibrations, which is not the case in Crenorn’s paper.
It may be observed that in our problem we have to do with a

system of an infinite number of variables in which a dissipation-
function couples the variables; for eliminating / from (12) and (13),
we obtain

ele uy

Ps + 2s P= — =e
sok s

The dissipation /#’ takes the form

Groningen, Sept. 1914.

Physics. — “Accidental deviations of density and opalescence at
the critical point of a single substance.” By Dr. LS. OrnstErn
and F. Zernike. (Communicated by Prof. H. A. Lorentz.)

(Communicated in the meeting of September 26, 1914).

1. The accidental deviations for a single substance as well as
for mixtures have been treated by SmoLucHowsk!’) and EINsTwrn *)
with the aid of Bonrzmany’s principle; by Ornstein *) with the aid
of statistical mechanics. It appears as if the considerations used and
the results obtained remain valid in the critical point. SMoLUcHOWSKI
has applied the formula found for the probability of a deviation
to the critical point itself, and has found for the average deviation
of density

He has used this formula to express in terms of the mean density

') M. Smotucuowsk1, Theorie Cinétique de l’opalescence. Bull. Grac 1907 p. 1057.
Ann. der Phys. Bd. 25, 1908, p. 205. Phil. Mag. 1912. On opalescence of gases in
the critical state. W. H. Kersom, Ann. der Phys. 1911 p. 591.

2) A. Einsrernx. Ann. der Phys. Bd. 33, 1910, p. 1276.

5) Ornstein, These Proc., 15, p. 54 (1912),

794

the accidental deviations in a cube, the side of which is equal to
the wave-length of the light used in the experiments on opalescence,

Now there is a difficulty with this formula, to which, indeed,
lead also the considerations of Ernsruin as well as statistical mecha-
nies when worked out in an analogous way for the critical point.
In all these cases the mutual independence of the elements of
volume is presupposed. Now, let there be given for the element of

volume v the mean square of deviation viz. (n—n)*. Consider p

equal contiguous elements of volume v,,v,, ete., in which n,,,, ete.
particles are situated, 7,,7, ete. indicating the mean values of these
numbers.

Hence in the volume V=v,-+2,-+... there are N=n,-++n, +...
particles.
_ For the mean value of NV we have

N= sem er we.

subsequently

(N — WN)? = ((n, — n,) + (n, a) SS e Pe ae
since, the elements of volume being supposed independent of each
other, the means of the double products vanish. So we find for the
deviation of density that the product of volume and mean square
of deviation must be a constant.

Indeed the above-mentioned formula of probability for the devia-
tions of density is so far inexact, as the terms of higher order
appearing in if are at variance with the mutual independence of
the elements of volume, which underlies the deduction of the fre-
quency-law. In fact this deduction is only valid for such large elements
of volume that these terms are no more of any influence. It is
easily seen that this limit, above which the formula is valid, in-
creases indefinitely in approaching the eritical point. This explains
also mathematically the wrong dependence on v found for the mean
deviation in the critical point itself.

Now one could try to deduce the formula to a farther approxi-
mation. However, also the supposition of independence of the ele-
inents of volume is inexact in case these are small, and it would
thus be impossible to ascertain how far the formula would yet differ
from reality. *)

1) A deduction of the inequalities in which the inexact terms of higher order
do not at all appear, is given by ZeRNiky in his ‘thesis, which will shortly
appear. As this deduction too uses the independence alluded to, the objection men-
tioned holds here also.

The remark of Euyster (lc. p. 1285) that there would be no principal difficulty

795

2. Now, in order to avoid the difficulties mentioned, it is necessary
to take into account the influence of deviatious in the one element
on the state in another. Let us divide the system into infinitely
small elements of volume. A molecule is considered to lie in the
element when its centre is situated in it. We consider an element
dv, in the origin of coordinates. Around this element we imagine
the sphere of attraction i.e. the region in whieh a molecule must
lie when it is to have any influence on the state in dv,. We determine
the numbers of moiecules for the elements of the sphere of attract-
ion in giving the deviations »,,r, etc. from the mean number of

molecules per unit of volume.

We suppose the mean value of the density »,, when », etc. are
given, to be a linear function of the deviations y, ete., i.e. we put’)
De C eipardia falda ese 14 ke 8.0. (ll)

Taking the mean value of », over all possible values of »,, it

0
appears immediately that C= 0, hence
De ide eed O ee eehg San At ont (2)
The coefficients 7 denote the coupling of the elements, they only
depend on the relative coordinates, i.e. here, on «yz. That the in-
fluence of an element, when the density is given, must be propor-
tional to its size is immediately seen by considering the influence
of uniting two elements in (2).
We shall now write the sum (2) as an integral. For the density
in the element dv dy dz we put v,,-; further, we can dispose of /
in such a way that 7(9,0,0) =O. Then for (2) we get

Rae
m= {ff ise inane) Cuan we 8 Va ve (8)

The integration may be extended here from —o@ to +m, /
being zero outside the sphere of action *).

in extending his deduction to a further approximation, is therefore mistaken. On
the contrary, the consideration of higher terms so Jong as the independence is
made use of, will not lead to anything.

1) Putling things more generally, we could write a series in Y, ete. instead of
(1). However, for the purpose we have in view, (1) is sufficient.

2 The quantity » can only take the values 1—adv and —adv, hence » is a
discontinuous function of the coordinates. One might be inclined therefore, to continue
writing a sum instead of the integral (3) and to solve the problem dealt with in
the text with the aid of this sum. In doing so one gets sum-formulae which are
wholly analogous to the integrals we used. However, we prefer introducing the
integral, as the discontinuous function v has entirely disappeared from formula (6)
only the function g appearing in it, which is continuous when the function / is

796

On the contrary, if », is given, > has another value for the
surrounding elements, than if », = 0. Be in the element at xyz
Dive SSO DOr ed a bd B 0 0 o (4)
and let us try “to determine the function g, the function / being
given.
Now take the mean of formula (3), a fixed value », being ascribed
to yp in a certain element dv, dy, dz,.
In w, y, z, according to (4)
Veyz = g(&@—2,, y—y,, 2—Z,, v, dv,dy,dz,). ». - . (0)
For the first member we therefore get
Ht, Ys 2, v,de,dy,dz,)
as jf and g do not depend on the direction of the line joining the .
elements. In the integral, (5) cannot be applied to the element
dx, dy, dz,; owever, this element gives
Di Fi (@anyan ey) cn ay az.

Further taking g (0,0,0) zero, as it may arbitrarily be chosen,

we get
4
G(@ 454 132,50, 42, dy, dz,) = [ foe#rane-sumdondin de) fey? dadydz-4-
e/fe
—o

= Dif (#141921) dx, dy,dz,.
This is true for all values of », dz, dy, dz,, hence g must contain
this quantity as a factor, and we obtain

Now put e«—a,=6& y—y, =, z—2z,=5, and omit the index,
then for g we get the integral equation

+a
a5y/,2) a [Jr +§, yt, e+) o(Sy6) d&dyd> = f(xyc). . (6)

For g we have
Dayz = 9(ey2) Dis ss 5 oe ee
from which it appears immediately that

Daye v= y(ayz) v,? Cer oS 5 ((e)

continuous. The integral-formulae obtained in this way are easier to deal with
mathematically, and besides the integral equation (6) has been solved, this being
not so easily found from the analogous sum-formula.

797

Now let us consider more closely the coefficient of g in (8).

Let a molecules be present in the unit of volume, then the mean
number of molecules in dv is equal to adv. If we take dv very small,
there may be no or one molecule in it. The chance for one molecule

l
is, therefore, adv; for none 1 — adv. In the first case » = Ey a,
av
in the latter it is — «a, thus
z a .
D> = — — ar
du
or
Baye ee eS, Ue ete tee ee (9)

Introducing this into (8), we find for the two elements «,y-2, and

UY Ze

pv. = a — Vey Ys— Yry 25—2r) : . : . : (10)

This result can be used to indicate the values of (W—NV)? = A N?
for any volume.
We have

JIN = fra

AN? = foe dv, dv- +{{ rv. da, dy; dz, dz- dy~ dz-

VV VV

from which applying (9) and (10)

AN? =aV-+a g (@s— 2x, Ys —Yry 22 —2z) daz dys dz, dz, dy- dz.
VV
This holds for every size and form of V. Elaborating it for a
cube with side / the dependence on |’ is seen more clearly. Putting
Lf — kt, = 6, Yo — Yr =, 2% — 2 = $, and integrating only for $45
positive, by which '/, of the integral in question is found then, we get

U az l Li
AN* = N+ 80f {fotsnt) | { (ae dye de
000 gus
Ee
ee so | (PP ($4445) + lGyt+ 8+ 55) — Sud) g ds dy db.
000

79S

é +] Jay)
AN? ap “rr
2 = | g (ayz) dedydz — 3 {ff — gq dadydz
N a/e/e aes e/eu l =
oe ®,
+1 ane
even “77 |a°|
3) — gda dy dz — —_q dx dy dz.
arg) ney

Every integral in this formula is always smaller than the prece-
ding one. If / is large with respect to the distance for which g has
an appreciable value, there remains only the first integral. For
any great volume we have

= = 1+ oda dyidz ~~ =) aes)
3. In trying to determine the function / by means of statistical
mechanics, we meet with difficulties. Still something may be found
about the quantities v.»- by applying the statistie-mechanieal method
to our problem. Indeed statistical mechanics permit to introduce a
mutual action of the elements of volume.

We will avail ourselves of a canonical ensemble. We suppose the
moleeules to be spherical and rigid, and to attract each other for
distances which are great with respeet to their size. Elements small
with respect to the sphere of attraction therefore may still contain a
great number of molecules. But now we drop the supposition of the
sphere of attraction being homogeneously filled for all systems (or
at least for by far the greater part of them) *).

In calculating the number of the various distributions, we
must, for the potential energy of attraction, take into account the
mutual action of the elements; whereas, in calculating the exclusion
of definite contigurations of centres, we may neglect the fact that
there is some correlation on the borders of the elements. For the
dimensions of the elements have been supposed large with respect
to the molecular diameter.

The mutual potential energy of the » +7 molecules contained in
an element dv, will be represented by

in this formula » represents the number of molecules contained in
the volume dy for the most frequent system. In this system the
distribution is homogeneous.

) Cf OrwsSTEIN, Toepassing der Statistische mechanica van Gipss op molekulair-
theorelische vraagstukken. Diss. Leiden 1908, p. 43 and p. 110.

799

Of course, the potential energies will not strictly be the same for
different configurations within the elements, but we shall neglect this
complication. Further we will represent the mutual potential energy
for the two elements o and 9 by

== (Oa a) (Bhat T2) Pos
does: xt Hi
all elements of volume being put equal.
For the total potential energy we find, in this way

l
ey aT Sines ee
oa +- %) &_(Y + To) cr.

For the frequency §¢ of a system with the given distribution of
molecules we find

les 2 »
nf ——— Selves) Sp Wr) os
F(—— — Or dV) Ee «(o, dV y IT p2Odv ‘
(v1, Ww-tr, Hie

Here w is the function defined in the quoted dissertation on p. 48.

Supposing & & py and developing, we get,

1 1 Ila) 1 Loy !
— na Pee § (— a gee si et

S—C wr a-” e Y vp da da Odv

The number of molecules per unit of volume represented there
by n, has been put @ in this paper. The function @ and the faculties
are developed in the same way as in the quoted dissertation. The
double sum in the exponent gives the forms +.» u1-y7.,and +12 ry...
These forms are identical, as they consist of the same terms differ-
ently arranged, further 2y., is the same for all molecules and
Yt. = 0, consequently both sums vanish.

The constant C' contains the factor / Tew/O

do not depend on the volume by summing up (12) over all possible

along with quantities which

values of < (and taking into account that +r; =O) we get JN, the
total number of systems in the ensemble. So we find
) 2
— Y all ae 3S ¢ oc
e O— _—_ wy Vn 929 4
VA

the quantity A being the discriminant of the quadratic form in the
exponent.

When we write 2,9,; =a, we find for the pressure p= — —

53
Proceedings Royal Acad. Amsterdam. Vol. XVII.

800

Den dlgw aw
SS SP i SS
7) J dy

A—s being very small with respect to the other factors, we may

20. V?

neglect its influence in w?'). The equation of state has the same
form as vAN perk WaAALs’ equation. However, the correlation is sensible
in the accidental deviation; for it changes the value of 17; and
rt, which vanish if the correlation is neglected, obtain values
deviating from zero.

Denoting by A. and by 4,. the minors of the discriminant,

we have

= = (k—1)

“ 7,02 = — (k—1) ’)
A
where J is the number of elements into which the volume is divided.
as if Res tea Oe) E
rhe condition &4 =O is equivalent to the condition = 0; For
au
if we write down the determinant in some arrangement, and if we
add all rows to the first row, we get a determinant of which all
terms of the first row have the form
l ld .dlgw 1

| a =
Y yp da da Odv

NPs:

Strictly speaking, this is not true for some terms at the end of the row,
but as we have neglected the action on the borders, we may neglect
this fact too. In reality our considerations are only true for an infini-
tely great volume, where this difficulty disappears, as A is then an
infinite determinant.

Now if

De eee

— U = i=
yp Y da Odv oe
then Ay—10)
OrmitAv=="()
d _dfw a
——a ~—+ —-a=0
da da (0)
i ; _, dp
which therefore agrees with 5 = (i),
dv

1) Cf Le p. 129.
2) Cf. Ornsvery, Accidental deviations in mixtures. These Proceedings 15,
p. D4, (1912).

801

The quantities rr, ete. here found are related to those mentioned
above. And though a statistical deduction of the function / enter-
ing into details’ may lead to difficulties, yet it is clear that
statistical mechanics yield a correlation analogous to that expressed
in g.

If we should wish to continue the deduction of the conditions of
the critical point, we should have to use higher powers of r,, which
can be done without difficulty; we then find for the second condition
ee)
de?

If we drop the supposition that the sphere of attraction is large,
we can use the function %, defined in the quoted dissertation. In
order to take into account the correlation, we must suppose the
integrals

é Gh Pon oc dan Tt, w (n,)

r — &/0

defining %, to depend on nz for the element in question and also
on the numbers of molecules in the surrounding elements. Therefore,
in general, the numbers of molecules of all elements will appear in
: O9n,
9n, , but the influence of distant elements is so small that ——
Ne
‘an be put zero.
By considerations analogous to those used in the quoted disserta-
tion, we can show that %(n,) has the form
Ny Nx
V, (@ dy Dy, Dy)
in which n,n, denote the densities (molecular), in the elements
with which V, is in mutual action. The values of all n, are equal
for the most frequent system.
Now we find for ¢
Ga nia (uns ny Ms ts eae
where P is a quadratic form in the deviations for the various
elements, containing squares as well as double products. The form
might be easily indicated, but we will omit it, as it is only our
purpose to show how in general the statistic-mechanical considera-
tions, changed in the sense of a correlation of elements of volume,
lead to formulae analogous to those given in § 2. Here too the
mean square of deviation and the means of double products are
represented by quotients of minors of the discriminant of P and

eeu : the “Freee :
this quantity itself. Here too for : =0( the discriminant vanishes.

av
53%

802

4. The above considerations can be applied in ealeulating the
critical opaleseence. For that purpose we use the simple method
indicated by Lorentz"), whieh consists in superposing the light-
vectors caused by the intluenee of every individual molecule in a
point at great distance.

Consider in the substance through which a beam of light passes,
a volume J” great with respect to the wave-length, and take a distant
point P, the direction |7P forming an angle gy with the incident
Tay.

All molecules lying in one plane perpendicular to the line which
Take therefore a
system of axes with the Z-axis parallel to this line, then the con-

bisects the angle y, will cause equal phase in 7.

tribution of one molecule will be

_ Qa
B sin — (ct + 22 cost gp)
ud

where p. depends only on the kind of molecules, on 4 and on the
distance |’P, w being the index of refraction.
The number of molecules in dv dy dz amounts to
(a + v) dex dy dz.

The total light-vector in P? thus becomes

2 fe +r) sin = Ae +22 cos bq) da dy dz.

:
and the intensity
pile
»
re _ 2a
Bp? ell [J a-+ p;) (a +-v-) sin — (ct4-22, cos } gp)
ud
) are

on
sin

\-
~

~—

dx; - dz, dv. dy- dz-.

Integrating with resp. to /, we get

. 4n } -
ae: # {fie -a(v,+ py.) -| v.»-! cos a (2,—<-) cos 8 y } da, dy,dz,da,dy-dz..
uA
VV

The-mean value of this must be caleulated. The term with », +- v-
vanishes, and that with a? yields no contribution proportional to V.
We introduce the value of »,»- from formula (10), and for c=t
from form. (9). This gives

1) H. A. Lorentz, On the scattering of light by molecules, These Proceedings 13
p. 92 (1910).

803

— ap : ay ie ) = ( =v ) i ]
i = Yes Wr, a Yrs So ez SNe Sr) diigo + MY =
ali av -{- Ee [fo (Ws Ury Y UE cos 0 7]
VV

For a great volume one integration over VV can be performed

(compare the deduction of formula (41)); further we put aV=N

. Ax
and for the sake of brevity —cos}gy=C, then we get

{ur
Ps
1 — ws ye
ue Als J feos Cz (#, y, 2) dadydz 5 oie 4(t8))

The integral appearing here will be represented by G,, that of
formula (11) by G. It will be seen that the deductions criticised in
§ 1 yield an opalescence proportional to v*,a quantity which accord-
ing to the above is proportional to i + G, whereas the opalescence
is proportional to 1+ G.

With the aid of the integral-equation (6) we can express G and
(, in the corresponding integrals of the funetion f. which we will
indicate by / and F..

Integrating (6) with ah to xyz eat —o to + om, we find
=
[J fo wyz) da ty de (fos smi ffi + §,y +-3),2 +$) dudyde=
de
ne
{ffi ‘(ayz) dndydz
or i
ean At eh od
1—F
Multiplying (6) by cos Cz and again integrating, we get
pa as al
G. — SL (S75) azine f fosc (2+$) cos CO4- sin C (z +8) sin CS

——@
F(@+§, y+n, 248) dedydz = F,.
The integral with the sines disappears because / and g are even
functions; we find
F.
(a ek ie |)
1— Ff,
In order to apply the results obtained and to test them experi-
mentally, one might try to deduce f from molecular theory. This
would at best be possible under very simplifying suppositions and

S04

even then only an approximation can be obtained. Therefore we
will take another way. As remarked in § 1, the exact value of x?
for very great volumes was already known. In our notation we have

=) TEP ae
; cio aN dp
yeas

where .V is the number of AvoGrapo, v the molecular volume.
According to formula (4) we have

In the critical point = 1. ')
The formula of opalescence first arrived at by Kresom and Ensrern

1) There appears to exist a closer correspondence between the given statistic-
mechanical method and the method using general considerations of probability, than
perhaps might be expected. The elements of the discriminant (which is an infinite
determinant in the former) agree with the function f in the latter. The former finds
from this the value of ¥- vz as the quotient of a minor with that discriminant,
the latter deduces this value from an integral-equation. In the critical point the
discriminant vanishes, corresponding to this the FrepHotm determinant of the
integral-equation is likewise zero. Thal this is the case when /’=1, appears by
more closely studying the equation

a (Sys) — i fo (S76) f (@-+8, y+, -+$) d§dnd§ = 0

which only permits appropriate solutions if 1= >, (i e. this is the only proper

I
value). For /=1 this is therefore the case with the equation (6) without second
member.
From the formula (15) it will be seen that form. (6) can be solved by aFourtER
integral. Putting

+a
l| {eo ma cos ny cos lz f (wyz) dadydz = —p (m, n, 1)
afte
—o
we have ‘
+a
1 “CC pm, n, 2)
g (ayz) = ———— cos mw cos ny cos lz dmdndl.
82° JIT 1—e(m, n, 1)
wo

805

(#)
ee | =
Top, 22°V RIT dv
Ope ie Aioast eee berate. 5s 2, (16)

BE DPR Pa

in which represent
PD distance of observation
mw index of refraction,
y angle of electric force in ineident light with direction of
observation,
will likewise be found by using in (13) the value found for instead
of #.. The exact formula then will result by multiplying by

2 2)

* f(ayz) dedydz.

bass

||
ro} Q
23

Representing this integral by « and introducing the value of C,
we get
7 7 2 é %
F— F.= 4n’ (1 + cose) { —}).
te
The formula of opalescence then will be:

Top. ID Iss dv
= = BS aed enol KC)
i dp RI El\a
— — + 4n*? — (1 + cos)
dv vy a2
In the critical point itself it therefore is
1 2
ONS ae ere w
Lop. J dv
—— eG eee lee age Oe)

IT Dt Ne (t + cos)

The greater exactness of form. (17) as compared with (16) is
5

confirmed by the measurements of one of us (Z.). According to these

measurements, which however bear upon a mixture of liquids the

1) According to this formula the proportionality of the opalescence to d~4,
which holds for higher temperatures, changes continuously in the immediate
neigbourhood of the critical point, into proportionality with %—2. This rea/ “getting
whiter” of the opalescence should not be confused with the appurent changing of
colour which is always observed much farther from the eritical point. The latter
indeed is only a result of the method of observation, as is clearly proved by the
measurements of one of us (cf. ZuRNIKE thesis).

806

reciprocal value of a quantity proportional to the opalescence changes
linearly witb the difference of temperature 7’—7;, but by extrapolation
does “not vanish for 27. “but for 777 — 10.0125 aWihen
therefore for this value of 7—TZ;, the denominator of (17) is equal
to zero, we can find from this, using VAN DER Waats’ equation, an
estimation for ¢/,. The calculation yields :

€ A »
= = 00,0022 or ¢ = 1,2.10—* em.

The quantity «is a measure for the size of the sphere of attraction. For

+x
1
— Affe T (eyz) dadydz
o -

(go distance to origin) whereas in the critical point
of

{ F (wyz) da dy dz=1.

ve}
If f were constant within a sphere with radius R, then «* would
be */, R?, and the above estimation would give

el Omercits

SUMMARY.

1. The known formulae of critical opalescence give an infinite
value at the critical point. Efforts to escape from this difficulty have
furnished formulae for the deviations of density with a dependence
upon the volume, at variance with the assumed mutual independence
of the elements of volume.

2. In order, to obtain formulae applicable in the critical point, it
is found necessary to take into account the mutual influence of the
elements of volume, it being shown that near the critical point this
influence is sensible for distances large in comparison with the radius
of the sphere of attraction.

3. Two functions are introduced, one relating to the direct inter-
action of molecules, the other to the mutual influence of two elements
of volume. An integral equation gives the relation between the two
functions.

4. Corrected values are found for the mean deviations, and in
the formula of opalescence a correction is introduced. The latter
depends upon the sphere of attraction which can thus be calculated
from observations.

5. Further it is shown that the same results may be arrived at
by taking into account the mutual influence of the elements of
volume in the deductions of statistical mechanics,

Groningen, Sept. 1914.

A. A HIJMANS VAN DEN BERGH and J. J. DE LA FONTAINE SCHLUITER. ,, The identification of
traces of bilirubin in albuminous fluids.”

Bilirubin from human ascites fluid 3ilirubin from human ascites fluid
(Aether-method) (Chloroform-method)

Proceedings Roval Acad. Amsterdam, Vol. XVII.

807

Physiology. -- “Zhe identification of traces of bilirubin in albu-
minous fluids.” By Prof. A. A. Hismans vaAN bEN BrrGu
and J. J. pe ua Fontaine Scuiurrer. (Communicated by
Prof. H. J. Hampureer).

Several investigators have tried to demonstrate the presence of
slight quantities of bilirubin in albuminous substances, for instance
in normal human bloodserum. Most of them did this by adding
various oxidizing substances, either directly to the serum or to an
alcoholic extract of the latter. The first oxidation-stages of bilirubin
having a green or a blue colour, the presence of bilirubin was
regarded as established if an addition of these oxidizing substances
eave rise to a green or a blue colour (OpeRMAER and Popper, STEIGER,
Gitpert') and others). AvucnHé*) employed a much more reliable
method based on the fact that bilirubin, in alkalic solution in the
presence of oxide of zine, is changed, by careful oxidation with
iodine, into a substance with a characteristic spectrum. This reaction
had already been deseribed by Sroxvis, but Avcné, who mentions
Sroxvis’ work, owns the merit of having stated accurately the con-
ditions required if the reaction is to take place with absolute cer-
tainty, so that it may be used to demonstrate the presence of bilirubin.

Undoubtedly the reaction of Sroxvis-AucHE can be used with success.
Only the spectrum-line is very slight in the case of the small amounts
of bilirubin dealt with in this treatise: if the presence of bilirubin
is to be demonstrated in normal human serum by means of this
method, the layer of fluid intended for spectroscopic investigation is
to have a thickness of ten centimetres. And even then the result is
not always a positive one. For quantitative determinations this method
cannot be used.

Bieri extracted the serum at once with chloroform and carried
out his reactions with this *).

The reaction of Enrucn has supplied us with an excellent means
of tracing bilirubin in bloodserum and other albuminous fluids and
of determining it quantitatively ‘). The characteristic difference in
colour between av alkaline and an acid medium increases its relia-
bility, whilst the reaction is an extremely sensitive one. It must,

1) OBerMAWER u. Pepper. Wiener Klin. Wochenschr. 1908.

Sreicer. Dissert. Ztirich 1911.

Gitpert. See for his werks the bibliography in: Clinique médicale 1910/1911.

2) Aucueé. Compt. rend. Acad. d. Sciences 108.

3) Bieri. Folia Haematolog. 1906 ILI. 189.

') Hismans van pEN Berg and Snapper. Deutsch. Arch, f. klin. Med. 1913,

808

however, be admitted that neither this nor any other colour-reaction
enables us to identify the presence of bilirubin with absolute certainty.
The possibility of other substances contained in the serum giving
the same reaction with the diazo-body may be esteemed less probable,
it cannot with absolute certainty be denied.

As far as we know it has hitherto been found impossible to
isolate bilirnbin from normal human serum, which would have
afforded an incontestable proof of its presence. HAMMERSTEN has
attempted it’). But though in a great majority of cases he obtained
fine bilirubin-erystals from horse-serum, he never succeeded in ob-
taining them from normal human serum. From the terms used in
the latest edition of his Handbook of Physiological Chemistry we
eather that this investigator is not quite convinced yet of the presence
of biluribin in normal human serum.

With a view to researches on anhepatic bilirubin-formation we
needed a method which would enable us to identify with absolute
certainty the presence of small quantities of bilirubin in bloodserum,
exsudates and transsudates, if possible by obtaining the pigment in
the form of erystals. After some experiments we have succeeded in

this, starting from the property of bilirubin — which we have not
found mentioned anywhere — of dissolving readily in acetone.

To 10 em*. of bloodserum 20 em’. of pure colourless acetone are
added. An albumen precipitate is formed, which is centrifugalized.
The fluid at the top, coloured more or less intensely yellow, contains
all the bilirubin and only traces of albumen. This liquid is evaporated
in vacuo at the ordinary laboratory temperature.

If one has a good vacuum-pump at one’s disposal the liquid soon
begins to boil; after some minutes the acetone is evaporated. A watery
fluid remains in which, besides other serum-substances, all the bili-
rubin is dissolved. Then the fluid is shaken 2 times or more with
aether to remove the fatty bodies as much as possible.

These pass into the aether which is pipetted. The last traces of
aether are removed in vacuo. The aether may of course also be
removed by means of a separatory. Then a certain amount of chloro-
form e.g. 2 em*. are added, the fluid is slightly acidified with HCl
and shaken. The bilirubin then passes into the chloroform. By centri-
fugalization the watery fluid can easily be separated from the chloro-
form. The chloroform is washed thoroughly with water to get rid of
all the hydrochloric acid and centrifugalized onve more, the water being
removed by means of a separatory or by pipetting. Traces of water,
however, remain mixed with the chloroform, which sometimes renders
; 1) Hanmarsren, Maly’s Jahresber. 1878 Il. 119.

809

the fluid slightly troubled. These traces of water are removed by
shaking with glowed sulphate of sodium. The latter is removed by
filtration. The result is a very pure solution of the yellow pigment
in chloroform (solution A). It may be easily proved that this yellow
pigment is bilirubin.

1. If the chloroform solution is shaken with diluted KOH or NaOH
the pigment passes into the latter, while the chloroform loses its
colour (solution £).

2. If now some acid is added till the fluid reacts distinctly as an
acid, then the fluid at the top loses its colour, the pigment passing
into the chloroform at the bottom.

3. If to the alkaline solution (see sub 1) HNO, containing some
HNO, is added, the result is the well-known colour-play of the reaction
of GMELIN.

4. If a slight quantity of a diluted iodine-solution in alcohol
(1: 100) is carefully poured on to the alkaline solution, a blue ring
is formed.

5. If to the alkaline solution first an equal volume of alcohol is
added, and then +} of the original volume of the diazo-mixture ot
Enriuicu, a red colour is the result. An addition of a few drops of
concentrated HCl changes the red colour into blue.

_All these reactions together, prove conclusively that the pigment
obtained in the above way is indeed bilirubin.

Crystals of bilirubin can be easily obtained from the pure chloro-
form-solution (sol. A) in the following manner. The latter is poured
ont into a wateh-glass which is covered with another watch-glass
and placed in the ice-safe. The chloroform evaporates slowly and
on the watch-glass the microscopically visible, pretty, yellow bilirubin-
crystals are left. When HNO, containing HNO, is added, these
crystals present under the microscope the reaction of Gmrnin.

We can also dissolve the yellow crystals again in some solvent
(chloroform, dil. NaOH ete.) and carry out the above-mentioned
reaction with them.

If one has no good vacuum-pump at one’s disposal the method
ean also be applied with the following modification suggested by
Dr. SNAPPER.

10 em* of bloodserum are precipitated with 20 em* of acetone.
The albumen-precipitate is centrifugalized. To the pipetted upper-
fluid some drops of water are added; then this fluid is washed
carefully with aether a few times, to remove the fatty substances
as much as possible. These volumes of aether are removed with
the pipette every time. Then some drops of ice-vinegar and 1 em*

810

of aether are added to the fluid. All the bilirubin passes into the
mixture of ice-vinegar and aether, which separates entirely from
the fluid underneath. If this yellow-coloured aether is pipetted and
placed in an ice-safe in a loosely covered watch-glass, we likewise
observe that crystals are formed.

The accompanying ~ picture is a micro-photograph of bilirubin
crystals which we obtained from the ascites-fluid of a heart-patient,
and from normal human serum.

Attempts to produce bilirubin-crystals by the above-mentioned
method from the intensely yellow-coloured serum of two icterus-
patients, led to a remarkable experience. If namely we placed the
chloroform-solution which, as appeared from various reactions, con-
tained much bilirubin, in the ice-safe, for the purpose of a slow
evaporation, the yellow colour at a certain moment when, owing to
the evaporation of the solvent the concentration had reached a certain
value, suddenly passed over into a green one, evidently by a change
of the bilirubin into biliverdin. The same phenomenon occurred
when we evaporated the chloroform-solution in vacuo. It must be
distinctly understood that this occurred only with the solution obtained
from the serum of patients suffering from obstructive jaundice. We
cannot give an explanation of this phenomenon. Most likely the
icterus-serum contains substances promoting the oxidation of bilirubin
into biliverdin.

Botany. — “Gummosis in the fruit of the Almond and the Peachal-
mond as a ‘process of normal life.” By Prof. M. W. BrisErinck.

(Communicated in the meeting of September 26, 1914).

[t has hitherto been generally accepted that the formation of gum
in the branches of the Amygdalaceae always is a process of patho-
logical nature. I have found that this opinion is erroneous, and that
gummosis occurs normally in the fruits of the Almond (Amygdalus
communis) and the Peachalmond ( Amygdalus amygdalo-persica )
DunameL Dumoncrav. *)

1) In some Dutch nurseries the peachalmond is simply called *Almondtree”.
The difference is in fact very slight as it consists only in the drying up of the
almond fruit before the epicarp opens, and the position of the flowers in pairs,
whereas the fruit of the peachalmond remains fleshy even at the dehiscence, and
its flowers are mostly single. Between leaves, flowers and branches no con-
stant differences are found.

GRENIER et GopRon (Flore de France T, 1, Pag. 512, 1848) call the peach-

S11

Contrary to what might be expected the phenomenon is the more
obvious as the trees are better fed and more vigorous. In specimens
on sandy grounds it can only be observed with the microscope.

As gummosis is the effect of a wound stimulus, if is of import-
ance that this process also takes place in the normal development
of the healthy plant. The subject is moreover of practical interest.
All the chief facts relating to gum formation can almost unchanged
be apphed to the production of gums in general, of gum resins,
and of resins, among which are substances of great medical and
technical value. As the study of the influence of parasitism has made
it possible to produce gum, and no doubt many of the other sub-
stances mentioned, in a more rational way than has been done till
now, a short review of the whole subject seems not superfluous.

Wound stimulus as cause of gummosis. Poisoning, and
parasitism also causes of this stimulus.

Gummosis in the Amygdalaceae is a process of cytolysis, whereby
young cells, freshly sprung from cambium or procambium, and
sometimes also young parenchyma, are more or less completely
dissolved ‘and converted into canals or intercellular spaces, filled
with gum. In dissolved parenchymatous tissues usually remains of
not wholly disappeared cell walls are found; the gum of the phloem
bundles is more homogeneous, but always the microsomes of the
dissolved protoplasm are found. The nitrogen of the gum springs
from the dissolved protoplasm.

Formerly we proved’) that by such different causes as poisoning,
parasitism and mechanical wounding gummosis may be experimentally

almond Amygdalus communis var. amygdalo-persica. At present the name
Amygdalus persicoides (Koon, SERINGE, ZABEL) is also used, as in the Hortus
of the University of Leiden. The opinion that it is a hybrid is not sufficiently
founded. When grown from seed the tree seems constant (see Mreter’s Conver-
sationslexikon, Articles “Mandel’’ Bd. 11, p. 853 and “Pfirsich” Bd. 13, p. 782, 1896)
and identic with the “English almond”, of which Darwin reproduces a stone
(Domestication, 2nd Ed., Vol. 1, p. 858, 1875). The fruit is fleshy and bursts
open, the kernel is edible, not bitter. At Delft sowing experiments have been
going on a long time already, but under unfavourable circumstances. The root
cannot resist the winter temperature of the soil, hence, grafting on the plumtree
is required.

1) M. W. Bevertnck et A. Rant. Excitation par traumatisme et parasitisme, et
écoulement gommeux chez les Amygdalées. Archives Néerlandaises, Sér. 2, T. Il,
Pag. 184, 1905. — Centralblatt f. Bakteriologie, 2te Abt., Bd. 15, Pag. 366,
1905. — A. Rant: De Gummosis der Amygdalaceae. Disserltatie Amsterdam,
Bussy, 1906.

provoked in many Amygdalaceae, as almond, peachalmond, apricot,
peach, plum, cherry, and bird’s cherry.

But these three groups of causes may all be considered from one
single point of view, by accepting that gummosis is always the effect
of a wound sumulus, proceeding from the slowly dying cells, which
are found as well in every wound, as at poisoning and parasitism.
These dying cells may change into gum themselves, but besides, exert
their influence on cambium tissues to distances of some centimeters.
This distance-influence is the principal effect of the wound stimulus.
But poisoning by sublimate or oxalic acid, introduced under the bark,
can as well excite gummosis as an incision or a wound by burning
or pricking. Neither the dead cells nor the poison are the active
factors here; the stimulus proceeds from the slowly extinguishing cells,
so that gummosis is essentially a necrobiotic process. Probably the
dying cells, after the death of the protoplasm, give off an enzyme
or enzyme-like substance, a lysine, fixed during active life, but, which
being freed by necrobiosis and absorbed by the young division produets
of the cambium causes their cytolysis. This reminds of the eytolysimes
of the animal body, originating when foreign cells are introduced,
which liquefy the corresponding cells, for example the haemolysines
which dissolve the red blood-cells. Furthermore of the bacteriolysines
and of cytase, the enzyme of celiulose.

If the hypothesis of the existence of a “gumlysine” is right, — and
I think it is, — this substance must be of a very labile nature, for
when bark wounds are infected with gum, quite free from germs
of parasites, no more abundant gummosis is observed than at
mechanical wounding only. But a difference, however slight, will
certainly exist.

Gummosis produced by wound stimulus.

The influence of this cause is best studied in the following experiment.

A deep wound, penetrating into the cambium of a branch of
almond or peach, commonly soon heals completely, but it may be
that gum flows from the wound. This is the case when the trees
are in sap, thus in February or March at temperatures above 20° C.
and below 33° C. The experiment succeeds best with cut branches
in the laboratory. When the wounds are made in the open air in that
season no gummosis ensues, the temperature then being too low.) In

1) If the wounds are infected with Corynewm, an extremely copious gum production
follows in spring, as the parasite then finds abundant food in the branches. There
is, however, no season when wounds, infected with Corynewm, do not sooner or
later yield gum.

813

summer the cambium of the still longitudinally growing part of
young green branches may be caused to form gum by punctures or
incisions, but these wounds heal quickly, except when ‘kept open”
by Coryneum or other parasites.

As to thicker branches, wounded in spring, the microscope shows
the following.

Around the wound a great number of gum canals are formed in
the cambium, about parallel with the axis of the branch, some centi-
meters long, which become the thinner and shorter as they are
more remote from the wound. The canals are separated by the
medullary rays, which are with more difficulty converted into gum than
the phloeoterma. All the gum canals together form a kind of net-
work, whose meshes are filled by the medullary rays. The whole
network has the shape of an ellipse, the “gum ellipse’, the wound
lies in the lower focus towards the base of the branch. The stimulus
extends over the ellipse, evidently farthest in the direction of the
branch, less far towards the base and sideways. So it may also be
said that the wound stimulus extends farthest opposite to the “de-
scending” current of nutrient inatter, following the phloem bundles,
or along with the “ascending” water-current, following the wood.
Evidently the gum canals are more easily formed in the better fed
ceils above the wound than in those beneath it, where the nutrition
must be worse. This is especially obvious in ringed branches. Wounds
in the cambinm, directly above the ring produce much more gum
than those immediately below. ’)

Under ordinary circumstances the branches, after simple mechanical
wounding, are soon completely healed, and if the cambium at the
outside of the gum canals then again begins to produce normal
secondary wood, the gum canals may later be found back in the
wood itself.*) Evidently the healing takes place as soon as the
stimulus ceases, and so it is not strange that when it continues
by poisons or parasitism the gum production also continues.

1) The nature of the power, by which the food transmitting, ‘“descending”
sap current moves through the phloem bundles, is not known, It is thus not
impossible, that if the cause of gummosis is of a material nature, a lysine, moving
through the tissues, it is able to run in opposition to the ‘descending’ current.
I think, however, that the extension of the stimulus does not go along the phloem

but along the xylem bundles and the young wood, with the “ascending” sap.

2) [ have never seen distinct gum canals in the secondary wood, but according

to the descriptions they occur eventually.

sl4

Parasitism as cause of guinmosis.
The connection between wounding and parasitism.

Wounds in peach branches treated with poisonous substances,
such as sublimate, produce gum much longer and more copiously
than the like wounds without sublimate. Other poisons have quite
the ‘same effect. Now it is clear that the direct intluence of para-
sitism on the organism must be sought in the action of some
poisonous substance. Hence it seems ceriain that what these three
causes have in common, namely necrobiose, or the slowly dying of
the cells surrounding the dead ones, is the base of gummosis, and
that parasitism, where necrobiose lasts as it were endlessly, must
be the most powerful instigator of the process.

That this simple view of the question has not yet taken root in
science is proved by the most recent treatise on our subject by
Mikoscu,') illustrated) with beautiful anatomical figures. After the
publication of Dr. A. Rant and myself of 1905, he described the
relation of mechanical wounding to gummosis. But he did not think
of poisoning experiments, nor has he any belief in the influence of
parasitism on gum formation. Wisner, in his recently published
paper on gums in the new edition of his ‘“Rohstoffe des Pflanzen
reichs’, is also of the same opinion as Mixoson.

For my. object a short discussion of a few examples of parasitism
will suffice.

The little caterpillar Grapholitha weberiana makes borings into the
bark of plum and apricot, and if the outermost corklayer is removed
by shaving it off, the butterfly finds so many fit places for deposing
its eggs, that the larvae creep in by hundreds and make new borings
from which later the gum flows out. These holes are coated with
a layer of slowly dying cells, whence the stimulus extends, which
produces the gum canals in the contiguous “cambium”. By cambium
I simply understand the not yet differentiated division products,
“young wood” and young phloeoterma. The necrobiotic cells, clothing
the continually extending holes in the bark, and the great numbers
of new individuals of the caterpillars, make the gum production a
chronical process.

To explain the formation of the enormous quantities of gum
produced in this way, it seems only necessary to think of mechanical
wounding and not of any special excretion from the animal. But it
must be noted that the space, where the caterpillar lives during its

1) Untersuchungen tiber die Entstehung des Kirschgummi. Sitzungsber. d. Kais.
Akad. d. Wiss. in Wien. Mathem. naturw. Klasse. Bd. 115, Abt. 1. Pag. 912, 1906.

S15

erowth, namely a vertical narrow canal in the inherbark, very near
to the cambium, could not possibly be imitated artificially.

Fig. 1. (Natural size). Gum producing peachalmond in September, whose
summit is cut off; the gum from the gum canals is afler drying, swollen by
moistening with cold water.

Much more common and interesting than the animal parasites are
the gum producing Fungi of the Amygdalaceae, five of which are

found in our country.') The commonest and most vigorous is Cor-

1) Coryneum beyerinckii OupEMANS, Cytospora leucosioma Prrsoon, Monilia
cinerea BonorDEN, Monilia fructigena BoNnoRDEN and Botrytis cinerea PERSOON
(see Rant, l.c. p. 88). German authors also mention bacteria as instigators of
cummosis, | never found them.

Proceedings Royal Acad. Amsterdam. Vol. XVII.

SI6

yneum bejerinckii Ouvemans (Clasterosporium carpophilum Apgru.).")

Pure cultures of Corynewn in bark wounds of almond, peachal-
mond, peach, cherry, plum, bird’s cherry, sloe, virginian plum, develop
with remarkable quickness and soon make the bark die off, evidently
in consequence of the secretion of a poison. Around the dead cells
ihe necrobiotie are found from which the stimulus issues, which,
penetrating into the cambfum .in the usual way, forms gum
canals in the young wood. Many mycelial threads of the parasite
itself are then cytolised and converted into gum. I think this facet
remarkable and a strong argument for the material nature of the
stimulus.

Undamaged branches are with difficulty infected by the parasite, but
it is easy, even by very slight wounds and artificial infection, if —
only the wounds be numerons, to obtain great quantities of gum.
This circumstance explains why nursery men dread wounds in the
trunks and branches of stone-fruit trees.

In the green shoots, especially of the peach, the formation of
anthocyan is observed in’ the enfeebled tissue around the wounds
infected with Corynewim when exposed to sunlight. *)

The supposition that secretion products of the parasitic caterpillar
or the Fungus could be the direct cause of the stimulus, is contrary
to the positively existing relation between mechanical wounding and
o1UNMOSIS.

Gum canals in the fruitilesh of almond and peachalnond.

To the preceding facts, long since stated, I wish to add the following.
Already in my first paper of 1883 I called attention to the cireum-
1) BetERINCK, Onderzoekingen over de besmettelykheid der gomziekte bi planten.
Versl. d. Akad. v. Wetensch. Amsterdam, 1883. — Contagiosité de la maladie de
gomme chez les plantes. Archives Néerlandaises, 1é Sér., T. 19, Pag. 1, 1886, —
Cc. A. J. A. OupEMANS, Hedwigia, 1883, N°. 8. — Saccarpo, Sylloge Fungorum,
Vol. 3, Pag. 774, 1884. — AprERHOoLD, Ueber Clasterosporium carpophilwm (LEy.)
ADERH. und dessen Beziéhung zum Gummifluss des Steinobstes. Arbeiten der
Biolog. Abt. am Gesundheitsamte zu Berlin. Bd. 2, Pag. 515, 1902. ADERHOLD
has experimented with pure cultures of Corynewm, which | had made and sent
him. He himself has not executed any isolations of gum parasites. His determination
as Clasterosporium amygdalearum (L&y.) is thus founded on the imperfect de-
scriptions from the older mycological literature, in which OupEMANS was no doubt
better at home than he. Like Linpau [ reckon Clasterosporiwm to another family
than Coryneum.

2) The apperance of anthocyan in the light is commonly a token of diminished
vitality and often a consequence of necrobiose in the adjoining cells. Hence, wounds,
poisons and parasitism cause anthoeyan production in the most different plants.

817

stance, that in the fruit-flesh of the peachalmond, and as I may add
now, also in that of the almond itself, there is a system of gum
canals, precisely corresponding to that of the vaseular bundles. Of
these the phloem bundles are converted into gum canals by cytolysis,
either entirely or with the exception of the outer protophloem ; the gum
canal (gp Fig. 2 and 3) thus, is always immediately contiguous to
the woody bundle 2d.

Fig. 2 (38). Gum canals in the transverse

section of the fruit-flesh of a peachalmond :

ha. hairs on epidermis ; 20 dermoidal tissue;

bp chlorophyll-parenchyma; #/ xylem bund-

les; ph phloem bundles; gp gum canals
sprung from phloem bundles.

Fig. 2 and 3 are reproductions from my

above mentioned treatises of 1883 and 1886.

The presence of gum in the canals of the fruit is easily shown.
In August or September the summit of a peachalmond fruit is cut
off and the fruit, or the branch with the fruit, is placed in water.
After some moments all over the section droplets of gum are seen
evidently issuing from the vascular bundles. As these bundles
are distributed through the fruit-flesh, running longitudinally and
transversely, and are partly reticulated, the number of droplets is
very great and they are of different size. In particular near the stone
they are big. If in August the gum is allowed to flow out in cold
water it dissolves completely or nearly so. In September the dissolving
is nO more complete. By drying the gum, its solubility in cold
water gets almost lost, but it continues in hot water.

From lateral incisions also much gum flows out. In Fig. 1 the
drops are represented after drying, followed by swelling up in cold
water.

Although this gum does not only consist of dissolved wall material

54*

$18

but also of cell contents, the microscope can only detect fine granules,
evidently corresponding to the microsomes of the protoplasm, which
are not dissolved during the eytolysis [ could) not find back the
cell nuclei in the gum, but in the cells of the not yet cytolised
phloem bundles, they are neither perceptible. As under normal cir-
cumstances the gum does not flow out, ifs volume must be about
as great as that of the phloem bundles which are cytolised. It is,
however, certain that the capability of the gum to swell up by
imbibition is much greater than that of the cell-tissue which gave
rise to its formation. It seems thus certain that imbibition with

Nie

Fig. 3 (360). Gum eanal with surrounding ;
gp gum; x/ xylum bundles, unchanged; ph non-
dissolved cells of the phloem bundles; cd thread-
shaped cells in a gum canal, originating from the
phloem bundles.

sufficient access of water must lead to a perceptible pressure and
also. some thickening of the fruit-wall. This must promote the
opening of the fruit as well as the remarkable detaching of the
stone, although the required mechanical power for these processes
must, no doubt, chiefly be the tension of the tissue of the paren-
chyma of the fruit-wall existing independently of the gummosis.
Finally the stone is found quite loose within the fleshy shell, which
mostly opens like a bivalvate mollusk, but sometimes shows three
or four fractures. The vascular bundles, which pass from the fruit-
flesh into the stone, are thereby torn off clear from the stone. At
the base the separation seems provided for by an intercepting layer,
as at the fall of leaves.

819

The portion of the phloem bundles within the stone of the peachal-
mond is never converted into gum; in the almond itself such gum
is found in rare cases inside the shell.

Wound gun in the fruit-wall as a consequence of mechanical
stress of the tissue. Gumming almonds.

In many cases real wound gum is found in the fruits of the
almond and the peachalmond, not proceeding from the gum canals
but from fractures in the parenchyma of the fruit-flesh. Its origin
must undoubtedly be sought in the tension or stress of the tissue,
which causes the opening of the fruit. An additional circumstance,
however, is required, namely a loss of vital strength, by which the
regenerative power of the tissue that coats the fracture is annihilated.
The therefrom resulting incapability of regeneration is associated
with the ripening of the fruit in a way not yet explained and
should rather be attributed to superfluous than to poor nutrition.
Parasitism is wholly absent in the production of wound gum from
the parenchyma of the fruit.

The fracture is mostly at the side where the two edges of the
carpels are grown together and the fruit later opens. Not seldom
in this case is wound gum seen to flow spontaneously from the
base of the fruit along the short peduncle. In other cases the wound
is at the side of the middle nerve of the carpel. Always the edges
of the fracture are coated with cells in a condition of necrobiose,
which is evident by their quickly colouring brown at the air, which
normal living cells do not. These necrobiotic cells and the adjoining
tissue produce gum. With the microscope not quite dissolved cell-
walls may be found in the gum, showing that the cells were about
full-grown when the process began.

In common almonds gum is sometimes found within the hard
shell,') and eventually part of the kernel itself is then also changed
into real wound gum with still recognisable remains of the cell-
wall. In such almonds the phloem of the vascular bundles, whieh
run through the stone to the funiculus, is always changed into a
eum canal, so that the gum can reach the surface of the young
seed.

If we suppose that gummosis originates by the action of a cytolvsine,
if seems very well possible, that the lysine which has flowed inward
together with the ‘canal gum’, is able to attack the developing
1) The small quantity of gum found, especially in “hard almonds”, at the
surface of the shell, proceeds from the gum canals of the fruitflesh. The sugar
Jayer which covers the shell of the ‘soft’ species is dextrose.

820

seed and is yet too labile to be demonstrated by infection of bark
wounds with gum. Experiments in this direction may perhaps be
effected with the peachalmond.

Wound stimulus as factor of development.

Formerly I thought that the presence of gum canals in the fruits
was accidental and should be explained by parasitism, although I
could not find any parasites.

In later years, with better knowledge, 1 again examined the gum
canals in the peachalmond and their surroundings repeatedly. Never
did I find a fruit without them, but they were not equally developed
in different trees from different gardens. In specimens of sandy
grounds they can sometimes only be found with the microscope.
Neither mucroscopically nor by experiments has it been possible
to detect gum parasites. This makes it quite certain that in the
formation of gum eanals parasitism is excluded. *)

The great ease wherewith mechanical tension causes wounds in
the fruit-flesh of the peachalmond, gives rise to the supposition, that
the normal gum canals may be the product of some hidden wound
stimulus.

If this supposition is true, ave cannot think of wounding in
the common sense of the word. When the flowers fall off, a
ring-shaped wound forms around the base of the young fruit,
but this is a normal process, taking place in an_ intercepting
layer and soon followed by complete healing. In the flowers of
peach, plum, apricot, cherry, we observe the same without any
formation of gum canals in the fruit-flesh. Moreover, although the
peculiar structure of the layer between the woody peduncle and
the stone, along which the ripe fruit detaches, reminds of rent
tissue, no gum is formed at that spot and the layer also exists in
the other stone-fruits, where no gum canals occur.

So long as nothing else has been proved it must therefore
be accepted that in the phloem bundles of the fruit of the peachalmond,
where cytolysis takes place, the same factor of development is active
as that, which gives rise to the pathological gum canals in the cambium
of the branches. This leads to the conclusion, that the wound stimulus
belongs to the normal factors of development of this fruit, although
nothing is seen of external wounds. When considering, that the
phloem bundles are built up of extremely thin and _ soft-walled cells,

') The supposition, sometimes met with in literature that the gum of the Amyg-
dalaceae should consist of bacterial slime is quite erroneous. That parasitic bacteria
eventually occur as gum parasites, as is stated by some authors, I do not think
impossible, although till now I only found caterpillars and Fungi as active agents,

821

it is conceivable, that by great tension of the tissue in the surrounding
parenchyma, they undergo strain and pressure causing mechanical
rupture and necrobiose, centre and prey of the wound stimulus
being the phloem bundles themselves.

This conception is in accordance with the fact that the gum
canals are broad in the fruits of well-fed trees on rich grounds,
which have a hard and solid flesh, wherein stress and strain are
certainly very great. Only here and there remains of the protophloem
along the gum canals are still to be found in sueh fruits. But in the
softer fruits of sandy soils, along the much narrower gum canals
not only the protophloem is still present, but also stripes of the
secondary phloem.

Summarising we come to the following conclusions.

Mechanical wounds in growing tissues of Amygdalaceae will some-
times heal directly, sometimes after previous gummosis.

The chief tissue, which is transformed into gum is the young
secondary wood newly sprung from the cambium and not yet
differentiated. By the wound stimulus a network of gum canals
is formed around the wound. In thick branches, with a bark wound,
this network has an elliptical circumference, the wound being in the
lower focus of the ellipse,

If the stimulus is removed by the cure of the wound, the cam-
bium again continues to produce normal secondary wood, so that
afterwards the gum canals may be found in the wood itself.

If the stimulus continues the gum formation also becomes lasting.

The stimulus issues from the cells that die slowly by wounding,
poisoning or parasitism. Probably a cytolysine flows from these cells
into the young wood or the procambium; these bind the lysine and
liquefy to gum. Hence, gummosis is caused by necrobiose.

Young medullary rays and phloembundles are with move difficulty
converted into gum than the young secondary wood. But in the
fruit-flesh of the almond and the peachalmond it is the phloem
which changes into gum. The protophloem of the bundles often
remains unchanged.

Although gummosis in these fruits belongs to their normal develop-
ment, a wound stimulus is nevertheless active. This stimulus springs
from the strong tension in the parenchyma of the fruit-wall, which
gives rise to tearing, necrobiose and gum formation in the delicate
tissue of the phloem bundles. Consequently the wound stimulus is
here a normal factor of development.

It might also be said that the almond and the peachalmond are
pathological species, but thereby nothing would be explained,

822

Chemistry. — “The allotropy of Lead.’ I. By Prof. Ernst Conen
and W. D. Hinprrman.
(Communicated in the meeting of Oct. 31, 1914.)

1. Indications concerning the existence of allotropic forms of
lead are found not only in the earlier chemical literature. Fourteen
years ago Ernst Cowen’) pointed out in his studies on tin a clause
in Piorarcr’s (50—120 A.D.) Symposiaca (VI, 8) in which allusion
is made *) to the fact that lead is sometimes disintegrated spontaneously
at low temperatures.

This clause runs as follows: ‘No, the craving for food is not caused by the
cold, but in the body something takes place similar to that which happens with
metals in a very strong winter. There it is seen that cooling not only causes
congealing, but also melting, for in strong winters CKOvEL o2(3dov (pieces of
lead) occasionally melt away, consequently something similar may be supposed to
take place in the intestinal process, elec... .”

Moreover THESOPHRAST (390—286 B.C.) mentions such phenomena in his book
aeQi AVQdS: “xatTitEQoY yo uci zat WoAUBdoy Ydy TaxFvae tv TO
IIcvt adyou xa yEmoOrog drtog veavizot, yadxov dé Oayiva.”
(It is told that tin and Jead melted sometimes in the Pontos when it was very
cold in a strong winter, and that copper was disintegrated.

2. Samre-Ciaire DevitLe*) stated that the density of lead is a
function of its previous thermal history. He gives the following
figures (water at 4° — 1; Temp. ?)

After quick cooling of molten lead 11.363.
er slow - * A ellen nae

In a second experiment he found:

Density of lead electrolytically deposited 11.542.
After melting and rapid cooling 11.225.

About the value 11.542 he says:

“Mais telle est la rapidité avec laquelle se carbonate a l’air ce plomb extréme-
ment diviseé, quil a fallu le transformer en sulfate pour en déduire ensuite le
poids de la matiére employée. Cette complication introduil-elle quelque incertitude
sur le premier nombre, ou ne doit on pas plutot ladmettre comme représentant
la densité de ce plomb parfaitement cristallisé ?”

3. These values as well as others given in earlier literature have
to be aecepted with reserve as generally no data are given about

1) Proceedings of the meeting of Jan. 26, 1901, p. 469. Zeitschr. f. physik.
Chemie 36, 513 (1901).

*) PLurarcut Chaeronensis varia scripta quae moralia vulgo yocantur. Lipsiae,
ex officina Car. Tauchnitii 1820, Tomus IV, 339,

Prof. ERNST COHEN and W. D. HELDERMAN, ,,The Allotropy of Lead I”.

(Natural size).

Proceedings Royal Acad. Amsterdam, Vol. XVII.

823

the purity of the material experimented on and as there often
exists some uncertainty concerning the method whereby the density
has been determined.

4. Kanipaum, Rotn and Siepier') found the density of a pure

91°

specimen of lead prepared by distillation in vacuo to be do 11.541.

5. The values given by different authors for the specific heat of
lead vary within wide limits, as may be seen from the table given
in Arneae’s Handbuch der anorganischen Chemie.*) Moreover it may
be called to mind that Le Verrier’) stated, that the specific heat
of lead is a function of its previous thermal history.

6. The facts mentioned above as well as the investigations of
Storpa, *) and those of Orro LEHMANN *) render a new investigation
of the subject very desirable. ‘

7. A year ago we carried out some experiments in this direction.
As the results were negative we experimented with other metals,
which yielded a more favourable result. Since a fresh investigation
on lead has given positive results, as will be proved below, we
give here also a short description of our earlier experiments, which
taken together with the new experiments furnish a confirmation of
the results obtained by us in the case of other metals (bismuth, cad-
mium, copper, zinc, antimony).

8. Our experiments have been carried out with lead which
contained only 0.001 per cent of copper and 0.0006 per cent of
iron (Blei-‘‘KaaLBAUM’-Berlin). °)

The metal was turned into shavings on a lathe and washed with
dilute nitric acid, water, alcohol and ether. After this it was dried
in vacuo over sulphuric acid.

9. The density of this material was found to be

0
P= de, 116398;

b. 11.330,

_ We put the, metal into an aqueous solution of PbCl, and kept it
for 48 hours at 100°. After washing and drying it, we found:

1) Zeitschr. f anorg. Chemie 29, 177 (1902).
2) Bd. 3, 2te Abteilung, p. 633 (Leipzig 1909).
3) Comp. Ernst Couen, Proceedings 17, 200 (1914).
4) Journ. f. prakt. Chemie 94, 113 (1865); 96, 178 (1865).
5) Zeitschrift f. Kristallographie und Mineralogie 17, 274 (1890).
Ernst CoHen and Karsusr Inovyi, Zeitschr. f. physik. Chemie 74, 202 (1910),
6) Mytius, Zeitschr. f. anorg. Chemie 74, 407 (1912),

824

d aa G5 1aES 297
d. 11.328,
Another part of the original material was melted and chilled in
a mixture of alcohol and solid carbon dioxide. The determination
of the density gave the following result :
25°

ioe

e. 11.330,
fF: dio33;

10. As our determinations had been carried out with an accuracy
of 3 or 4 units in the third decimal place, it is evident from the
experiments described above that we had not been able to detect.
any transformation in the lead experimented with.

11. However, some months ago Mr. Hans Heuer at Leipzie was
kind enough to call our attention to some phenomena which he
described in the letter which follows :

“Gelegentlich eines Vorlesungsyersuches, der einen sogenannten ‘Bleibaum”
zur Darstellung bringen sollte, bereitete ich eine Lésung von 400 gr. Bleiazetat in
1000 ec. Wasser unter Zusatz von 100 ce. Salpetersiiure (spez. Gew. 1.16), die
als Elektrolyt bei der Bleiabscheidung diente. Als Elektroden dienten bei dem
Versuch Stiicke aus reinem Blei. Diese -Bleistiicke bliehen nach der Elektrolyse
etwa 3 Wochen in der Lésung stehen. Als ich sie alsdann herausnehmen wollte,
bemerkte ich, dass sie ihre weiche, dehnbare Beschatfenheit véllig verloren hatten
und eine spréde, bréckelnde Masse geworden waren. Der Gedanke, es hier mit
einer stabilen Modifikation zu tun zu haben, erschien mir um so wahrscheinlicher,
als das spréde Blei ganz dem grauen Zinn gleicht, beide Metalle zu der gleichen
Gruppe des periodischen Systems gehéren und Metastabilitét unserer Metalle nach
Ihren Forschungen nichts Befremdliches mehr ist.

Kurze Zeit darauf brachte mir ein Kollege ein Bleikabel, das an verschiedenen
Stellen eine weisse pulvrige Beschaffenheit zeigte von ganz ahnlicher Art, wie ich
sie an den vorhergenannten Bleistiicken beschrieb. Wir machten darauf den Ver-
such reine Bleistiicke unter konzentrierle Salpetersiiure zu bringen und sie mit ein
wenig unseres spréden Bleies zu impfen. Der Erfolg blieb nicht aus: nach
wenigen Tagen hatten sich betrachtliche Teile der Bleistiicke zu der bréckligen
Modifikation verwandelt.”

Mr. Hetiwr kindly invited us to continue these investigations ;
repeating his experiments with our pure lead we were able to corro-
borate his statements.

12. The lead was melted, chilled in water and cut into small
blocks (8,5 & 2 x 0,5 em.). We put them into glass dishes which
were filled up with the solution mentioned by Henier. The dishes
were covered with glass plates. The temperature of the solution was
15°—20°. The addition of some nitrie acid has the effect that the
surface of the metal remains bright during the experiment,

In this way the electrolyte is in constant contact with the metal
and the inoculation which occurs can go on undisturbed.

The photographic reproductions (natural size) which accompany
this paper illustrate the development of the phenomenon. Fig. 1
shows a plate of pure lead in its original condition. Fig. 2 represents
the plates after having been in contaet with the solution for some
days; there are to be seen deep cracks, which show that the material
has shrunk locally. In consequence of this an increase of the density
was to be expected which was proved by means of the pyenometer
(comp. § 19). Fig. 3 shows the plates after three weeks in the same
conditions: the metal has been disintegrated.

Repeating the experiment with 15 or 20 blocks we got in all
cases the same results.

13. We shall prove below that the phenomenon is not a chemical
one; the following experiment may give already an indication in
this direction. One of the blocks (+= 40 grams) was put into a cali-

brated tube which had been filled up with the solution mentioned.
This tube stood in a small dish containing the same solution. After
three weeks no evolution of gas had occurred, either at room tem-
perature or at higher temperatures.

14. After this the phenomena described above were investigated
by means of both the pyenometer and the dilatometer.

A. Measurements with the Pycnometer.

15. We exclusively used the instrument (Fig. 4) described by
Apams and Jounston'), following the indications given by the authors.
Moreover we took the precaution of dipping the pycnometer into
water before weighing (empty) and wiping the
water off with a dry cloth. If this is omitted a
slight error occurs. as the surface of the pyenometer
is then not in the same condition as at the sub-
sequent weighings, after it has stood in a (water)
thermostat.

All determinations were carried out in duplicate
with two pycnometers (C and D) which contained
= 25 cem.

16. Our investigations on bismuth, cadmium ete.

had shown that the pyenometer measurements have
to be carried out with special care. The volume
changes which accompany the transformation of the

1) Journ. Americ. Chem. Soc. 34, 563 (1912).

826

different modifications are, it is true, not inconsiderable, but they
may be partially compensated in consequence of the simultaneous
presence of different forms. In order to detect the remaining volume
changes, very accurate determinations of the density must be made.
We shall see below that special precautions must also be taken
with lead. Evidently it is to be aseribed to such compensations that
these phenomena have escaped the attention of earlier authors.

17. We used toluene as a liquid in the pycnometer.

Its density was found to be:

9KO

d —~ 0.86013 by means of the pyenometer C.
4° . .

0.86013 nimi 8 D.

The quantity of lead used for each determination was 40—-60
grams. The thermometers (divided into 0.05 degrees) had been checked
against a standard of the Phys. Techn. Reichsanstalt at Charlotten-
burg-Berlin. The weighings were carried out on a Bunex-balance
with telescope. The weights had been checked by the method
deseribed by TH. W. Ricuarps ').

18. In the first place we determined (at 25°.0) the density ot
the lead immediately after its preparation for the experiments.
It was melted, chilled in water and filed to powder. It was then
treated with a magnet in order to remove traces of iron from the
file. We washed the powder with dilute nitric acid, water, alcohol
and ether, and dried it in vacuo over sulphuric acid. Its density
was now:

gro

av
d 7 11.325, (Pycnometer C).

The metal was then washed and dried again in the same way ;
ORO

d =e 11.322, (Pyenometer D). After treating again in this way we

9FO

a0
found d ie 11.324, (Pycnometer D).

19. We brought the metal into the solution of the acetate (temp.
15°). After standing for 3 weeks the material was washed and

95°

dried. Its density was now d io 11.340, (Pycnometer C)

11.3842, (Pvenometer JD).

1) Zeitschr. f. physik, Chemie 33, 605 (1900),

827

The figures show that there has occurred at 15° an increase of
17 units in the third decimal place.

20. We put the metal again into the solution which was kept at
50° (in a thermostat) for 120 hours. We found after washing and
drying

[> ral e}

d = 11.313, (Pyenometer C

11.312, (Pycnometer D).

The density had decreased 28 units in the third decimal place.
21. The experiment was repeated again, this time at 25°.0 (in a
thermostat) for 144 hours.

9ro

We found: ie 11.327, (Pycnometer C)

11.3829, (Pycnometer D).

An tinerease of 15 units in the third decimal place had occurred.
22. Our table I contains the results of these determinations:

AT IN 18} VG EE

252.

d 40

Without any previous treatment | 11.324
After treatment at 15° 11.341
s rf ee |} 11.3i3

|
” » n 25° | 11.328

B. Measurements with the dilatometer.

23. This investigation was carried out in the same way as has
been described in the case of cadmium *).

Some kilograms of lead were melted in a spoon and poured out
into an iron form. The metal cooled in contact with the air. After
filing it we treated it with a magnet and put it into the solution of
the acetate. Here it remained (at 15°) for 15 X 24 hours. After this
it was washed and dried in the way described above. We used
+ 600 grams in the dilatometer. (Bore of the capillary tube 1 mm.).

1) Proceedings 16, 485 (1913); Zeitschr. f. physik. Chemie 87, 409 (1914),

828

At 50°.8 the decrease of the level was 700 mm. (34 hours).
5 74°.4 5p rise 9 % . ” 275 oo) ( DH ” Ns

Whilst the first preparation (§ 20) had shown at 50° a decrease
of density, we now find an imerease. From this result we may
conclude that there are more than two allotropic forms simultane-
ously present.

24. Special attention may be paid to a phenomenon which we
observed with all our preparations and which stands in close con-
nexion with the fact that lead as it has been known up to the
present, forms a metastable system containing simultaneously several
allotropic modifications of this metal.

It is generally known that when a bar of any metal which is
more electro-negative (resp. electro-positive) than lead is suspended
in a solution of a lead salt, the lead is thrown out of solution and
a lead tree is formed.

We found that the same phenomenon occurred when our pure
lead was placed in the solution mentioned above or in a (neutral)
solution of lead nitrate (30 grams of nitrate, 70 grams of water).
Both at room temperature or at higher temperatures (50°) a lead
tree was formed in a few days.

25. We are in the case of lead in specially favourable cireum-
stances for the observation of this phenomenon. The galvanic current
which is generated between the stable and metastable modification
decomposes the solution. The metal which is electrolytically deposited *),
shows in this case a characteristic form (lead tree) so that the
phenomenon is very striking *).

26. We hope to report shortly on the different pure modifications
of lead and their limits of stability.

Utrecht, October 1914. van 't Horr- Laboratory.

1) That the phenomenon is not to be attributed to the presence of iron (0.0006
per cent) or copper (0.001 per cent) is proved by the investigations of OBERBECK
{Wied Ann. 31, 337 (1887)] and by those of KénIGSBERGHR and MiLueER [Physik.
Zeitschr. 6, 847 and 842 (1905).

2) We also carried out an experiment with tin: white and grey tin were putin
contact in a solution of SnCl, (Temp. 15°). After some time a great many
beautiful crystals of white tin were deposited by electrolysis upon the white metal.
(Comp. Ernst CoHen and E. Gonpscumipt, Zeilschr. fiir physik. Chemie 50, 225
(1905)].

829

Mathematics. — “On an integral formula of Stiuises.” By Prof.
J. C. Kivuyver.

(Communicated in the meeting October 31, 1914).

In the Proceedings, and Communications, Physical Section, series
3, 2, 1886, p. 210, Stivites treats of definite integrals, referring
to the function

Y= ==
‘ 1—y4 NI.
In this function @ stands for a positive odd integer without qua-

dratic factors, and ( ) represents LEGuNDRE’s symbol with the ex-

tension given to it by Jacopt.
nile
As poles of the function f(y) only the points y=e* are to be

taken into consideration, and for the residue, belonging to such a
pole, one finds

From the well-known fundamental equation

ey ae
> é a —7 2 sa Va
h=1 a

Qik

it follows, that a pole is only to be found in those points y= e-¢
in whieh & is prime to a. Consequently y= 1 is not a pole of the
function, and we have,

1 '=a—1 /),
hy) == Gz
a h=1 a

from which it follows that —«af(1) is equal to’the sum of the
: h
numbers smaller than «, for which @E- (residues), diminished
a
. . 4 : be
With the sum of the numbers smaller than a, for which ( i — 1
Ka,

is (non-residues).
In the paper quoted, Stipirsjus considers the definite integrals
a

<3)
ee , tate: has. ata
J (e—) sin da and aI f (e—*) cos dx,
é 2a 7 2m

0 0

830

and he calculates the value of the first integral for the case
a= 4w + 1, the value of the second integral for the case
a = 4w — 1. .

In the following I give a shorter deduction for these results.

I suppose that the two positive, otherwise arbitrary numbers 3
and y have a for product, that ¢ is a positive parameter and now
consider the integral

pa file )aneas,

In order to valeulate this integral, it is not necessary, as STIELTJES
does, to fall back on an integral formula treated by Lecrnpre and
by Aber. It need. only be observed that in the upper half of the
complex v-plane for inereasing values of |.) the modulus of the
integrand approaches sufficiently rapidly to zero, to permit us to
equate the integral / to the sam of the residues in this upper half
plane, multiplied by 222.

Qnx
The poles of the integrand are the poles of Fle 8 ie that is to
E ki
say the points z= —(#= 0,1, 2,:..), where & is prime to a. The

”

‘
residue of such a pole is

1 h=a=1 AN * | 5 LN ea
é / SS ) ¢ | ( = a 2 ) Va = || Uo
2ay Swe any a

hence

a—| bey ees 7 _ 2akt a 1\2 a al
eG, Pe i 2 ) > Ge v = 2 es 2 me a
Y Nae Y

We ought to distinguish now between the two cases a= 4w-+ 1
and a = 4w — 1.
For a= 4w-+1 we have

is wey seals (a=
ie) =-+ ( =) and consequently / C B ) =—f fe B ) ;
a a

so that it follows from the result found for J, that

5 (ae /2 mee
mc oe ree ee r). (c=40 - 1) ee)
wv 2
0

On the other hand for a= 4w—-1

h =) == =
.) ——— (=) and consequently / (« i ) = +s(4 i ) :
a a

so that in this case it may be concluded from the integral formula that

272 2rt

a ; 2
{ole ip ) cos 2zta da =} ye = if (« 7 ; oe (@ — 4A es (OL)
wy Y

nh
|

As may be proved the equation (II) remains true if we suppose
¢=0, and if the expansion in series

2r2 2rmx

: ee 10 “m ss
PEALE B = 2 — | |e B '
M11 Nea

is made use of, we get in this exceptional case

m =e m\ 1 ae rd ha 1 fe)
Ss -}|—= — f(1) = — > ( h. (a= 4w — 1)
ee MO Ya aya j= a

The results found by Stipitses have been derived with this, the
equations (1) and (I]) may now, however, be used, to find other
results less known in the theory of numbers.

For real values of « the function / (e~**) has the property of approach-
ing rapidly to zero for positive and negative values of x of increasing
modulus. This leads. to the conclusion that Fourimr’s general sum-
mation-formula

may be applied, if we write

(a) 7 aa
£1

Distinguishing again the eases a=4v+1 and a=4w—1, the

and if we suppose 0<

value of the integrals in the right-hand member may be determined
by means of the equations (I) and (Il). It should be taken into
consideration in the summations in the left-hand member, that / (¢-*)
changes ifs sign together with « or not, according as @ is equal to
dw +1 or to 4 — 1.

In this way the two following general equations are derived from
the summation formula.

One sa 2n(n--5) 2rn(n—é) Y
oF pt) n= ES ze SS Ee,
ih (« B ) 5H i(- le ) ==) (- 8 ) = ]
i) | :
p n= Zan |

he fae = sin sani (« 7 ) , (a= 4w + 1)

7 n=!)

Proceedings Royal Acad. Amsterdam. Vol. XVII.

832

p oa eee , _ onln-ts) ys 2n(n—F) \
! (’ i ) = i(< : ) : I (« : ) | = ]
=|

(IV )

7u=—=

; ae Q7n
as} t ray HED) SS cos Bank « 7 )| te

Y n=l

If in both members of these equations the functions / are expanded
into series, the summations indicated are to be executed still further.
1 shall, however, perform these reductions only for special values
of the parameter §, in consequence of which the general results are
simplitied.

In the equation (IID) I substitute therefore §= 4, at the same
time L replace 3 by g and accordingly y by 2y. I further write

us T
Be =f, Cin OKe
The numbers g and g’ are then positive and smaller than 1;
they satisfy the relation
! m*
log qex log ns
a
but are for the rest arbitrary.

In this way the equation (III) passes into

re 3B n=
2S) (—1)" F (q+) — > (—1)" F(t),
n=O of n—0

and if the functions / are expanded into series, we shall find

| ; 1 ne (“) qn rs | i ] ven (=) q” a
oO” — ——<—<——— og a aid = = ToD a= w+l (V
“ qG m=1 a) 14-92" i rj} 3d Qh ( ) )

In the equation (IV) I substitute $—=0O. We have then in the
first place

: no i /B é 1S As
70) +2= Fq) =)" a) +25 70%,
rm y N=

and if again use is made of the expansion into series of the functions
J we tind

Vig | soya (2) 2.
qd a y) = gFuc

/, 1 Z LUE IL g2m /
=! log ar) vay +23 ee ' (a = 4w—1) . (VI)

qd m=1 \@ —q'2m

The equations (V) and (VI) completely symmetrical with regard
to y and gy’ are again conspicuous for the remarkable properties of

833

; m : Ae,
the arithmetical symbol ( For the rest they show some similarity
ct
with f

formulae in the theory of

the functions, and point to a

‘ ’ z 1
certain connection between the functions & (« a) and or "

{ Y

So it may be observed, that, from the equation

F
ae A v, U,
4 1 re it) B mn gq”
Fe (ea See Se a
p p

—_= 4 = —— ¢os 22 mv
a t m1 l--qm
Dv, Osho

a la @
fe: ment rn ap

Or 0, <7 vo, (Nee = = SS a 4
B B h=1 r oe

e h 7
1 i iN US ig . (| B
VA vd, 0, | v, (0, | ve =
i {

— = \@ ae (a = 4w + 1)
( 3)
remains unchanged, if 3 is replaced by y
In a similar way we conclude from

(3)
N v, —
1 B

m=o
tA CA

= (ple

- otunm + 4a S ——— sin 2x mv
U m=1 [—gen

(Pas =
B

for the case a= 4w —1 to

7 ( |
—=7— }) os a? We m= e6 27
Le Banded Oot BOSH

feat (a 1 PUVA) san Ye? a I=

a ae

m1
We can prove now, that

h=v—1 h ath
>> ia 2Va Ff (1)
h=1 a
consequently it ensues from the aneaede (VJ), that the expression
5 ic -)
1 t=a—1 Sh ale a
— 2 4 eS (a = 4w — 1)
Vl jot NG € ,)
a ee
p

holds its value, if 8 is changed into y

on
or
*

Physics. — “On unmiving in a binary system for which the three-
phase pressure is greater than the sum of the vapour tensions
of the two components.” By Dr. F. E. C. Scuerrrr. (Commu-
nicated by Prof. J. D. van per WaAats).

(Communicated in the meeting of Sept. 26, 1914).

l.-In my investigation on the system hexane-water the remarkable
phenomenon presented itself that the three-phase tension of the two
liquid layers by the side of gas appeared to be greater than the
sum of the vapour tensions of pure hexane and pure water‘). When
the tensions of the pure substances at a definite temperature are
denoted by P, and P,, the three-phase presstwe by /, then for
temperatures which are not too far from the critical end-point

| cae eee el a

If we could speak of ‘partial pressures” for such an equilibrium,
this result would be impossible. A proof of this is found in VAN DER
Waats--Konnstamm’s “Thermodynamik’, which however is only
valid when the gas-laws*) hold for the saturate vapours. When the
vas-laws do not hold for the gas phases, in other words if the gases
possess surface layers, the proof is not valid, and the statement that
the three-phase pressure must always be smaller than the sum of
the vapour tensions of the components, holds therefore only for
rarefied saturate vapours.

In my paper on the system hexane-water I have shown that the
contradiction with the second law of thermodynamics, which at first
sight may be supposed to exist in the observed phenomenon, is only
an apparent one. We might, namely, be inclined to reason as
follows: If the three-phase mixture possesses such a high pressnre,
the pressure exerted by the water and hexane molecules, or at least
that of one of them will have to be greater than the pressure of
water vapour, resp. hexane vapour over the pure components. If we
therefore bring the three-phase mixture by means of a semi-permeable
membrane into contact with pure hexane and with pure water
under their own vapour pressure, bexane or water will pass through
the semi-permeable membranes from the three-phase mixture towards
the pure liquid. We should then get splitting up of the three-phase
mixture, whereas just on the contrary the so high three-phase pressure
sets in of its own accord from pure water and pure hexane. This
is in conflict with the second law of thermodynamics.

1) These Proc. 16. 404. (1913).
2) Thermodynamik. Il. S. 476.

835

I have shown in the cited paper that the conclusion that the
three-phase mixture will expel water through a membrane permeable
to water, is really correct, and that probably mutatis mutandis the
opposite thing will apply to hexane. The error in the above reasoning
lies therefore only in the very last conclusion. I have pointed out
loc. cit. that it is, indeed, possible that two liquids, each under its
own vapour pressure, mix to a three-phase mixture that possesses
the property to get unmixed again into the pure components through
semi-permeable membranes; that this is not in contradiction with
the second law of thermodynamics, but that on the contrary this
phenomenon will be frequently met with in my opinion, also for
systems which do not present the special behaviour mentioned at the
head of this paper. Thus solutions of gases which are but sparingly
soluble in water will certainly expel water, when they are osmotic-
ally brought in contact with pure water of the saturate tension. The
observed phenomenon is therefore not in conflict with our theoretical
considerations.

2. To get an answer to the question whether the system hexane-
water presents an exceptional behaviour in the appearance of a
three-phase pressure which is greater than the sum of the vapour
tensions of the components, I have investigated a number of other
systems in the hope of findiug the remarkable phenomenon there too.
First of all I have chosen the system pentane-water. The pentane
which I had at my disposal, was however KaAHLBAUM’s ‘normal
pentane’, which is no pure normal pentane, but a mixture of normal
and isopentane, which can only be separated with great loss of
substance and time, as the boiling-points of the. two substances lie
near room-temperature, and differ only little (slightly more than
8 degrees). This slight difference of boiling-point involves that the
pentane mixture behaves pretty well as a pure simple substance;
the isothermal pressure ranges for condensation are slight. I have
therefore given up the separation of the two pentanes, and compared
the vapour tensions of the pentane mixture and of pure water with
the three-phase tension of a pentane-water mixture. It is clear that
both the pentane mixture and the three-phase mixture must possess
a tension dependent on the volume at constant temperature, but
also the three-phase tension appeared to be only little dependent on
the volume. To execute this comparison of the pressures as exactly
as possible I have determined the pressures for final condensation
and for about equal volumes of gas and liquids both of the pentane
mixture and of the three-phase mixture.

836

TABLE I.
a i = al |
|
Pentane mixture.
| Pressure (atm.)
Tem | =i a |
| -, |
perature. Erle : |
V, =V
condensation L G |
51S) es M65 |
|
| 151.9 | 17.8 |
161.1 20.6 |
|
161.45 20.8 |
169.95 Pele |
170.1 | 23.7
180.1 21.6 |
180.3 27.8 \\ =a)
| 190.25 32.15 |
| | |
i 400.30" i sS205).5 ul
| 193.3 | 9) 33:6

TABLE II.
Threephase mixture.
Pressure (atm.)
Tem- 2 a
perature. Ende
Vi Va
condensation| 4 G
150.15 22.45
150.7 22.7
160.6 27.25
160.7 27.35
166.5 30.3
170.25 32),55
170.35 32.65
180.3 39.0
180.5 3925
|
187.1 44.1

When the values of pressure and temperature indicated in the
above tables are graphically represented, it appears that the line
for the end-condensation coincides fairly well with that which holds

for

equal liquid and vapour volume both for the pentane mixture

and for the three-phase mixture: the difference is nearly everywhere
smaller than O.1° atmosphere, and

is therefore of about the same
value as the errors of observations. When the pressure values are
read for definite temperatures from the graphical representation, the
values of table 3 are found.

IWAVBsL ET
| oe Three-phase | Pentane | ;
Temperature | pressure pressure Waterpressure | Difference
— _— — —_—____—_- —_ ————_——— | ————— — — ==
150 22.4 7s} 4.7 0.4
160 27.0 20.3 6.05 0.65
170 32.4 23.7 7.8 0.9
180 38.8 27.6 9.8 1.4
187.1 44.1 30.7 11.6 1.8

The values for the vapour tension of water lave not been derived
from earlier observations, but determined by myself to prevent an
eventual deviation of the thermometer from vitiating the comparison.
All the observations have been carried out with a normal thermo-
meter, and with an Anschiitzthermometer verified by the boiling
point of pure aniline.

We draw the conclusion from the last column of table 3 that
the three-phase tension is again greater than the sum of the vapour
tensions of the pentane mixture and of pure water. The difference

appears again to. be greatest at the critical endpoint —— in all thie
tables the critical values are printed in bold type —; with decrease

of temperature the difference decreases rapidly, and according to
the theory it must reverse its sign at temperatures where the saturate
vapours follow the gas laws.

The above described example shows therefore again a case of
very high three-phase pressure. Though these experiments would
have to be repeated with the pure substances to get perfect certainty
about the behaviour of the binary systems, the conclusion that the
pentanes and hexane behave analogously with respect to water,
seems yet sufficiently certain to me. Also the relative situation of
the critical end point with respect to the critical points of the com-
ponents is the same as for the hexane-water mixtures.

Finally I will still point out that the above only proves that there
exists a pentane-water mixture that possesses the repeatedly men-
tioned remarkable property, and this suffices also for my purpose ;
other proportions of pentane mixture and water will probably give
rise to some change in the three-phase tensions because the pentane
mixture is not a simple substance; for the solubilities of the two
pentanes in water will probably not be in the same proportion as
the quantities of the pentanes in the pentane mixture; the difference
in the fifth column can therefore undergo some modification for
another ratio of the two “components”.

§ 3. The experiments of § 2 confirming my supposition that the
abnormal value of the three-phase pressure would be a phenomenon
of frequent occurrence, | thought I had a great chance to find the
same peculiarity also for other binary systems. I have therefore
looked for binary systems of which it was known that for low
temperatures the threephase pressure lies higher than the vapour
tensions of the pure components separately and is about equal to
the sum. Dr. Bicuner drew my attention to the systems carbon
tetrachloride-water and benzene-water, which possess three-phase

838

tensions according to Rrexavir, which deviate little from the sum
of the vapour tensions of the pure substances. ReGNauLT even asserted
that the tension of carbon tetrachloride-water mixtures is somewhat
higher than the sum, and thought he had to ascribe this to slight
contaminations; GerNpz has shown later that the three-phase tension
is really slightly smaller than the sum of the vapour tensions, which
is therefore in harmony with the theory. I have now tried to inves-
tigate the two systems at higher pressure; I have, however, not
succeeded in doing so with the system carbontetrachloride-water, as
the components act on each other at higher temperatures. The inves-
tigation is possible for the system benzene-water, and also this system
appeared really to furnish an example of the remarkable phenomenon.

Benzene free from thiophene (negative isatine reaction) was distilled
from phosphorus pentoxide; the boiling point under normal pressure
was 80°.2, and was therefore in perfect concordance with the value
given by Youne. The vapour tension line of this benzene was deter-
mined, and then the three-phase tensions of a benzene-water mixture
were measured and compared with the vapour pressure line of water,
which was also determined by the aid of the same thermometers.
To avoid corrections I have measured the three pressure values

TAB ie AV:
Temperature | Bo | Waterpressure | re | Difference
0
150.0 10.6 | 4.7 5.9 0
160.0 13.2 | 6.05 Tht 0.05
170.0 16.4 | 71.8 8.5 0.
180.0 20.1 | 9.8 10.2 0.1
190.0 24.6 12.35 12.15 0.1
200.0 29.8 15.3 [OS aks 0.2
210.0 | 35.9 | 18.75 | 16.7 0.45
220.0 | 42.9 | 22.8 19.45 0.65
230.0 50.9 | 27.5 22.5 0.9
2AO ele Ne e602355 9/0 8330 25.95 1.4
250.2 | 70.65 | 39.1 | 29.55 | 2.0
260.1 82.15 | 46.1 | 33.7 | 2:35
967.82 dul ok ode7 ‘cale.(52.4) ‘cale.(37.35) 2.95
268.2 | = 52.6 37.5 —
| =

839

always at the same temperatures; if a slight error should occur in
the absolute value of the given temperatures, this has no influence
on the pressure differences. The thermometers which I used in this
investigation, have been tested by a resistance thermometer, the
resistance of which was determined for boiling water, naphthaline,
benzophenon, and sulphur. The obtained results are given in table 4,
the pressures are given in atmospheres.

It appears from the last column of table 4 that the difference at
150° to 200° is only slightly greater than the errors of observation,
that the three-phase tension becomes appreciably greater than the
sum of the vapour tensions at 210°, and that this difference rapidly
increases with ascending temperature.

4. When we combine the results of the system hexane-water
and those of § 2 and 3, it appears that in the three systems the
three-phase tension is always greater than the sum of the vapour
tensions of the components in the neighbourhood of the critical
endpoint. Moreover these three systems present the same shape of
the plaitpointline in the 7-x-projection; the upper critical endpoint
always lies lower than the critical points of the two components ;
the plaitpoint line presents therefore a minimum temperature in the
T-x-projection (homogeneous double plaitpoint). Though in my opinion
it is probable that the systems will behave perfectly analogously, a
furtber investigation would have to decide whether for all this
homogeneous double plaitpoint lies in the metastable region; | have
shown this for the system hexane-water in my cited paper. It is
remarkable that in the system ether-water the homogeneous double
plaitpoint appears in the immediate neighbourhood of the ether axis
or would perhaps lie outside the figure, so that the eritical endpoint
in contrast with the above discussed systems lies between the critical
points of the components. In this system the said peculiarity does
vot occur. Accordingly I think I have to conclude that the systems
which present critical endpoints which lie lower than the critical
temperatures of the two components possess three-phase pressures
which are higher at high temperatures than the sum of the vapour
tensions of the pure substances, whereas the opposite is the case for
systems for which the critical endpoint lies between the critical
temperatures of the components. Perhaps this conclusion may contribute
to account for this remarkable phenomenon.

Anorg. Chem. Laboratory of the

June 25, 1914. Ae : :
University of Amsterdam.

840

Physics. — “Contribution to the theory of corresponding states.”
By Mrs. T. Exrunrest-Aranassyewa. D. Se. (Communicated by
Prof. H. A. Lorentz).

(Communicated in the meeting of September 26, 1914),

§ 1. Mestin') has tried to demonstrate that every equation of
state which contains the same number of material constants as
variables, is to be reduced to a universal shape (.e. to sucha form
that no parameters occur any more which vary with the substance),
if the variables are replaced by their relations to suitable special
values, which may be designated as “corresponding” for different
substances.

On closer investigation it appears, however, that the equality of
the number of the parameters and that of the variables is neither
necessary nor sufficient for the existence of corresponding states.

A method will be given here to decide whether a given equation
allows the existence of corresponding states. This method furnishes
at the same time the possibility to calculate the eventually corre-
sponding values of the variables for different substances.

§ 2. In the first place we shall define the term ‘corresponding
states” in a somewhat more general form. Let an equation be given

between a system of nm variables: 7,,.v,,...%, and a number m of
such parameters: C\, C,,...C, that they can vary with change of

definite circumstances (for evample of the substance).

Let an arbitrary system of special values: 2,',2,',...2,' (we shall
briefly denote it by a) of the variables 2; be known, which satisfies
this equation for definite special values C;' of the parameters C;.

Let us introduce the following new variables:

a, vs &y

R= RS Se = =
2, vy an

ee (ik

All the constants S; of the thus transformed equation ean be
calenlated as functions of the former constant coefficients, of the
values Cy) and of the values 2,/.

When the parameters C; assume other special values C;", other
systems of special values of the variables will satisfy the original
equation.

The case may occur that there is among them such a system of
values :

}) Mestin: Sur lVéquation de vAN DER WAALS et la démonstration du théoréme
des élats correspondants C.R. 1898, p. 180.

S41

. PL roy ht
Uy Uy 02+ Uy

that on the substitution of

for vi, the constants of the transformed equation assume exactly the
same numerical values S; as in the first case. We call such values

Na ae Vat ald: thie
state defined by the values 2;", correspondent to that defined by the

a .t, correspondent to the values x,', x,
1?

M1 9 Ug yee

values a; (or corresponding to it).
The form to which the given equation is reduced in this case
XL vi

by the substitution y; = —, resp. yi= —

will be indicated by the
Xi vi

word universal.

§ 3. When for the system a; the system 2; corresponding to it
has been given, the system aj" can be easily caleulated, which cor-
responds with every other system 2’ of ; values, which satisfies
the equation in the first case, by the aid of the following equations:

Indeed the values 2;' resp. v;" satisfy the original equation, when
the parameters C; assume in it the values (;' resp. Ci". When now
the substitution

ABS P
ee ee ke ee 28)

vi
has been earried out, the constants S; which we have calculated,
assume other values, e.g. S41, and we must now find the values 2",

it)

which keep the quantities Sj, invariant on substitution of Gy tom Ge
when the substitution :

i Geet ies) oo Gaetan ca)
LY
is carried out.
The values x;', however, satisfying the given equation,
; Qe
ya =,
ly
satisfy the transformed equation. The constants of the transformed
equation do not change, when

ll 9 f
av; Vi

" !
Ly Li)
is substituted for Yar:

842

The fraction:

" t
2; wey

wi" wit!
belongs therefore to the corresponding values ;", hence wv’ corre-
sponds to ay".

Hence it is proved that im the case of a system of values corre-
sponding to a system of solutions, there also enists a system corre-
sponding to every other system of solutions (when C;’ have been
replaced by C;").

§ 4. To find a system «;", if the system x,’ has been given, we
take into account every product of powers of the variables:
[OR (OES og 0 F Bain. <0
which appears as separate argument in the given equation. We
shall therefore write the given equation as follows:
@(K,P,, K,P,,..:: KePpj Ly Dy. 0. ti) = 0
K; and LZ; are constants with relation to 2;, Z; are those constants
which do not oceur as factor of Pi, but in any other way. Among
the A; and Z£; are therefore also included the variable parameters
(for their funetions).
Let us put that the constants A;, 4; in the first, resp. second case
have the special values:
K;', 0’, resp. Ky", 1,"
(those among them which are independent of C;, have the same
values in both cases); they are to be considered as given. We can
write every variable also in the following way :
CS ge —— ie Yi-
(05
If we put them in this form in the equation (7), it assumes the
following form:
D(Qi Pina. 2 Qe Lay) oe) 0 (8)
in which

Q) Kp! vo: ee
Pg JOA gp (002 aon Pee (10)
P:(y) = y ol yt? Wane yn tin Se (11)

Now it is evidently the question to find such values z;" that when
Ci' is replaced by Ci" and «2;' by @;", all the constants Q; and ZL;
— eventually with the exception of one factor, by which all the
terms of the equation can be divided — assume the same values.

843

When we carry out this division — let the factor in question be
FR (it can be both one of the Q, and one of the Z;) in all A+/—1
constants remain, which can have four different forms:

ee : lca
The required 2;" must now satisfy the following equations:
Q = &"
Siena
RR eae ee)
L;' L;"
Ses ae
and besides the following equations must hold:
Eko a eee titantron att). TLS)

The number of equations (12), in which 2;" occurs, is quite
independent of the number of mm of the variable parameters C;.

When all equations (13) are satisfied, and all those among the
equations (12) which do not contain a;", the three following cases
can occur.

1. Equations (12) are in conflict with each other (a group of s
of the sought values is defined by more than s independent equations.

2. They have one, or a finite number of systems of solutions. (It
is required, though not sufficient for this that the number of independent
equations in which 2;" occurs, is equal to xn. Hence m must not be
greater than 7).

Which of the systems of solutions corresponds with the given
system ;', has to be decided by a further investigation in every
separate case.

This is the case in which we have corresponding states. /

3. They have an infinite number of systems of solutions. (It is
required for this that m is greater than the number of the equations
that are mutually independent). In this case we may speak of corre-
sponding states for the same conditions (e.g. for the same substance).

§ 5. We shall now examine how Mesuin has come to another
conclusion. Mersin starts from the conviction that all the constants
of an equation are independent of the choice of the unities, when
every variable in the equation bas been divided by a special value
of it. This is perfectly correct. It is also true, as we have seen, that
every equation can be reduced to a form as meant here.

It is however not true that those constants that do not change
throuyh exchange of the unities, would also have to be unive. sal.

S44

Mrstin seems to be not quite free from a confusion, which is indeed
pretty widely spread: between the change of a number occurring
in an equation through change of unities, (“formal” change) and its
change through transition to other conditions (to other specimens of
the quantities which are measured by this number) (‘“‘material”
change).

In connection with this the assertion that in case of an equal
number of variables and parameters the latter can always be com-
pletely expressed in the former, is to be rejected.

§ 6. We shall illustrate what we have discussed by examples,
which though fictitious, are as simple as possible. Their claim to
physical signification, can indeed always be vindicated in this way
that they are interpreted as equations for the geometric shape of
some physical system.

1. y=ar’+ea+t+d QS23,. i=):

a. Introduction of special values of the variables

y BNE a
Yo == ax,” rs ap vo =F b
0

Yo ey ‘

6. Division by @,=¥,:

y Dal ac a ae b
Foes (joe =) |) fe SS Sh
Yo Yo vy Yo Xo Yo

c. Determination of the numerical values of the special values
of the variables satisfying the equation and of the coefficients :

1
i ; ie—=10
a
ax,” 1
Yo ab
L, 1
Yo ab
b
3S) Ile
J)
d. Determination of the system of corresponding values :
ign l
— — 2 !
Yo. ab Y=
ae. 1 , b!
= — — i
yo! ab H ab
b i Hep. capley 1
ale Me ath? ab’

845
from which would follow that a'b'! = ab, whieh would be possible.
only when we have really but one independent parameter.
It follows, however, from the thesis of § 3 that if for one system
of solutions there is not to be found a corresponding one, there

does not exist one for any other system of solutions.
Hence the given equation cannot be reduced to a universal form.

2. y=au? + abe + Db? (oh 2n rt 2)
D BENE a i
a Yo — =@e, + abe, — + b?
Yo a oe
b yo wef“ aby,c 6
ae aio ve
Yo Y 0 a 0 Yo a 0 Yo
‘ —b
t ys? : “= —
a
Gnas ae b?
—— = | c i) = i : = = |
Yo Yo Yo
' ! b
d ye — 02 Co
a
3. y Save? +e (rol)
D az \* a
a Uy = = Ge || I) Sa ae
Yo x4 &
5, y vei ain (Z i ae eh
Yo Yo vo Yoo
1 2
C. e, = H y=
a a
dine 1 ip. I
=- ; —-=-
Y «4 Yo 2
1 9
d i ; y=
; — : a
a a
41). pu=A+t BIT CT? (35, 12 3)
Pp v En ah bs 5 pp 2
a. Po% —— =A -f Blo TCL, r
Poo 0 0

Gmp Diplo! ct A Al: BSB as Cie = OT.

B : C
As 7 independent of Cc T,*, the two last comparisons are contra-

dictory, so that even if A= A’, we should not have corresponding
states.
Leiden, August 1914.

1) This example fails in the Dutch text.

846

Chemistry. -— “The nitration of the mixed dihalogen benzenes”’.
By Prof. A. F. Honieman.

(Communicated in the meeting of Oct. 31, 1914).

When in benzene are present two substituents and a_ third
is introduced, the substitution velocity caused by the two groups
already present is unequal. From the data given in the literature
it may be deduced that those velocities for the substituents poimting
to the p-o-positions decrease in the subjoined order:

OH > NH, > halogens > CH,.

The question now arose how to express those velocities also in figures.

Dr. Wipavut has done this for chlorine and methyl by determining -
in what proportion the isomerides are formed in the nitration of
o-chlorotoluene. In this compound the positions 4 and 6 are occupied,
under the influence of methyl, by a nitro-group, the positions 3 and

OU, 5 under the influence of chlorine. If now we determine
Ns the proportion in which the mononitro-chlorotoluenes 4 —-+ 6
L ; are present in regard to the isomerides 3+ 5 in the
N nitration product, this is then also the proportion of the
substitution velocities caused by methyl and chlorine, because they
can exert their action in this o-chlorotoluene independently of each
other; for the positions which are substituted under the influence
of methyl are different from those that ave substituted under the
influence of chlorine. For this proportion was found CH, : Cl=1: 1.475.

Dr. vAN pen AruND had previously determined the proportion in
which the nitro-p-chlorotoluenes are formed in the nitration of p-chloro-
toluene. If now, with the above mentioned ratio, we calculate the
relative quantities, those calculated figures appear to agree approxi-
mately with the observed ones.

These researches, carried out in my laboratory, have now been
continued, partly by Dr. Hrinkken, so as to determine also the ratios
of the halogens. The method followed previously for the quantitative
determination of the isomerides, namely by means of the solidification
curves, could, however, not be applied here as the two nitro-p-
chlorobromobenzenes give a continuous series of mixed crystals and
because it was to be expected, on account of the fact that the
properties of the nitrodihalogen benzenes present a strong mutual
resemblance, that this would oceur in other cases also.

Hence, for the quantitative determination of the isomerides present
in the nitration mixtures, we made use of the property that a halogen
in nitrohalogen benzenes is taken from the nucleus by Na-methoxide

S47

only then when it is placed in the ortho- or the paraposition in
regard to a yee Of the isomerides

aes Ds Br ie iy

Ome ne | Iv
oe

3r NOs

val

I, IV and VI only chlorine, of If, IIL and V only bromine will be
replaced by OCH,. Hence, if we determine the proportion in which
chlorine and bromine are split off from the nitration product of
p-chlovobromobenzene and trom that of o-chlorobromobenzene, we
get at once the proportion wherein in the first nitration product
I and II are present in the second one IV + VI on one side, UI + V
on the other side. This method has also the considerable advantage
that all the isomerides for the construction of the fusion lines
now need not be prepared individually and that in the nitration
products the various isomerides need not be separated; this latter
attempt in particular would, presumably, have failed owing to
insuperable obstacles.
The results obtained are as follows

Nitrationproduct of p-chlorobromobenzene contains 45,.2°/, of the
Cl

JNNOz

compound | ; and 54.8°/, of the isomeride 1, 3, 4.

NZ
Br

Cl cl
Br NO, Bi
Nutr. product of o-chlorobenzené consists of 55.5°/, of +
NO,

T\ ne

th | ; orin molecular proportion 1 :0.80,

Ye NON

The substitution velocity caused by chlorine and bromine when

and of 44.5°/, of

present together in the benzene nucleus is therefore as 1: 0.80.
When caleulating this proportion from the composition of the nitration
product of p-chlorobromobenzene it must be remembered that in the
nitration of chlorobenzene there is formed 30.1° , of the o-compound,
but in that of the bromobenzene 38.3°/, of the same. If we eall
wv the ratio of the velocities caused by chlorine and bromine we have
30.1 : 38.382 = 45.2 : 54.8,
ob
Proceediugs Royal Acad. Amsterdam. Vol. XVIL

S45

from which «= 0.96. Hence, the result is here Cl: Br = 1: 0.96,
The mean result of these two experimental series is therefore:
Cle Br sAOrSse:

The nitration of p-chloroiodobenzene caused the separation of large
quantities of iodine with formation of p-chloronitrobenzene. Hence,
for my purpose it was unsuitable.

In the nitration of o-ch/oroiodobenzene, there was also some separation
of iodine, but the formation of o-chlovonitrobenzene did not amount
fo more than about 3°/,. When determining the proportion in which
Cl and I were separated from the nitration product by NaOCH, a
correction for this must therefore, be applied. For the velocity ratio
Cl: 1 was thus found the mean value of 1:41.84.

It now became interesting to also investigate the nitration product
of o-bromoiodo benzene quantitatively as to its components. For, as

Cl: Br was found —1:0:80 and Cl:1=1:1.84, Br:] should
be = 1: 2.80, if indeed the two halogens present, aet quite indepen-

dently of each other.

Also in this nitration a little separation of iodine took place; the
content of o-bromonitrobenzene in the nitration product was in
this case 4.4°/,. Applying a correction for this the mean ratio
Br: 1} 1:1.75 was found, which rather differs from the calculated
figure. If, however, we caleulate the percentages of the isomerides
with the ratios 1.75 and 2.380 the theoretical value gives 69.7°/, of
the isomerides Br, 1, NO, = 1, 2,3 +1, 2,5, and the experimental

value 63.6°/, which may be considered as a sufficient approximation

0
if we bear in mind the difficulties of these quantitative determinations.

The conclusions from the above are obvious. Since it has
appeared that two substituents simultaneously present in ortho- and
in parapositions do not sensibly interfere with their respective
actions in regard to a third entering group, we shall be able to
calculate from the figures now found with sufficient probability in
What proportion are formed the isomerides of other compounds, for
instance in the nitration of o- and of p-bromotoluene.

The above mentioned order of the substituents towards the decreasing
substitution velocity caused by the same now becomes :

OH > NH, >I >Cl> Br > CH,.

Hence, the ratio OH: NH, and NH,:1 still remains to be deters
mined. As, however, in the nitration of the iodoanilines great diffi-
culties may be expected, A. F. H. Losry pr Bruyn has taken
in hand a quantitative research of the nitration of o- and p-chloro-
aniline in the above direction. As a preliminary result of his experi-

849

ments it may be mentioned that the ratio Cl: NH, is very large.
The above velocity series must, therefore, be resolved into two parts:
OH and NH, which cause a great substitution velocity and which
are presumably of the same order of magnitude; on the other side
the halogens and CH, with a lesser velocity, also of the sanie order
of magnitude. A more detailed deseription of the above experiments
will be published in the Recueil.

Oct. 714. Org. Chem. Lab. University Amsterdam.

Physics. — “The reduction of aromatic ketones. U1. Contribution
to the knowledye of the photochemical phenomena.” By Prof. J.
BorseKen and Mv. W. D. Congnx. (Communicated by Prof. A.
F. Honinman).

(Communicated in the meeting of October 31, 1914).
I. The reduction of the aromatic ketones in a perfectly neutral medium.

In our former communications?) we have shown that the reduction
of the aromatic ketones does not proceed any further than to pinacone,
which is presumably formed from the primary generated half pina-
cone molecule by vapid polymerisation. The fact that in an alkaline
medium hydrol is always obtained, must be attributed to the rapid
transformation of the pinacone, under the influence of the hydroxyl-
ions, into an equimolecular mixture of hydrol and ketone, the latter
of which can be again reduced to pinacone.

This explanation was confirmed by the study of the reduction of
ketones by means of aluminium amalgam.

Here is formed a mixture of pinacone and hydrol; the proportion
in which these two substances are formed differs from ketone to
ketone and now it appeared that the quantities of hydrol ran strietly
parallel to the velocities with which the diverse pinacones are con-
verted into a mixture of ketone and hydro! under the influence ef
sodium ethoxide.

Hence, aluminium amalgam in 80°/, alcohol may by no means
be considered as a neutral reducing agent.

The only modus operandi that gives the necessary guarantee that
complete neutrality would prevail during and after the reduction is
the action of the aromatic ketone on an alcohol under the cooperation
of sunlight. The original intention of this part of the research,

1) Proc. XVI. p. 91 and 962 (1913).
56*

$50

namely the tracing of the progressive change of the reduction, was
soon attained by applying this method.

A series of ketones dissolved in a great variety of alcohols and
a few other substances, was exposed to sunlight (or to the light of
the quartz-lamp); dn all cases where reduction set in, not a trace of
hydrol was obtamed.

The ketone was usually quantitatively converted into pinacone ;
occasionally, namely with benzylaleohol and a prolonged exposure
to sunlight a combination of the half pinacone molecule with a
eroup of the benzylaleohol, namely triphenylglycol was obtained as
a by-produet. *).

When to the aleohol some ethoxide was added hydrol was formed,
as was to be fully expected.

Hence, we arrive at the result that in the reduction of aromatic ketones
the hydrogen unites exclusively with the oxygen.

The experiments were carried ont as follows :
Quantities of 5 grams of the ketone were dissolved in 50 ce of

alcohol rendered carefully anhydrous *) and exposed in sealed tubes
of common glass to direct sunlight.

The drying of the lower terms was performed by successively
boiling with CaO, allowing to remain over metalli¢ calcium at O°,
and distilling; the higher ones were purified by distillation and both
were then immediately sealed into the tube together with the ketone.
After exposure to the light for some time, during which the course
of the reduction could be traced by noticing the deposition of the
sparingly soluble pinacone, the tube was opened, the pinacone was
filtered off, the filtrate distilled, the residue united with the pinacone
and in the distillate the aldehyde or ketone was tested and in
some cases determined quantitatively.

The exact details will be published elsewhere by one of us, a
few remarks may suffice here.

First of all was investigated the behaviour of benzophenone in
regard to methyl, ethyl, -propyl, sec.-propyl, cso-butyl, n-heptyl,
sec.-oetyl and cetylalcohol. The latter only was not attacked, not
1) This had already been noticed by Cramrctan and Sitper (B. 36, 1577 (1903)) ;
the formation thereof is moreover a confirmation of our conception that as the
first reaction product the half pinacone molecule is formed.

*) Water acts in this reaction in a remarkable manner as a powerful negative
catalyst; in 80°, alcohol no reduction takes place after exposure for months,
whereas in absolute alcohol in the same conditions, about two grams of pinacone
are formed during ten hours’ action of sun-light.

851

even at higher temperatures ; the mixture however, was of a fairly
strong yellow colour.

The other alcohols reduced the benzophenone in some sunny
spring days, with the exception of methylalcohol which required a
much longer time.

The research was then continued with allylalcohol, geraniol, cyclo-
hexanol, benzylealeohol, phenylmethylaleohol, benzhydrol and cinna-
mylaleohol. Of these, the saturated alcohols reduced rapidly and
quantitatively ; the allylaleohol was attacked more slowly with form-
ation of acraldehyde (even after two months’ exposure to light, the
acraldehyde was unchanged, thus showing that the light alone does
not exert a polymerising influence on this mobile substance).

The geraniol was also oxidized very slowly, the cinnamylalcohol
remained unaffected (we will refer to this behaviour later).

A few tertiary alcohols were also investigated; if was expected
that these would remain unaffected and indeed this was the case
with the dimethyiethylearbinol after two months’ exposure; during
that period, diaethylmethylearbinol had generated 0,38 gram of pina-
cone; with methyl-di-nu-propylearbinol the separation of pinacone
started after a few days and after two months 0.7 gram bad formed.

From this we notice that when the chain becomes longer, the
activity of the hydrogen of tertiary alcohols gets enhanced, which
enables it, with the cooperation of sun-light, to attack an aromatic
ketone; what gets formed from the alcohol has not been investigated
by us.

From observations of Ciawician and SiLBer') it is known that the
hydrogen of some hydrocarbons, such as toluene, is already active
enough to cause this reduction. We have been able to show that
also the hydrogen of the cyclohevane is transferred to the ketone,
on the other hand, hydrogen itself was not capable of acting.

Besides benzophenone some other ketones — particularly those
that. were previously subjected by us to the action of aluminium
amalgam — were subsequently exposed in alcoholic solution to
the light.

Nothing but pinacone was ever obtained, but the phenomena
occurring in these photo-reactions induced us to systematically repeat
a large part of these purely qualitative observations in such a manner
that on using a very simple modus operandi a relatively-quantitative
result was still obtained.

1) B. 48, 1537 (1910),

Il. The photo-reaction: ketone +- hydrogen'= pinacone.

In order to obtain a relatively-quantitative result we could make
use of a constant source of light and allow this to act on the differ-
ent solutions under the same conditions; for this purpose a small
7 em. quartz-mercury lamp was at our disposal. Yet we have em-
ployed this method but rarely, for instance in continuous dark
weather, because on account of the unequal distribution of the light,
at most two little tubes could be placed in front of the lamp in
such a manner that it might be assumed that they existed under
equal conditions.

When it had been ascertained by us that the reduction took place
quite as well in ordinary white glass as in quartz, from which it
appeared that a very large part of the actinie rays was situated in
the visible spectrum, the experiments intended for comparison were
carried out as follows:

A number of equally wide tubes of the same kind of glass and
having walls of approximately the same thickness were filled with
the same quantity of solution, and all placed at the same distance
in front of a white screen, which was placed close to a large labora-
tory window.

In this manner it was attained that the quantity of light that
fell in the same time on each solution was practically the same,
and perfectly comparable results were thus obtained. s

It speaks for itself that even then only the figures of a same
experimental series were mutually comparable. *).

A photo-reaction is distinguished from a reaction in the dark by
two points.

It is of a lower and frequently of the O order in regard to the
substance which is being activated and the temperature coefficient
is smail. *)

As we found that the active light was situated in the visible
spectrum and that the alcohols do not absorb visible rays, the
ketones are in this reaction the sensitive substances, and so we could
expect that the quantities of pinacone would be independent of the

1!) Also comp. O. Gross Z. phys. Gh. 37, 168 (1901) and E. GoupBere Z. phys.
Ch. 41, 1 (1902).

*) The first property is due to the activation occurring in the outer layer; from
the sensitive substance only a limited number of molecules can be raised by the
same quantity of light to the same degree of activily; even at a moderate dilution,
the reaction becomes, on this account, indevendent of the concentraticn of the
sensitive substance and therefore of the O order. This applies to slowly progress-
ing veactions where the sensitive substance can be rapidly supplied by diffusion
frora the dark interior to the light zone.

ketone concentration (in regard to the sensitive substance a reaction
of the O order).

By selecting the alcohol itself as a solvent the change in con-
centration thereof could be eliminated. (Table 1).

In order to determine the order of the reaction in regard to the
alcohol, benzene was chosen as being a general, non-absorbing and
non-reducing solvent. (Table Ia) (Chronologically these last experiments
were made after the position of the active light in the spectrum
had been ascertained; we, however, state them here because they
enabled us to give a complete image of the course of the reaction.)

We notice that this reaction is indeed independent of the con-
centration of the ketone, but not independent, however, of the con-
centration of the aleohol. As the quantities thereof had been chosen in
such a manner that they were amply sufficient even at the slightest
concentration, it follows from the figures obtained that the velocity
of the pinacone formation is proportional to the concentration of
the alcohol. *)

Thus we may represent the reaction by the kinetic equation :

Mpinacone) = K L, [Alcoh.|
dt

With a constant light-quantity, the velocity of the pinacone forma-
tion thus becomes proportional to the alcohol concentration; how
many molecules of the ketone act simultaneously cannot be ascer-
tained in this manner. As, however, pinacone and aldehyde are
formed and as according to the above equation one molecule of
alcohol is attacked simultaneously, the reaction scheme becomes :

€,H,OH -— 2(C,H,),CO = C,H,0 + (C,H,),(CO), ?).

In order to learn the temperature coefficient the ordinary tubes
(16 mm. diameter) were enclosed and sealed into a second tube
(244mm. internal diameter); the intervening space was filled with
conductivity water and now two of these tubes were exposed to
light as deseribed, one of them being kept at 25°— 28° and the
other at 752—78°*).

1) Here we have assumed that the change in concentration of the alcohol during
each of the four experiments was so slight that it could be regarded as being
constant; this, of course, is not correct and we really ought to have taken each
time a portion from larger apparatus. In that case, however, the experiments
would become much more complicated, because the light-quantilty did not then
remain constant during the experiment. Hence, we have rested content with the
above modus operandi which is sufficiently accurate for our purpose.

*) For a mixture of ketone and benzhydrole we have proved this reaction scheme
yet in another manner (see next communication).

, 5) Compare Rk. LutHeR and F. Weiaerv, Z. phys. Ch. 58, 400 (190d).

854

TASB EGE aE
ee eri |e reson
j-— —--——- = = — — =
Ist Series
1 0.1 gr. benzophenone 0.09 gr.
_; entirely converted
2 | OP ses ; O23,
3 | 050g "A 0.34,
4 OWS, , 0.36,
5 l— , 5 0:36)
2nd Series
1 1 gr. benzophenone 0.47 gr.
2 Aa 9 0.49 ,,
he F 0.49 ,,
\3rd Series|
1 0.1 gr.ochlorobenzophenone 0.09 gr. ,
5 | 025 , : sone entirely converted
3 | 0.50 ,, 1 0.38,
1 | OSs, %) 0.39 ,,
Bie |) ng - 0.39 ,,
6 2— ,, * 0.38 ,,
ea iat ea oeoso.e
Lan | ee 0.41 ,,
ASB EVE. Ta:
won | Gaveentiation/e] CRLOG in) | Gunster ore aes
(CsH;)2CO per 25 ce. pig eS
| 1 0.2527 gr. or 1 eq. 0.08 gr. 1
2 05054 ar wean arc ayy 0.18 ., 2.25
3 MOLOS ais ee 5 O36 4.50
4 PAWN" 55 gy 13 sp 0.66 ,, 8.25
5 © (pure alcohol) 0.69 ,, |

855

More accurate experiments were not considered necessary as we
did not care for the absolute value, but only for the order of mag-
nitude of the temperature coefficient.

Adjacent to the jacketed tube was also suspended an ordinary
tube to ascertain whether the presence of the jacket had any influence
on the pinacone formation.

The subjoined table II gives a survey of some series of experiments.

From these results it follows that the method is sufficiently accurate
for our purpose, the ketone reduction is indeed a_ photo-reaction
with a small temperature coefficient; this still falls below the mean
stated by PLornixkow') of 1,17 per 10°.

TABLE Il. Time of exposure 2—3 days.

a eee
| K
N° | Contents of inner tube 2 oes pinacone 4"
| Ay
a = = = ] =e ee = oe a —— =,
Ist Series) | | \
1 gee (CgH5)2 CO in 25 ce. alcohol | 25°—28° | 0.45 gr. |
without jacket | | | | |
2 | SAS tends: with eee | 0.76 ,, |
| {+ 50° | 1.06
3 Ns Re Nile eae —78° 02a
2nd Series) | |
1 |. - . « . without jacket | 25°—28° | 0.44 gr. |
2 1p 6-0 6 oo co WAU IECG: Fi ORK
| | | 50° | 1.065
3 WeMlerva tee ch SO my Skis, | ale =18e 0.96 ,,
| | a
\3rd Series
1 Ips (CICgH4)3COin 25cc. alcohol | 25°—28? | 0.27 gr. |
without jacket |
Be cals ses 7 with jacket ne al 0.35, |
|: a0 | 1.095 |
Sea 7°—18" | 0.55 ,, |
bs BL = 1 |
|| | |
4th Series
| |
1 . . . . . Without jacket | 25°—28° | | 0.24 gr. |
2 | aeecee? Gel swithtjacket ij | 0.30 ,,
| + 50° | | 1.10 |
ue re eae Cas | | 0.50 ,, |
: i, ao L

1) Jon. Prornikow. Photochemische Versuchstechnik. p. 273 (1912),

856

That the temperature coefficient for orthochlorobenzophenone is
really somewhat higher than for benzophenone seems to us rather
probable, but this can only be ascertained by more delicate measu-
rements ').

The independence of the concentration and the very small tempe-
rature coefficient now enables us to continue following this very
simple method in the quantitative investigation as to the influence
of the ketone to be reduced as well as of the reducing alcohol.

Influence of the alcohol.

The aleohols, as described above, were carefully dried over calcium
and, after distillation, poured at once into the tubes containing two
grams of ketone. These were then sealed and exposed to the light.

These tubes were suspended at such a distance that they could
not interfere with each other.

The subjoined table gives two series of experiments, the first series
was exposed for three and the second one for six days: particularly
during the first days it was sunny spring weather.

What strikes us here in the first place is the agreement in the
action of the aleohols 2—6; the secondary propyl alcohol gets
oxidised somewhat more rapidly. the amyl alcohol a little more
slowly. In the latter case a strong yellow coloration sets in.

Very much smaller is the velocity of the pinacone formation in
the case of methyl and allyl aleohol; as no interfering yellow
coloration occurred here and as the conditions were moreover quite
equal, this different behaviour must be attributed to the particular
position these alcohols occupy.

Although we cannot yet enter here into an explanation of the
process, if is obvious that the reduction of benzophenone will proceed
all the more readily when in the conversion of alcohol into aldehyde
(or ketone) more energy is set free.

The absolute extent of this energy is unknown to us, but still
some thermic data point to the existence of a parallelism in the

1) The remarkably greater reduction velocity in the jacketed as compared with
that in an ordinary tube, must be attributed to the larger quantity of light which,
owing to refraction in the jacket filled with water, falls on the inner tube. In fact
nothing could be noticed of this inner tube when the tube was entirely filled; it
looked as if the alcoholic solution has the width of the outer tube. In harmony
with this observation, it appears that the ratios of the velocities in the four series
namely 76:45, 70:44, 35:27 and 30:24 do not greatly diverge and are about
equal to the proportions of the sections of the outer and inner tube 24; 16.
(Compare Lurner and Weicert |. c. p. 391).

857

TABLE Ill.
lyst Nee 2 gr. benzophenone in 25 cc. panes Remarks
1 | methyl alcohol 0.29 gr
2 ethyl alcohol 0.84 ,,
3 | n-propyl alcohol (Oates) — sy | faint yellow
| coloration
4 | sec. propyl alcohol | ORE |
| |
5 n. butyl alcohol On84 55 I
6 _amylalcohol (Bp. 130 -133°), 0.75 _,, Sires yellows |
7 allyl alcohol Ok25) |
: Ratio |
ies Sees | | | i’: 1 ete:
= es ee
iV methyl alcoho! | 0.49 gr. | 1.69
| ea ethyl alcohol Vea ae | lhe wltgTA
| | yellow coloration
3f | n. propyl alcohol alts} a ea not much | 1.75 |
| | increased
4’ sec. propyl alcohol L605; 1.58
; x ( yellow coloration)
6 amyl alcohol (a. ab.) 1.05: |; par acre | 1.40
I solr ea allyl alcohol Q:42e 6 1.68

velocity of the reduction and the extent of the difference of the
molecular heat of combustion of aleohol and the correlated aldehyde
(or ketone).

The greater this difference the more energy will be represented
by the hydrogen atoms playing a role in that transformation.

As the heats of evaporation of the alcohols on one side and of
the aldehydes on the other side do not sensibly differ and as all we
require lere are a few figures for comparison, a correction for this
may be omitted here. We then find for these differences (according
to data from the tables of Lanpoir-B6rnstein-Rota). (See table IV.)

The heat of combustion of acraldehyde is not known, neither
that of formaldehyde. There is, however, a statement as to meta-
formaldehyde: if from this one calculates the molecular combustion
as if it were a monomeride, the difference amounts to 47 cal. As,
however, this also includes the heat of polymerisation the difference
is presumably considerably less than 47 calories,

858

TABLE IV.
a = ees vee
3 = methyl alcohol—(meta)formaldehyde lwernss 47.0 cal.
e = ethyl alcohol—aldehyde 47.075;
5 g n. propyl alcohol—propionaldehyde 505 0ieny
g 5 sec. propy: alcohol—acetone SOs
2 r amyl alcohol (?)—valeraldehyde Ac O las

The two series of experiments of table II] were started at the
same moment, the first was investigated after three and the latter
after six days; when the converted quantity of substance is proportional
to the quantity of light and no secondary hindrances occur, the
proportion of the quantities of pinacone at each of the numbers
1:1’, 2:2’ ete. must be the same; these ratios have been inserted
in the last column of the second series.

We notice that this ratio is indeed almost constant except in the
ease of amy! alcohol, where a hindrance in the form of an increasing
yellow coloration is distinctly observed.

Influence of the ketone.

The tubes were filled with solutions of one gram of ketone in
50 ce. of absolute ethyl alcohol. Two series were exposed simulta-
neously to the action of the light; the first was investigated after
three, the second after six days. Some pinacones remain very long
in supersaturated solution, hence the alcohol was always distilled
off and the residue shaken with 80°/, aleohol so as to remove all
unconverted ketone

The subjoined table V gives the results obtained and the ratios of
the velocities with those of the benzopinacone formation as unit.

Table VI gives a similar double series; most of the ketones
investigated here were not attacked.

Table VIL gives a survey of the results obtained in amyl alcohol
as solvent and as reducing agent.

1st. The velocity of the pinacone formation, according to this
survey, is greatly dependent on the nature and on the position of the
substituent. As regards the nature, there is only one group (the
methyl group on the two para-positions (N°. 7)) that appears to
accelerate the reduction velocity somewhat, for the rest the substitution
causes a decrease in velocity.

This decrease is strongest when the substituting group isa phenyl

859

TA'BLE V.
| Quantities of pimacone Ratio. | Ratio of the Re-
No.| Name of the ketone SeriesI Series i Series I Series I | with tat obo
In grams In millimols. (CoB CO as unit
1 | benzophenone 0.41 0.85 1.12 2.32 2.05 io
2 | 2 chlorobenzophenone 0.12 0.25 0.28 0.58 2.07 0.25
3 | 3 chlorobenzophenone 2 +0.10 - 0.23 — +0.1 (from II)
'4 | 4 chlorobenzophenone 0.32 0.75 0.74 1.73 2.34 0.66
5 | 4 methoxybenzophenone 0.39 0.80 0.92 1.88 2.04 0.82
6 | 4 methylbenzophenone 0.41 0.86 1.04 2.18 2.09 0.93
7 | 44’ dimethylbenzophenone 0.48 0.95 (off)| 1.19 — a 1.06
8 | 4 bromobenzophenone 0.51 0.98 (off) 1.— _ — 0.90
9!) | 44’ dichlorobenzophenone 1% 0.73 — 1.45 =| 0.63 (from II)
10 | 2.2.4.4’ tetrachlorobenzoph. 0.22 0.47 0.34 | 0.72 7512 | 0.30
11 | 2 chloro 4’ methyl ne | 0.27 | 0.55 0.58 | 1.18 2.03 0.52
12!) | 4 chloro 4’ methyl " 0.19 | 0.70 0.41(2), 1.50 3.66(?), 0.64 (from II)
|
ABE Vie
13. benzophenone 0.85 0. og (oft 2ESO | _ — 1
14!) | 4 phenylbenzophenone To | _ | _ — 0
15 | phenyl-~-naphtylketone a2 | es = | bs ue 0
16 | phenyl-3- 5 _ _ De el es — 0
17 | 2 methylbenzophenone _ == re es ere _— 0
18 | 3 methylbenzophenone | 0.80 | 0,96 (off) 2.03 — = 0.89
19 | 2.4.2’.4’ tetramethyl ,, ae a = | — = 0
20 | fluorenone } — |e Tels — 0
te |
TABLE VII. Amy! alcohol as solvent.
21 | benzophenone ) Osis 0.97 (off) 2.05 | -- 22 1
22 | 2 chlorobenzophenone | 0.22 | 0.33 | 0.51 0.76 1.49 | 0.25
23 | 4 chlorobenzophenone 0.65 0.96 1.49 | 2.20 1.48 | 0.72
24 | 4 methylbenzophenone 0.74 0.96 (off), Hash} |) — | 0.91
25 | phenyl «-naphthylketone | _ | _ | _ | — — | 0)

') These ketones had not entirely passed in solution in the alcohol.

S60

vroup, because 4-phenylbenzophenone (14) and the two phenyl-
naphthylketones (J5 and 16) are not reduced.

Halogen atoms and methyl groups do diminish the single substitution,
but (with one exception) do not prevent the same. Para substitution
has the least influence, ortho the greatest; this, however does not
apply to the chlorobenzophenones (3), so that we can hardly speak
of a universal rule.

The symmetry of the molecule seems to accelerate the velocity.

Whereas the 4-methylbenzophenone has a smaller velocity than
the benzophenone (5), the 4.4’-dimethylbenzophenone has a somewhat
greater one. The fairly considerable decrease in velocity in the
4-chlorobenzophenone (4) is not continued in the 44’-dichlorobenzo-
phenone (9). In connexion with the considerable decrease in the
2-chlorobenzophenone (2) that in the 2.2’.4.4’-tetrachlorobenzophenone
(10) is unexpectedly high.

A remarkable fact is the slight influence of the methyl group on
the meta position (18) in regard to the great one of the chlorine atom (8).

2nd. Of more importance is the fact that the aleohol, the reducing
agent, is of very secondary significance as regards the ratio of the
reduction velocities; this is shown from the comparison of tables
V and VII. The ratio of the velocities in ethyl and amyi alcohol
is practically the same. We have completed these observations with
a few on methyl and propyl! alcohol, selecting methy! aleohol because
the velocities therein are generally much less, whereas o-chloro-
benzophenone with benzophenone were compared as ketones, because
the velocities in ethyl (and amyl) alcohol differ strongly.

The subjoined table VIII gives a survey of the results.

thyl ketone | §

TABLE VIII.
fi kee = eras We ee:
Sol. C,H5;OH, |) Sol.C;H,,OH, | Sol. CHg OH, || Sol. nC3H;OH,
Ist Series |; 3rd Series || 4th Series 5th Series
| ~-— |. |X
Quantity Quantity | | Quantity | Quantity
| in Ratio in Ratio | in | Ratio in Ratio
| m.mols. | m.mols, m.mols. | | m.mols.
| Benzophenone|} 2.32 | 1.0 2.05) 91 ek Art |) “2.93. ad
/2Chloro_,, 0.58 0.25) 0.51 (0.25 | 0.46 | 0.24 || 1.08 | 0.27
| | |
(Ne . | 1.73 | 0.66 || 1.49 | | 0.72 |
[4methyl | 2.18 | 0.93 1.88 | 0.91
| | ] |
| phenyl «-naph- } 9 | eel 0
| |
|

861

First of ali it follows from this constant ratio that the hefore is
prominent in the photo-reaction, that this passes into a photo-active
condition. Further, that the diverse ketones are activated in a
perfectly analogous manner in such a way that either a number of
molecules (the same for all ketones) become photo-active, which molecules
then react with the alcohol with a velocity specific for the ketone;

or, a number of molecules specific for each ketone becomes
activated which, with a definite velocity which is independent of
the ketone, dehydrogenises the alcohol.

A choice from these alternatives can only be made by a further
study of the photo-reaction.

The active light of the ketone reduction.

The first attempt to ascertain the position of the active light in
the spectrum has been made by Cramician and Sinper'). They in-
vestigated, for instance, the reduction of benzophenone and alcohol,
employing two photo-filters.

As a red photo-filter was used a cold saturated solution of fluo-
rescein in alcohol (thickness of layer 15 mm.) which extinguishes
all light to 0.510 @; by adding gentian-violet the absorption could
be raised to 0.620 «.

As a blue filter served a 10°/, solution of cobalt chloride in alcohol
which transmits rays of a wavelength less than 0,480 uw; a ereen
band at + 0,560 w and a red one at + 770u remain, however,
unextinguished. They arrive at the result that all the reactions with
which they were engaged, took place under the influence of blue
light. We have used a larger number of photo-filters and carried
out the research in jacketed tubes; the inner tubes were those which
were used by us in the other experiments; the intervening space
was 15 mm. Above the liquid in the jacket the outer tubes were
covered with black lacquer, so that none but filtered light could
penetrate into the inner tube.

As photo-filters were selected :

I. Red: aqueous solution of chrysoidin *).

Pe Greeny:) ©; » 9, potassium dichromate + acid green
B. extra. ?)
Blue and violet.
ILI. 10°/, aleoholic solution of CoCl,.
IV. Cold saturated aqueous solution of erystal violet 5 B. O.?).
VALS 2 » 5 » acid violet 4 B. N. ?).
VI. Solution of iodine in CCl,.

1) B. 35, 3593 (1902)
2) Colouring matters from the “Gesellschaft f. chem. Ind. Basel’.

862

In agreement with that found by Cramiciay and Sitper for the red
fluorescein filter we found that the filters I and Il which only
red (690—598 we) or red and green (> 500 uy) absorbed
all actinic rays.

Also V, which besides red rays of about 700 ue still transmitted
blue and violet > 483 nu, completely prevented the reduction in the
inner tube. On the other hand an important reduction took place with
the filters 11], 1V, and VI which transmitted rays to the extreme, visible
violet + 400 ay.

The series of experiments were conducted in this way that a set

transmit

of four jacketed tubes with photo-filters were exposed to sun-light
for some days in front of the white screen: the results are contained
in the subjoined table.

eel

863

Now with this method we can only get a very rough determination
of the position of the active region, still it appears that the active
rays are presumably situated in the violet and have a wavelength
smaller than + 480 uu. In order to see whether in the beginning
of the ultraviolet active rays were still present, a small jacketed
tube was constructed from quartz, the alcoholic benzophenone solution
was put into the inner tube and in the jacket a cold saturated
solution of nitrosodimethylaniline') which absorbs all visible violet
and blue rays and transmits ultra-violet ones of 400—280 uu.

Neither in sun-light, nor in front of the quartz lamp did any
reduction set in; from this we could conclude that the active rays
were not situated in the ultra violet, but in the visible spectrum
< 480 and > 400 au.

A fortunate incident now came to our aid when we were engaged
in determining the correct position of the active light.

We had noticed that the ketones were converted with compara-
tively great rapidity into pinacones by means of the HerAvs quartz-
mercury lamp. ‘

The mercury spectrum must thus contain a great quantity of the
chemically active rays. This spectrum exhibits a very intensive blue
line at 436—434 wu and two violet ones at 407,8 uu and 404.7 wu?),

Photo-filter V completely removes the violet lines and leaves the
blue ones unchanged; as this filter in sunlight as well as in front
of the quartz lamp prevents all conversion of benzophenone as well
as of o-chlorobenzophenone, and as we have noticed that the ultra-
violet light of the lamp is inactive we may conclude that the active
light for the photochemical reduction of the aromatic ketones is
situated in the extreme end of the visible violet.

The fact that the nature of the source of light has no principal
influence on the reduction process is shown from the subjoined table,
in which are given the ratios of the quantities of pinacone that are
formed from diverse ketones when exposed either to sun-light or
mercury-light.

The exposure to mercury-light was carried out by placing a solution
of 0.5 gram of ketone in 15 ce of ethyl alcohol at a distance of
5 em from and parallel to the quartz lamp and exposing these for
10 hours; hence, the quantity of light was approximately the same
for all ketones.

The close agreement of these ratios also renders it probable that

1) Compare PLornixow etc. p. 19.
2) Lenmann, Plays. Zeitschr. 11, 1039 (1910),

Proceedings Roya! Acad. Amsterdam. Vol. XVII.

864

TMA E IE, 0G
3 | ene of pinacone a Semen Gaenaes of
to Hg light pinacone on
No. Name of the ketone | in m.mols. Gite ligtt with beng
in grams benzopinacone pinacone as
as unit unit
1 benzophenone 0.35 1 1
2 2 chlorobenzophenone 0.10 0.23 0.25
3 4 chlorobenzophenone 0.30 0.70 0.66
4 2 methylbenzophenone 0 0 0
5 4 methylbenzophenone 0.34 0.89 0.93
6 phenyl z-naphthylketone 0 0 0
7 fluorenone 0 0 0

the active rays are situated for the greater part at 407.8 and 404.7 wa *).
The action of light on mixtures of ketones.

The phenomena observed by us during the exposure to light of
ketone mixtures in absolute alcohol divulged a very strong mutual
influence.

In order to better understand these observations, the following
should precede:

We have noticed that the chemically active light comprises a very
limited part of the spectrum, yet, therein are rays of different
frequency and intensity.

A. We can now suppose that each of the ketones present wants
its own active rays without absorbing rays intended for the other

ketone; then — as the pinacone formation is independent of the
concentration — there will have formed in the tube with the mixture

the sum of the quantities of pinacone that are formed in the separate
tubes under the same conditions.

Those quantities within certain limits must also be independent
of the proportion of the concentrations of the ketones in the tube
containing the mixture.

1) Presumably, the action is in a high degree selective, as a layer of 3 dm 4°/,
benzophenone in absolute alcohol certainly caused a very distinct fading of these two
mercury lines, whereas nothing could be noticed of a curtailing or fading at the
violet side of the are lamp spectrum through that same liquid layer. We attach,
moreover, not much value to this subjective observation, for only an accurate
spectrophotometric investigation of the absorption spectra of the ketones can
properly delermine the connexion between absorption and chemical action.

865

b. As soon, however, as rays for the one ketone are also con-
sumed by the other one, the quantity of pinacone will be less than
the sum in question and, moreover, the proportions of concentrations
will no longer be a matter of indifference.

For in the layer where the photo-reaction takes place each molecule
of the one ketone requires a part of the light-energy also wanted by
the second ketone, so that the hindrance experienced by the latter
will become greater when its relative concentration gets less.

C. The extreme case would be that both ketones require just
the same rays; we should then obtain a quantity of each of the
ketones which in equimolecular concentration is equal to half the
quantity that forms in the tube with the separate ketone (always
supposing that no other obstacles occur).

The phenomena recorded by us are now best understood from
the supposition B; a ketone does require specific rays from its
neighbour. Some of the observations approach to A, others to C,
some even exceed this extreme case, showing that the action is
more complicated than was at first supposed, as will appear from
the subjoined tabulated survey.

HAGE I ENeX
| Ist | Solution of 2 gr. of o-chlorobenzo- ind50cc, Quantity
/Series phenone and varying quantities of Aohal pinacone Remarks
No. phenyl z-naphthylketone in gr.
} | og nr
| 1 |2 gr. o-Clbenzophenone pure 0.84 |S, ES
| ; ; ae
ae 62 * +-0.1 gr. phenyl z-naphthylketone 0.30 5 5305S
| eoFag 5
3 - SOIR 5 , PO) ea eee aI)
coy ee! vas
4 +0,50 , i 0 Sesgeco.
” s} » tr oor aS
-
5 ” ail ” » ” 0 ve Sd%a
ea c& oc
° ees iS =
= fe 3 s A
v =
esezas
zie As above o-Cl benzophenone and varying Quantit
jopaccite s above o- one ¢ ary uantity) , spe
pees quantities of o-methylbenzophenone pinacone Remarks
| i = BAN RIN :
| 1 | 2gr. o-Cl benzophenone pure Ose
2 a +-0.1 gr.o-CHg3benzophenone 0.36
|| ees és + 0.25 Fe 0.30 As above
| 4 | . + 0.50 ; 0.26
j |
fect i + 1 ; | 0.15

866

We notice that when one of the ketones does not get reduced it
exerts a very powerful retarding action on the reduction of the
other. ketone.

This action, particularly with phenyl-e-naphtylketone is much
more important than we should expect even in the extreme case C;
besides the elimination of the chemically active rays, the molecules
of the naphtylketone must cause an impediment, which may, perhaps
be put on a par with the obstruction caused by oxygen in the
photo-halogenations.

TABLE XII.
ree ewes -
p> 3 Seo ol ee
Solutions of various ketones, which are | 5 oo Re SEs
N : : [See o2w | oes] Remark
reduced separately in 50 cc. solution. SSS Bae | sso
ole m°S|ros
| ° =
; moe eT be eee lll 3
ee ee
WN) | | = cH
1 2gr. benzophenone Neel ite |p - Boe.
| | =%27y2
2~|2 > + 2gr.0-Cl benzophenone | 2.31 | 4.16 5 Eta
2.37 3.8) efea
Su ane > +1» > 2ST} | 3.46 8 M4 ot oe
oLor
7 : = es = 2
2f | sige
jan oo
1 | 2gr. benzophenone 166" || 1667) a E Bus g
| : Qa,
2 |2> > +2gr.pClbenzophenone 2.18 9.19 | | S°5E
2.76 1.2: Saas
3 |2 > +1» > 1.69 \ 3.19 | fees
os a
2 ; ee (S788
ze | 338e
oO oO | ats
a | eels
1 2gr. benzophenone . 0.85 0.85 —_ = 5 2 ae
WS Sw
Qu | 2s > + 2gr.pBrbenzophenone | 1.65 | 23.9 | |= ae iS
1.95 19.0 | w@E&
3 12> r iis ‘ 1.05 |) 11.4 || \oe 8

From Table XII it appears that, in the case when both ketones
are reduced, we have demonstrated a considerably less impediment
than in the case that one of them is not reduced. Still, there is
always a negative influence, we obtain in all cases a quantity less
than the sum of the quantities which we should have obtained, in
separate tubes; we are always dealing with case B.

In this we notice the smallest mutual hindrance in the mixture
of benzophenone and o-chlorobenzophenone, yet we notice plainly
that the impediment increases when one of the ketones is present

in large excess (18tseries N’. 3) and that in such a case that present
in the smallest amount is the most strongly impeded. Much more
pronounced is the hindrance observed with mixtures of benzophenone
and p. Cl- or p. Br-benzophenone; the sum of the pinacones remains
here far below the calculated quantity. The halogen ketone has as
a rule a stronger impeding action than benzophenone, for even in
smaller quantities than the molecular ones (N°. 2 of the three series)
the halogen pinacone in the mixture is predominant. Only with a
considerable excess of benzophenone the halogen pinacone is repelled
and mostly so in the cases where the greatest hindrance is present
(compare N°. 3 of the three series).

We thus find in rough traits what we could expect; there occur,
however, particularly when one of the ketones is not reduced
separately, such great hindrances that they cannot be satisfactorily
TABLE XIill.

| Quantity

< ; ; | #38 Y the blank tube
| 20 ce. abs. aluohol | solution of 4 grams: 2 ej aan tit

| :

wn —- = = = = == = =
~ Vv
,n°s
25

n }

Te | alcohol (blank-exper.) | 0.64 — | 1.—
2 p CH; benzophenone 0.28 | 0.66 0.44
aes | oCl benzophenone | 0.18 0.19 0.28
|
| 4 | phenylz naphthylketone trace 0 | trace

=F —— 77 == 4
ro |
Sis]

N VU)

a
Hele| alcohol (blank-exper.) 1.05 - 1.—
| |
Hee o CH3 benzophenone | 0.50 0 0.48

3 ‘phenyl-naphthylketone) 0.28 0 0.27

4 fluorenone 0 0 0
|

wi a ———_=. ci aoa = 73
aeig)

6 5)

w) | |

1 | alcohol (blank-exper.) | 0.79 | — 1.—

2 p Brbenzophenone | 0.42) 1,18~ 0.54

3 p Cl benzophenone 0.38 | 0.83 0.47

| 4 benzophenone 0.29 | 0.93 0.37

868

explained in the above cited manner. There seems to be a connexion:
here between the extent of the impediment and the non-appearance
of the photo-reduction.

Now, in order to eliminate the hindrance which might eventually
take place owing to the mixing, the oft-quoted jacketed tubes were
filled in such a manner that in the inner tube was alivays inserted
a definite ketone and in the jacket diverse other ketones,

The light then first traversed a + 2 mm. thick layer ofa ketone
then to exert ifs action on the benzophenone; in this way we could
form a better opinion as to the absorption of rays of light by the
one ketone (in the jacket) which were needed for the other ketone
(in the inner tube).

There exists no doubt that a// ketones absorb actinic rays intended
for the benzophenone; the degree of this absorption is certainly
very different and specific.

The ketones which were attacked in the jacket were, during the
experiment, reduced in concentration, so that the conditions for the
reducing of the benzophenone in the inner tube gradually became
more favourable; this causes, however, that we can only consider
as fairly comparable the experiments where no reduction takes place
in the jacket. Hence, a few ketones have been placed in the jacket
in benzene solution whilst in the inner tube was again present a
solution of 2 grams of benzophenone in 20 ec. of absolute alcohol ;
the following result was thus obtained:

It appears that several ketenes absorb rays of light which effeet
the benzophenone activation, even when they are dissclved in
benzene.

The reversible yellow coloration of this benzene solution, however,
tells us to be careful, for the activated ketone can form with benzene

R69

a light-sereen, thus causing the absorption effect to be greater than
when the ketone had been present in alcoholic solution.

In each case a circumstance oecurs owing to which the phenomenon
becomes more complicated, so that from these last experiments we
may at most draw the conclusiun that rays of light are indeed always
absorbed by the one ketone, which the other required for the oxidation
of alcohols.

The most powerful absorbing ketones appear mostly — but not
always — to oxidise the alcohol slowly or not at all, so that we

gain the impression that a liberal absorption does take place, but
that the possibility of the setting in of a reaction and its velocity
does not only depend on the aleohol, but in a great measure on
the ketone.

It speaks for itself that the experiments on this almost quite
unexplored region can only bear a very provisional character ; still
we believe we have attained, with very siinple means and methods,
some results which will prove of importance for the insight into
the photochemical reactions.

For the moment, however, we wish to refrain from an attempt to
explain the phenomena observed until more accurate spectrophoto-
metric data are at our disposal.

SUMMARY.

I From aromatic ketones and alcohol are formed, in the light,
exclusively pinacones; these latter are, therefore, the products
to be first isolated in the reduction. Hydrols are, in the reduct-
ion of the aromatic ketones, always formed secondarily (see
Proc. XVI 91 and 962) either from the pinacones or from
the primarily formed half pinacone molecules.

II 1. The photo-reduction - of the ketone by alcohols was studied
by exposing simultaneously to the light a set of tubes of
equal dimensions and filled with equal quantities of liquid,
thus causing the light-quantity (i.t) for each object of a
serial experiment to be equal.

2. The velocity of the pinacone formation appeared to be inde-
pendent of the concentration of the benzophenone and propor-
tional to the concentration of the alcohol. Hence, it satisfied
the equation :

d pinacone

—= KT. [alcohol

and, therefore, the reaction scheme:

dt
2 ketone + alcohol = pinacone + aldehyde,

870

3. The temperature coefficient was small: 1.06—1.11 for 10°.

4. The velocity of the pinacone formation is greatly dependent on
the aleohol; for instance, the methyl aleohol and the allyl
aleohol were oxidised much more slowly than other primary
and secondary alcohols.

5. The velocity of the pinacone formation is greatly dependent
on the ketone, the benzophenone is attacked rapidly, most of
the ketones as yet examined less rapidly, many not at all.

6. The ratio of these velocities in different alcohols is constant.

7. The aetive light of the ketone reduction is sure to be situated
in the spectrum between 400 and 480 «qe and very probably
in, or adjacent to, the rays 404.7 and 407.8 of the mercury
quartz lamp.

8. The ratio of the velocities of the pinacone formation in sun-
light and in mercury light is the same.

When two ketones are present simultaneously one of them
absorbs a part of the rays required by the other ketone; this
also appears when the light passes through a solution of the
one ketone and falls on that of the other.

Particularly in the case of the powerfully absorbing ketones
the hindrances are stronger than was to be expected.
Delft, October 1914.

Physics. — “Simplified deduction of the formula from the theory
of combinations which PLanck uses as the basis of his radiation-
theory.” By Prof. P. Eurenrest and Prof. H. Kammrtincu ONNEs.

(Communicated in the meeting of Oct. 31, 1914).

We refer to the expression
, (N—1+4P)!
oN ™ ae )! (4)
ted PN—1)!

which gives the number of ways in which .V monochromatic reso-

nators f,, R,,... Ry may be distributed over the various degrees
of energy, determined by the series of multiples 0, ¢, 2¢... of the

unit energy ¢, when the resonators together must each time contain
the given multiple Pe. Two methods of distribution will be called
identical, and only then, when the first resonator in the one distri-
bution is at the same grade of energy as the same resonator in the
second and similarly the second, third,.... and the Vth resonator
are each at the same energy-grades in the two distributions.
Taking a special example, we shall introduce a symbol for the
distribution. Let NV = 4, and ?=7. One of the possible distributions

871

is the following: resonator A, has reached the energy-grade 4e (R,
contains the energy 4s), R, the grade 2s, R, the grade Oe (contains
no energy), R, the grade «. Our symbol will, read from left to right,
indicate the energy of R,, R,, R,. R, in the distribution chosen, and
particularly express, that the total energy is 7s. For this case the
symbol will be:

(EES 0FHO00H]

or also more simply :

ceeeOreQOr]]

With general values of .V and P the symbol will contain P? times
the sign ¢ and (.V—1) times the sign O'). The question now is,
how many diferent symbols for the distribution may be formed in
the manner indicated above from the given number of ¢ and O?

The answer is

(N—1+4P)/

el ee ea)

Proof: first considering the (M—1-+ P) elements ¢...2, 0...0
as so many distinguishable entities, they may be arranged in

(NGA OP Re tytn ee na 2,
different manners between the ends ][ [[. Next note, that each time
(NMRA PROT em inl ee UR (3)

of the combinations thus obtained give the same symbol for the
distribution (and give the same energy-grade to each resonator), viz.
all those combinations which are formed from each other by the
permutation of the P elements ¢7*) or the (N—1) elements 0. The
number of the different symbols for the distribution and that of the

1) We were led to the introduction of the (N—1) partitions between the NV
resonators, in trying to find an explanation of the form (NV — 1)! in the denomi-
nator of (A) (compare note 1 on page 872). Pranck proves, that the number of
distributions must be equal to the number of al! ‘‘combinations with repetitions
of N elements of class P” and fur the proof, that this number is given by the
expression (A), he refers to the train of reasoning followed in treatises on com-
binations for this particular case. In these treatises the expression (A) is arrived
at by the aid of the device of “transition from nton-+-1”, and this method taken
as a whole does not give an insight into the origin of the final expression.

*) See appendix,

872

distributions themselves required is thus obtained by dividing (2) by
(3) q. e.d.*).

AGP AE BENG DFIEXe

The contrast between Purncx’s hypothesis of the energy-qrades and
Einstein's hypothesis of energy-quanta.

The permutation of the elements ¢ is a purely formal device, just as the per-
mutation of the elements 0 is. More than once the analogous, equally formal device
used by PLANCK, viz. distribution of P energy-elements over N resonators, has by
a misunderstanding been given a physical interpretation, which is absolutely in
conflict with PLANCK’s radiation-formula and would lead to Wien’s radiation formula.

As a matter of fact PLANCK’s energy-elements were in that case almost entirely
identified with Ernstern’s light-quanta and accordingly it was said, that the difference .
between PLANcK and Erysrein consists herein that the latter assumes the existence
of mutually independent energy-quanta also in empty space, the former only in
the interior of matter, in the resonators. The confusion which underlies this view
has been more than once pointed out *). EINSTEIN really considers P similar quanta,
existing independently of each other. He discusses for instance the case, that they
distribute themselves irreversibly from a space of NV, cm’ over a larger space of
Ng em® and -he finds using BoutzMan’s entropy-formula: S = klog W, that this
produces a gain of entropy %):

2 N,\P
S— s, = ley (2) pete So. (3)

1) It may be added, that the problem of the distribution of N resonators over
the energy-grades corresponds to the following: On a rod, whose length is a mul-
tiple Pe of a given length -, notches have been cut at distances ¢, 2e, ete. from
one of the ends. At each of the notches, and only there, the rod may be broken,
the separate pieces may subsequently be joined together in arbitrary numbers and
in arbitrary order, the rods thus obtained not being distinguishable from each other
otherwise than by a possible difference in length. The question is, in how many
different manners (comp. Appendix) the rod may be divided and the pieces distri-
buted over a given number of boxes, to be distinguished from each other as the
Ist 2nd,.... Nth, when no box may contain more than one rod. If the boxes,
which may be thought of as rectangular, are placed side by side in one line, they
form together as it were an oblong drawer with (N—1) partitions, formed of two
walls each, (comp. the above symbol in its first form, from which the second
form was derived by abstracting from the fact, that each multiple of < forms one
whole each time), and these double partitions may be imagined to be mutually
exchanged, the boxes themselves remaining where they are. The possibility of this
exchange is indicated by the form of the symbol chosen.

As a further example corresponding to the symbol we may take a thread on
which between P beads of the same kind, (N—1) beads of a different kind are
strung, which divide the beads of the first kind in a Ist, 2nd... Nth group.

*) P. Enrenrest, Ann. d. Phys. 36, 91, 1911, G. KrurKow, Physik. Zschr. 15,
133, 363, 1914.

3) A. Eysrern, Ann. d. Phys. 17, 132, 1905,

Sie

i.e. the same increase as in the analogous irreversible distribution of P similar,
independent gas-molecules, for the number of ways in which P quanta may be
distributed first over N,, then over Ny cells in space, are to each other in the ratio
INERT tas 5. Cate oe ee (O)
If with PLanek the object were to distribute P mutually independent elements
« over N resonators, in passing from N, to Nz resonators the number of possible
distributions would in this case also increase in the ratio (=) and correspondingly
the entropy according to equition (z). We know, however, that PLANncK obtains

the totally different formula
(V,—1+4+ P)! Ned SI
(N= 1)! P! (N= 1) P! (”)
(which only coincides approximately with (@) for very large values of P) and a
corresponding law of dependence of the entropy on N. This can be simply
explained as follows: PLancKk does not deal with really mutuaily free quanta < ,
the resolution of the multiples of ¢ into separate elements <, which is essential in
his method, and the introduction of these separate elements have to be taken
“cum grano salis”; it is simply a formal device entirely analogous to our permut-
ation of the elements = or O. The real object which is counted remains the number
of all the different distributions of NV resonators over the energy-grades 0, ¢, 2, ...
with a given total energy P:. If for instance P= 3, and N=2, Erysretn has to
distinguish 23— 8 ways in which the three (similar) light-quanta A, B, C can be

distributed over the space-cells 1, 2.

ae B= €C
Teleie mete 1
Hee tari eee
i te eee
Wet, 22
op Bagh See
VIP 2p yet. 2
Vil 2a ae
VII | 2-2 2

PiaNncK on the other hand must count the three eases II, Ill and V asasingle
one, for all three express that resonator R, is at the grade 2, R, at<; similarly
he has to reckon the cases IV, VI and VII as one; R, has here ¢ and R, Qe.
Adding the two remaining cases I (A, contains 3¢, Ry Oe) and II (R, has Oz, Ry Be)
one actually obtains

(N--1--P)! (2—1+8)/
Wren C= 37
different distributions of the resonators R), R, over the energy-grades.

We may summarize the above as follows ; Etysrrtn’s hypothesis leads necessarily
to formula (z) for the entropy and thus necessarily to Wren’s radiation-formula,
not PLANCK’s PLANCK’s formal device (distribution of P energy-elements < over
N resonators) cannot be interpreted in the sense of Etysrern’s ligit-quanta.

(December 24, 1914).

Q Akademie van Wetenschappen,

57 Amsterdam. Afdeeling voor
Ads de Wis- en Natuurkundige

Werk Wetenschappen

pu. dL Proceedings of the Section
Physical & Of Sciences

Applied Sci.

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